Summation based benchmark for calculators

12212017, 12:40 PM
(This post was last modified: 01092018 10:22 PM by pier4r.)
Post: #1




Summation based benchmark for calculators
There are plenty of tests for calculators, some more organized, some less.
See http://www.hpmuseum.org/cgisys/cgiwrap/...i?read=700 or the ones collected in the wiki4hp. http://www.wiki4hp.com/doku.php?id=start&do=index (see the benchmark section). Seeing the work of Eddie. http://www.hpmuseum.org/forum/thread5047.html I thought that when a benchmark includes a summation, like the savage benchmark a bit, but the savage benchmark uses the previous result to compute the next iteration. Such a benchmark could be generic enough for programmable and scientific calculators with summation abilities and could also include different instructions. While the 8 queens benchmark does not really scientific math functions. I will try something when I have time. Results in the post below. note to myself: to collect info it helps to send PM . Thanks to all the contributors! Wikis are great, Contribute :) 

12222017, 09:41 PM
(This post was last modified: 03062024 07:02 PM by pier4r.)
Post: #2




RE: Summation based test for calculators
So as said the summation based test will be very similar to the savage benchmark and I wonder how many similar tests were developed on various forum or groups regarding calculators.
Anyway, inspired by the test done in the thread of Eddie linked in the 1st post, I decided to pick randomly some scientific functions to assemble a summation that may give an idea of the performances of a calculator for common math functions. The idea is to have a loop working on an increment of the 'x' value that is somewhat independent from the step before (while the savage test uses the value picked from the step before) . Furthermore while the idea of using a function and its inverse is pretty neat (see savage benchmark), some calculators may be very carefully coded figuring this out and therefore simplifying the expression. I am not that interested in the accuracy, as it is well analyzed in many other posts using other examples (especially by Dieter, that for me will always be the ULPs man). Surely speed without accuracy is not that neat and so one could go on and build a metric that weights accuracy and speed, as done by a recent HHC (about egyptian fractions), anyway I will collect only timings. Timings will be collected here, and then moved on the wiki4hp if there are enough of them. People are encouraged to post timings and results. So to recap the idea of this test is there because:  with a summation with increasing x (not dependent on the previous computed value) also some advanced scientific calculators can be tested. See casio fx991EX.  it is easier to type in and execute. It does not take much time (well unless one is forced to write a program to optimize some parts).  it may be used with a metric that combines speed and accuracy (a problem would be to get the right accuracy for the problem).  it avoids to use a function and its inverse to skip very careful optimizations done by the parser. (especially systems with CAS may use this)  this actually didn't always work as noticed by some users. CAS won and poor me not thinking much on the simplification between tan and sin. Here is the assembled formula (I guess there can be an infinity of formulas that capture the idea I am going to expose). \[ tan^{1}(x) \] So x can be incremented without problems. Picked among the trigonometric functions. \[ sin \left (tan^{1}(x) \right ) \] To let the value increase towards 1, although, after a while, very slowly. Still trig. \[ e^{ sin \left (tan^{1}(x) \right ) } \] to use either a common exponential or a logarithmic function without producing large numbers \[ \sqrt[3]{e^{ sin \left (tan^{1}(x) \right ) }} \] To make the final number even smaller. Using powers. Final formula to use (adapt the max 'x' value for speedy calculators. For example using 10k or 100k and so on) \[ \sum_{x=1}^{1000} \sqrt[3]{e^{ sin \left (tan^{1}(x) \right ) }} \] As said, it is an arbitrary formula picking functions among some of the most common types of functions: trig, exp/ln, powers. Trying to keep the final numbers small. I may have picked some other functions easier to check (to compare the accuracy). This one is pretty nasty. Anyway as I said I am interested in timings assuming that the calculators are as precise as they could with the digits that they have. I am really interested in what scientific calculators can do. I hope Eddie W. Shore sees this posts and contributes with a couple of models. Or jebem. Some redditors helping  https://www.reddit.com/r/EngineeringStud...ur_trusty/ Duplicated for versioning. http://www.wiki4hp.com/doku.php?id=bench...g_exp_root Second duplication if wiki4hp is not reachable: https://osdn.net/users/pier4r/pf/various...chmark.txt Mobile devices with programming apps having math libraries max = 1'000'000 ~ 5.22s  Nintendo New 2DS XL (2017) with SmileBasic A=1395612.15872538 post #159 max = 100'000 ~ 0.52s  Nintendo New 2DS XL (2017) with SmileBasic A=139560.97614105 post #159 Mobile devices with calculator apps max = 1'000'000 ~ 0.189s  ThetaCalc on iPhone 12 Sum=1395612.1587253837 p#227 ~ 9s  iPhone 12 DB48X v0.7.1 32bit IEEE754 p#248 ~ 9s  iPhone 12 DB48X v0.7.1 32bit IEEE754 p#248 max = 100'000 ~ 7.9s  Free42 iphone SE and 6s http://www.hpmuseum.org/forum/thread975...l#pid94029 ~ 17.3s  Emu48 HP50 on Samsung S20 userRPL p#216 ~ 32s  Emu48 HP50 on Samsung S9+ userRPL p#213 max = 10'000 ~ 3.2925s  Emu48 using flat HP50 on Samsung S9+ userRPL 13955.8578444 p#212 ~ 3.29s  Emu48 HP50 on Samsung S9+ userRPL p#213 max = 1000 ~ 0.3s Emu48 HP50 on Samsung S9+ userRPL p#213 Results physical calculators max = 10'000'000 ~ 84.1s  HP Prime G2 V.14603 Python p#239 ~ 103.724s  Prime using python p#238 max = 1'000'000 ~ 8.4s  HP Prime G2 V.14603 Python p#239 ~ 10.381s  Prime using python p#238 ~ 14.046s  Prime G2 Beta 2.1.14549 using Python 1395612.158725383 p#221 ~ 605s  DM42 DB48X v0.7.1 32bit IEEE754 p#248 ~ 806s  DM42 DB48X v0.7.1 32bit IEEE754 p#248 ~ 1748s  DM32 DB48X v0.7.1 32bit IEEE754 p#248 ~ 2188s  DM32 DB48X v0.7.1 64bit IEEE754 p#248 max = 500'000 ~ 3.5s  Prime G2 summation built in post #178 (this seems suspicious though, maybe simplifications happening?) ~ 8s  Prime A summation built in post #178 (this seems suspicious though, maybe simplifications happening?) ~ 1125s  TI30X Pro MathPrint summation builtin post #178 ~ 6300s  TI 36X Pro summation builtin post #178 max = 100'000 ~ 0.84s  HP Prime G2 V.14603 Python p#239 ~ 1.038s  Prime using python p#238 ~ 1.425s  Prime G2 Beta 2.1.14549 using Python 139560.9761410521 p#221 ~ 7.7s  HGPrime G2 , sum function http://www.hpmuseum.org/forum/thread975...#pid102818 ~ 9s  TI Nspire CX CAS, hardware version N0118AB (2018), OS 4.5.0.1180 (2017): C with Ndless. Post #147 ~ 9.5s  TI Nspire CX II CAS 13955.8579044; Sum function; original f(x); HW Rev. M0119AF; OS 5.1.0.177 p#185 ~ 12s  TI Nspire CX CAS, hardware version P0411A (2011), OS 4.5.0.1180 (2017): 139560,97614105 . C with Ndless. Post #143 ~ 17.7s  casio fx 9860GII power graphic 2 SHA4 overclock 236 +Ftune F5 preset C.Basic ver.1.73beta Sigma(Cbrte^sin tan^1 X,X,1,100000)  139560.976141052 ~ 19.2s  HPPrime , Home, Teval(), HP PPL. last os as 2017.12 ~ 19.5s  TI nspire CX II CAS M0720AK (2020), OS 5.2.0.771 (2020) micropython 139560.9761410522 p#205 ~ 20.5s  casio fx cg50 SH4A 192MHz ptune C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^1 X,X,1,100000)  139560.97614105 ~ 23s  HP 50g HPGCC 2.0  75 Mhz  139560.8013952589 ~ 29.9s  casio fx cg20 SH4A 118MHz C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^1 X,X,1,100000)  139560.976141052 ~ 36s  casio fx cg50 SH4A 118MHz C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^1 X,X,1,100000)  139560.976141052 ~ 47s  TI Nspire CX CAS, hardware version P0411A (2011), OS 4.5.0.1180 (2017): Lua max= 100000: 47.1s  139560,97614105 . Post #143 ~ 51.5s  TI Nspire CX II CAS: 139560.976284; Sum function and CAS simplified f(x)  f(x) = e^(x/(3*sqrt(x^2+1))) p#185 ~ 54.5s  TI Nspire CX II CAS 139560.976284; Sum function and ^1/3 power instead of cube root p#185 ~ 52s  casio fx 9860GII SH3 overclock 118MHz +Ftune F5 preset C.Basic ver.1.73beta Sigma(Cbrte^sin tan^1 X,X,1,100000)  139560.976141052 ~ 53s  casio fxcg50 micropython 139560.9761410521 http://www.hpmuseum.org/forum/thread975...#pid103457 ~ 57s  casio fxcg50 micropython 139560.9761410521 http://www.hpmuseum.org/forum/thread975...#pid103448 ~ 65s  numworks 139560.97614110521 micropython http://www.hpmuseum.org/forum/thread975...#pid103445 ~ 84s  numworks 2017.12 micropython ~ 94s  TI Nspire CX II CAS 139560.976284; Sum function and cube root; HW Rev. M0119AF; OS 5.1.0.177 p#185 ~ 95s  TI nspire CX II CAS M0720AK (2020), OS 5.2.0.771 (2020) Sum function, approx. mode 139561 p#205 ~ 117s  casio fx 9860GII power graphic 2 SHA4 normal 29Mhz C.Basic ver.1.73beta Sigma(Cbrte^sin tan^1 X,X,1,100000)  139560.976141052 ~ 147s  casio fx 9860GII SH3 normal 29 mhz C.Basic ver.1.73beta Sigma(Cbrte^sin tan^1 X,X,1,100000)  139560.976141052 ~ 176s  HP 39gii Program with For loop p#188 ~ 195s  Nspire CX sum function approx mode. ~ 222s  nspire CX CAS, sum function, approx mode. ~ 261s  DM42 on USB, RPN ~ 323s  9750gII upgraded to 9860gII OS {sum:eqn,x,1, 100000} gives me 139560.9761 CPU frequency sitting at 235 MHz (F5 in FTune) ~ 653s  DM42 on batteries, RPN ~ 2009s  9750gII upgraded to 9860gII OS {sum:eqn,x,1, 100000} gives me 139560.9761 ~ 7080s  casio fx570EX, 139560.9761 sum function p#206 p#207 max = 10'000 ~ 0.101s  Prime using python p#238 ~ 0.159s  Prime G2 Beta 2.1.14549 using Python 13955.857904429155 p#221 ~ 0.74s  HPPrime G2 , sum function http://www.hpmuseum.org/forum/thread975...#pid103311 ~ 0.74s  Prime G2 HPPL p#209 ~ 0.93s  Prime G2 HPPL p#209 ~ 1.8s  casio fx 9860GII power graphic 2 SHA4 overclock 236 +Ftune F5 preset C.Basic ver.1.73beta Sigma(Cbrte^sin tan^1 X,X,1,10000)  13955.8579042916 ~ 2.072s  HPPrime , Home, Teval(), HP PPL. last os as 2017.12 ~ 2s  HP 50g HPGCC 2.0  75 Mhz  13955.85790429154 ~ 2.1s  casio fx cg50 SH4A 192MHz ptune C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^1 X,X,1,10000)  13955.8579042916 ~ 3.1s  casio fx cg20 SH4A 118MHz C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^1 X,X,1,10000)  13955.8579042916 ~ 3.8s  casio fx cg50 SH4A 118MHz C.BasicCG ver.0.45alpha Sigma(Cbrte^sin tan^1 X,X,1,10000)  13955.8579042916 ~ 5.3s  casio fx 9860GII SH3 overclock 118MHz +Ftune F5 preset C.Basic ver.1.73beta Sigma(Cbrte^sin tan^1 X,X,1,10000)  13955.8579042916 ~ 8s  numworks 2017.12 python ~ 11.9s  casio fx 9860GII power graphic 2 SHA4 normal 29Mhz C.Basic ver.1.73beta Sigma(Cbrte^sin tan^1 X,X,1,10000)  13955.8579042916 ~ 12.5s  USB db48x for the dm42 https://www.hpmuseum.org/forum/thread20...#pid174581 ~ 14.9s  casio fx 9860GII SH3 normal 29 mhz C.Basic ver.1.73beta Sigma(Cbrte^sin tan^1 X,X,1,10000)  13955.8579042916 ~ 16s  numworks 2017.12 sum function ~ 18s  HP 39gii Program with For loop p#188 ~ 19s  nspire CX, sum function approx mode ~ 22.5s  nspire CX CAS, sum function, approx mode. ~ 20 sec  ti nspire handheld (2006). sum function. Degrees, float 12, approx. 13955.8579044 . OS 3.9.0.463 ~ 23.9s  HPPrime , Home, sum function. last os as 2017.12 ~ 26s  DM42 on USB, RPN ~ 32s  9750gII upgraded to 9860gII OS {sum:eqn,x,1,10000} gives me 13955.8579 CPU frequency sitting at 235 MHz (F5 in FTune) ~ 56,51s  Hp 50g newRPL 2017.12 FOR loop., 12 digits precision ~ 65.73s  DM42 on batteries, RPN ~ 97s  HP Xpander built in function 13955.8579043 p#210 ~ 184s  fx9860GIII , micropython result has reduced precision p#199 ~ 199s  9750gII upgraded to 9860gII OS {sum:eqn,x,1,10000} gives me 13955.8579 ~ 233s  casio fx 9860gII, sum function ~ 242s  hp 50g, sum function . It uses CAS to simplify the expression! See post #144. ~ 257s  HP200LX turbo c 2.01, 13955.857904 p#236 ~ 260s  hp 50g, sysRPL ~ 309s  hp 50g, userRPL ~ 330s  Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned off, post#165 13955.8579042908 ~ 376s  Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned on, post#165 13955.8579042908 ~ 402.91s  TI 84 Plus CE ~ 453s  Ti 92 plus, sum function ~ 465s  ti 89, approx mode, sum function. ~ 468s  41CL, v5 board, TURBO 50. Using the Sigma+ function to accumulate intermediate values. 13955.84859 ~ 472s  ti 89 titanium, 12 digits, approx mode, degrees, no pretty print. OS 3.10 (code sigma((e^(...))^(1/3), x, 1, 1000)) where 'sigma' is the greek letter . 13955.8579044 ~ 487.3s  HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144)  13955.8578444 p#185 ~ 487.3s  HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144)  13955.8578444 p#185 ~ 505.4s  HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT  13955.8578444 p#185 ~ 534.7s  HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT  13955.8578444 p#185 ~ 541s  hp 48gx, userRPL ~ 554s  hp 48gx, sum function ~ 986s  Ti 92, sum function ~ 1073s  casio fx570EX, 13955.8579 sum function p#206 p#207 ~ 1105s  casio fx 9750g, sum function ~ 1184s  DM11L (48 mhz), RPN ~ 1185s  Ti 82, ti basic ~ 1246s  hp28s, userRPL ~ 1501s  casio fx880p, casio basic ~ 1650s  fx9860GIII , Casio Basic p#199 max = 1000 ~ 0.036s  Prime G2 Beta 2.1.14549 using Python 1395.3462877433426 p#221 ~ 0.223s  HPPrime , Home, Teval(), HP PPL. last os as 2017.12 ~ 0.4s  DM42 DB48X v0.6.4 32bit IEEE754 p#248 ~ 0.7s  DM42 DB48X v0.6.4 32bit IEEE754 p#248 ~ 1.4s  DM32 DB48X v0.6.4 32bit IEEE754 p#248 ~ 1.7s  DM32 DB48X v0.6.4 64bit IEEE754 p#248 ~ 2s  HPPrime , Home, sum function. last os as 2017.12 ~ 2s  HP 39gii Builtin sum function (sum function can only do max. 1000) p#188 ~ 2.5s  nspire CX CAS, sum function, approx mode. ~ 2.6s  DM42 on USB, RPN ~ 4s  casio fx9750gII (upgraded with 9860gII OS 2.04) and overclocked to max speed with FTune (likely a ~ 5x overclock) sum function ~ 6.022s  Hp 50g newRPL 2017.12 FOR loop., 12 digits precision ~ 6.5s  Casio fxCP400 (classpad 400) , 1395.346288 sum function ~ 6.64s  DM42 on batteries, RPN ~ 7s  fx9860GIII with OS version 3.70.0200 mycropython p#245 ~ 8.2s  Hp 50g newRPL 2017.12 FOR loop., 32 digits precision 1395.346287743423 (I assume the result returned truncated on the stack) ~ 12s  HP Xpander built in function 1395.34628774 p#210 ~ 12.582s  HPPrime , CAS, approx mode. last os as 2017.12 ~ 13.5s  Casio fxCG50 (primz), 1395.346288 sum function ~ 18s  Casio ClassPad 330A, 1395.346288 (ClassPad is labeled on the back side as CLASSPAD300PLS, the 330A is written on the box) sum function ~ 18s  fx9860GIII , micropython result has reduced precision p#199 ~ 20s  Casio fx7400GII , 1395.346288 sum function ~ 22s  casio fx9750gII (upgraded with 9860gII OS 2.04), 1395.346288 sum function ~ 23s  casio fx 9860gII, sum function ~ 23s  Casio fx9860G Slim (hacked to 9860GII OS 2.04), 1395.346288 sum function ~ 24.5s  Hp 50g, 2.15, RPN mode, DEG, sum function . 1395.3462877 (approx mode). It uses CAS to simplify the expression! See post #144. ~ 24.5  CASIO Prizm fxCG10, sum function ~ 25.5s  Hp 50g, 2.15, exact mode sum function. It uses CAS to simplify the expression! See post #144. ~ 25.5s  Hp50g RPN; Sum function; Std number format; ~Num key; 1395.3462877 p#185 ~ 26.5s  hp 50g, sysRPL ~ 27s  HP200LX turbo c 2.01, 1395.346288 p#236 ~ 29.4s  Hp 50g newRPL 2017.12 FOR loop., 128 digits precision ~ 29s  HP15C LE ~ 33.8s  Hp 50g, 2.15, RPN mode, DEG (quick userRPL FOR loop, using, instead of XROOT, the 1/3 power. Surprisingly slower than the summation) . 1395.3462877 (approx mode) ~ 34s  HP40gs sum function, 1395.3462877 ~ 34.8s  Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned off, post#165 1395.34628774339 ~ 38s  sharp el9950 , 1395.346288 ~ 39.7s  Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned on, post#165 1395.34628774339 ~ 41.5s  TI 84 plus CE ~ 45s  Ti 92 plus, sum function ~ 46s  ti 89 titanium, 12 digits, approx mode, degrees, no pretty print. OS 3.10 (code sigma((e^(...))^(1/3), x, 1, 1000)) where 'sigma' is the greek letterl . 1395.34628774 ~ 46s  ti 89, approx mode, sum function. ~ 47.8s  HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144)  1395.3462877 p#195 ~ 47.8s  HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144)  1395.3462877 p#195 ~ 48s  ti 89 titanium, 12 digits, approx mode, degrees, no pretty print. OS 3.10 (code sum(seq((e^(...))^(1/3), x, 1, 1000))) . 1395.34628774 ~ 48s  41CL, v5 board, TURBO 50. Using the Sigma+ function to accumulate intermediate values. 1395.346260 ~ 51.0s  HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT  1395.3462877 p#195 ~ 53.9s  HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT  1395.3462877 p#195 ~ 54s  hp 48gx, userRPL ~ 55s  hp 48gx, sum function ~ 55s  48G+ , sum function with speed ui ~ 57s  TI Voyage 200 Sum function; 12 digits; "Approx ="; 1395.34628774 p#185 ~ 57s  Casio fx991CW , 1395.346288 p#237 ~ 59s  casio fx570CW, 1395.346288 (sum function) p#235 ~ 62s  ti 89 OS 2.09. (exact mode plus likely with pretty print) ~ 64s  sharp elw506x (abusing the integral function). ~ 76s  Casio fx9700GE , 1395.34628774 sum function ~ 95.5s  HP 48SX http://www.hpmuseum.org/forum/thread975...#pid103329 ~ 97s  sharp el506x (abusing the integral function). ~ 99s  Ti 92, sum function ~ 99.5s  casio fx9750g+ sum function ~ 102s  Sharp PCG850VS Basic, 1395.346559 ~ 103s  casio fx 9750g, sum function ~ 104s  TI30X Pro MathPrint 1395.346288 post #156 ~ 104s  TI30X Pro MathPrint (Europe) 1395.346288 post #237 (confirmed!) ~ 105s  TI83plus (ver.1.16) internal result=1395.346287744 post #161 ~ 108s  casio fx991 version , 1395.346288 (the fast batch reported by some users) sum function ~ 109s  casio fx570EX, 1395.346288 sum function p#206 p#207 ~ 115s  TI82  0497 Date Code Result=1395.346288 p#211 ~ 120s  DM10L (48 mhz), RPN post#170 ~ 120s  HP27S 1395.3462877 BENCH=Σ(X:1:1000:1:EXP(SIN(ATAN(X)))^.333333333333) ~ 121s  Ti 82, ti basic ~ 123s  HP28S userRPL p#213 ~ 125s  DM11L (48 mhz), RPN ~ 130s  hp28s, userRPL ~ 131s  casio fx991 version , 1395.346288 (the slow batch reported by some users) sum function ~ 131s  TI85 (ver.9.0) internal result=1395.346287744 post #161 ~ 133s  136s  DM15L , 48 mhz (interesting the difference with the 41L), 1395.346288 ~ 135s  Casio fx991EX , sum built in, 1395.3463 post #180 ~ 136s  TI85 nested Sum(Seq(f(x),x,1,1000,1)); Mode defaults; 1395.34628774 p#185 ~ 138s  TI86 nested Sum(Seq(f(x),x,1,1000,1)); Mode defaults; 1395.34628774 p#185 ~ 145s  Sharp el5250 (program with LblconditionalGoto) p#188 ~ 148s  HP 75D http://www.hpmuseum.org/forum/thread975...l#pid88453 ~ 153s  casio fx880p, casio basic. Another run 158s (see post #76). ~ 163s  Casio fx92+ Spéciale Collège 1395,346288 http://www.hpmuseum.org/forum/thread975...#pid103296 ~ 164s  fx9860GIII , Casio Basic p#199 ~ 166s  Casio fx5800P, 1395.346288 sum function ~ 168s  WP 34S double off, fix 2, sum function ~ 173s  Epson Hx20 . max 7 digits precision. 1395.36 ~ 173s  Epson Hx20 . max 16 digits precision. 1395.346369147301 ~ 171178s  HP 71B http://www.hpmuseum.org/forum/thread975...l#pid88453  http://www.hpmuseum.org/forum/thread975...l#pid90635 ~ 185s  WP 34S double on, fix 2, sum function ~ 200s  casio fx8500g, sum function ~ 206s  HP 32s RPN 1395.34628770 http://www.hpmuseum.org/forum/thread975...l#pid89004 ~ 209s  HP 33s RPN http://www.hpmuseum.org/forum/thread982...l#pid87566 ~ 218s  Ti 80, ti basic ~ 220s  fx9860GIII , built in sum p#199 ~ 241s  HP 32sII RPN 1395.34628770 ~ 245s  TI 36x Pro sum function ~ 253s  Hp 35s http://www.hpmuseum.org/forum/thread982...l#pid87766 ~ 256s  wp34s (DSEbased loop, DBLOFF), 1395.346287743423 ~ 285s  wp34s (DSEbased loop, DBLON), 1395.346287743423256291575365067091 ~ 287s  Hp35s, RPN program ~ 291s  HP 42s , RPN program ~ 298s  sharp el506w (abusing the integral function. Not really returning the wanted result from the summation). ~ 303s  wp34s (S command, DBLOFF), 1395.346287743423 ~ 332s  wp34s (S command, DBLON), 1395.346287743423256291575365067093 ~ 338s  casio fx4000P 1395.346288 http://www.hpmuseum.org/forum/thread975...#pid102725 ~ 375s  HP9821A, algebraic post#177 ~ 390s  HP9821A, algebraic, 1395.346288 post#173 ~ 404.93s  DM41L 48 mhz , RPN program ~ 502.2s  Sharp 516X sum function ~ 525s  Casio fx115ES Plus: 1395.346288 sum function ~ 573s  fx3600pv degrees 1395.3462707 p#203 ~ 574s  fx3600pv radians 1395.3462707 p#203 ~ 581s  casio fx570CW, 13955.8579 (sum function) p#235 ~ 633s  Casio fx3650pII , 1395.346288 for next ~ 633s  Casio fx50F PLUS , 1395.346288 for next ~ 840890s  Canon X Mark I Pro, 1395.346288, sum function ~ 1814s  Casio fx50F degrees 1395.34628605 p#198 ~ 1828s  Casio fx50F radians 1395.34628605 p#198 ~ 2844s  Sharp PC1201 p#228 max = 100 ~ 0.036s  HPPrime , Home, Teval(), HP PPL. last os as 2017.12 ~ 0.2s  HPPrime , Home, sum function. last os as 2017.12 ~ 0.28s  DM42 on USB, RPN ~ 0.6s  DM42 on batteries, RPN ~ 2s  fx9860GIII , micropython result has reduced precision p#199 ~ 2.5s  casio fx 9860gII, sum function ~ 2.7s  hp 50g, sum function. It uses CAS to simplify the expression! See post #144. ~ 2.8s  hp 50g, sysRPL ~ 3.3s  hp 50g, userRPL ~ 3.77s  Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned off, post#165 139.297187045924 ~ 3.85s  DM41X FOCAL stack, USB connected p#201 ~ 4s  ti 89, approx mode, sum function. ~ 4s  HP200LX turbo c 2.01, 139.297187 p#236 ~ 4.3s  Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned on, post#165 139.297187045924 ~ 4.61s  DM41X FOCAL fast mode, USB connected: result=139.2971873 p#200 ~ 5s  Ti 92 plus, sum function ~ 5.5s  HP 49G (ROM 2.10) radians real approx sum function (uses CAS see post #144)  139.297187047 p#195 ~ 5.5s  HP 49G (ROM 2.10) degrees real approx sum function (uses CAS see post #144)  139.297187047 p#195 ~ 5.5s  HP 49G (ROM 2.10) radians real approx UserRPL FOR/NEXT  139.297187047 p#195 ~ 5.7s  HP 49G (ROM 2.10) degrees real approx UserRPL FOR/NEXT  139.297187047 p#195 ~ 5.13s  41CL, v5 board, TURBO 50. Using the Sigma+ function to accumulate intermediate values. 139.297187 ~ 5.5s  hp 48gx, userRPL ~ 5.9s  hp 48gx, sum function ~ 6s  48G+ , sum function with speed ui ~ 7s  casio fx570CW, 139.297187 (sum function) p#235 ~ 10s  Ti 92, sum function ~ 11s  casio fx 9750g, sum function ~ 11s  Sharp PCG850VS Basic, 139.2971873 ~ 11s  TI30X Pro MathPrint 139.2971870 post #156 ~ 11s  casio fx991 version , 139.2971870 (the fast batch reported by other users) sum function ~ 12s  DM41X FOCAL stack, battery p#201 ~ 12s  casio fx570EX, 139.297187 sum function p#206 p#207 ~ 13s  Ti 82, ti basic ~ 13.2s  HP28S userRPL p#213 ~ 14s  DM11L (48 mhz), RPN ~ 14s  dm15L 48 mhz, RPN, 139.2971874 ~ 14s  casio fx991 version , 139.2971870 (the slow batch reported by other users) sum function ~ 14s  hp28s, userRPL ~ 14.33s  DM41X FOCAL fast mode, battery powered: result=139.2971873 p#200 ~ 15s  HP41CL / x50 speed: 100 iterations (139.2926) RPN ~ 16s  casio fx880p, casio basic ~ 16s  fx9860GIII , Casio Basic p#199 ~ 17s  Casio FX603P, casio basic ~ 18s  Epson Hx20 . max 7 digits precision. 139.297 ~ 18s  Epson Hx20 . max 16 digits precision. 139.297193646431 ~ 21s  casio fx8500g, sum function ~ 22s  sharp el9300 http://www.hpmuseum.org/forum/thread975...l#pid89345 ~ 23s  HP 33s RPN http://www.hpmuseum.org/forum/thread982...l#pid87566 ~ 23s  HP 32s RPN 139.29718705 http://www.hpmuseum.org/forum/thread975...l#pid89004 ~ 23s  Ti 80, ti basic ~ 25s  TI 36x Pro ~ 25s  fx9860GIII , built in sum p#199 ~ 26s  wp34s (DSEbased loop, DBLOFF), 139.2971870459241 ~ 26s  HP 32sII RPN 139.29718705 ~ 27s  wp34s (DSEbased loop, DBLON), 139.2971870459242385751150019615150 ~ 27.5s  Hp 35s http://www.hpmuseum.org/forum/thread982...l#pid87766 ~ 30s  wp34s (S command, DBLOFF), 139.2971870459242 ~ 31s  HP 42s , RPN program (confirmations: post #149 Result: 139.297187046 ) ~ 31s  Hp35s, RPN program ~ 33.8s  Sharp 516X ~ 34s  wp34s (S command, DBLON), 139.2971870459242385751150019615149 ~ 36s  Sharp EL5120 Solver 139.297187 http://www.hpmuseum.org/forum/thread975...l#pid88303 ~ 37s  HP9821A, algebraic post#177 ~ 38s  HP9821A, algebraic, 139.2971870 post#173 ~ 42.23s  DM41L 48 mhz , RPN program ~ 43  44 s  Casio fx720P 139.297187038 http://www.hpmuseum.org/forum/thread975...#pid102799 see also post #153 ~ 45s  CASIO PB 700  BASIC Result: 139.297187 post #153 ~ 58.9s  fx3600pv degrees 139.2971869 p#203 ~ 63s  dm15L 12mhz , RPN, 139.2971874 ~ 65s  Casio fx991ES PLUS sum function ~ 66s  HP9100B , algebraic 139.2971870  post #177 ~ 83s  TI95 Procalc, program "assembled" 139.2971870460 p#189 ~ 88s  Casio fx4500p released 1989 program 139.297187 p#220 ~ 91s  Sharp PC1401 Basic, 139.2971873 ~ 91s  Olivetti M10, basic ~ 91s  CASIO FX602P  KEYSTROKE PROGRAM Result:139.2971873 post #149 ~ 105s  TI67 released 1992 sum func 139.297187 p#220 ~ 146s  TI67 released 1992 program 139.297187 p#220 ~ 158s  hp 41CV (plain, fullnut, no turbo) , 139.2971874 ~ 158s  Casio fx2700P 139.29719 http://www.hpmuseum.org/forum/thread975...l#pid91994 ~ 182s  CASIO FX502P  Keystroke program (DSZ loop) post #164 139.2971870 ~ 187.1s  Casio fx50F 139.297187029 p#198 ~ 285s  Sharp PC1201 p#228 ~ 313  320s  hp15C , RPN , 139.2971874 ~ 316s  HP11C  RPN PROGRAM Result: 139.2971874 post #149 ~ 316s  HP10C  RPN PROGRAM Result: 139.2971874 post #151 ~ 329s  hp65 N=100, Result= 139.2971873 ~ 340s  HP67. RPN (139.2925695) ~ 419s  TI57 II  keystroke program (DSZ loop), 139.29719 p#197 ~ 434s  HP 55 , RPN program 139.2971873 max = 10 ~ 1< seconds  Hp 50g, 2.15, RPN mode 13.7118350167 (approx mode). It uses CAS to simplify the expression! See post #144. ~ 1s<  Saturn assembly for the HP48G/GX ( ROM version R ), Display and keyboard scanning turned on (or off), post#165 13.7118350167043 ~ 1s  casio fx570CW, 13.71183502 (sum function) p#235 ~ 2s  Epson Hx20 . max 7 digits precision. 13.7118 ~ 2s  Epson Hx20 . max 16 digits precision. 13.71183562278748 ~ 2s  casio fx570EX, 13.71183502 sum function p#206 p#207 ~ 2s  HP200LX turbo c 2.01, 13.711835 p#236 ~ 3s  wp34s (DSEbased loop, DBLOFF), 13.71183501670439 ~ 3s  wp34s (DSEbased loop, DBLON), 13.71183501670437880652763283584306 ~ 3s  wp34s (S command, DBLOFF), 13.71183501670438 ~ 3s  wp34s (S command, DBLON), 13.71183501670437880652763283584306 ~ 3s  HP 32s RPN 13.71183502 http://www.hpmuseum.org/forum/thread975...l#pid89004 ~ 3s  HP 32sII RPN 13.71183502 ~ 3.5s  HP 42S  RPN PROGRAM Result: 13.7118350166 post#149 ~ 4s  HP9821A, algebraic, post #177 ~ 4s  HP9821A, algebraic, 13.71183502 post#173 ~ 4s  Casio fx720P 13.7118350167 http://www.hpmuseum.org/forum/thread975...#pid102799 see also post #153 ~ 4.6s  CASIO PB 700  BASIC Result: 13.71183502 post #153 ~ 6s  dm15C 12mhz , RPN, 13.71183502 ~ 6s  fx3600pv degrees 13.711835009 p#203 ~ 6.5s  HP9100B , algebraic 13.71183502  post #177 ~ 9s  Sharp PC1401 Basic, 13.71183501 ~ 9.2s  CASIO FX602P  KEYSTROKE PROGRAM Result:13.71183502 post #149 ~ 9.5s  Olivetti M10, basic ~ 9s  Casio fx4500p released 1989 program 13.71183502 p#220 ~ 11s  TI67 released 1992 sum func 13.71183502 p#220 ~ 14s  TI59 Result: 13.71183502 p#183 ~ 15s  TI67 released 1992 program 13.71183502 p#220 ~ 16s  TI58c Result: 13.71183502 p#183 ~ 16s  hp 41CV (plain, fullnut, no turbo), 13.71183502 ~ 16s  Casio fx2700P 13.711835 http://www.hpmuseum.org/forum/thread975...l#pid91994 ~ 18.1s  CASIO FX502P  Keystroke program (DSZ loop) post #164 13.71183501 ~ 18.7s  Casio fx50F 13.7118350165 p#198 ~ 25s  Sharp PC1201 p#228 ~ 29s  HP25C (Woodstock): N=10, Result=13.71183501 ~ 31s  HP11C  RPN PROGRAM Result: 13.71183502 post #149 ~ 31s  HP10C  RPN PROGRAM Result: 13.71183502 post #151 ~ 32s  hp15C , RPN, 13.71183502 ~ 32s  hp65, Time= 32 sec, Result= 13.71183501 ~ 33s  HP97  RPN PROGRAM Result: 13.71183502 post #149 ~ 35s  HP29C (Woodstock) N=10, Result=13.71183501 ~ 39s  TI57 II  keystroke program (DSZ loop), 13.711835 p#197 ~ 43s  HP 55 , RPN program 13.71183501 ~ 44s  HP33C (Spice): N=10, Result=13.71183501 http://www.hpmuseum.org/forum/thread975...l#pid88370 ~ 46s  HP34C (Spice): N=10, Result=13.71183501 ~ 47s  sharp 506w (using X, formula memory F4 and M to sum) manually. 13.71183502 . ~ 51s  TI57 Result: 13.711835 p#183 ~ 56s  TI53 "... at a rate of one iteration every 5.64 seconds. " http://www.hpmuseum.org/forum/thread975...l#pid87729 ~ 63.5s  TI62, TI basic. 13.71183502 ~ 99s  MK 54 , RPN program 13.711835 ~ 100s  MK 61 , RPN program 13.711835 ~ 110s  MK 56 , RPN program 13.711835 PS: I forgot how full of apps was the ti89 and how awful is the official command reference compared to the 50g AUR. But with the ti89 one finds everything online. Ex: https://education.ti.com/html/t3_free_co...sson2.html Wikis are great, Contribute :) 

12222017, 10:18 PM
(This post was last modified: 12222017 10:22 PM by Arno K.)
Post: #3




RE: Summation based test for calculators
I ususally am not that enthusiastic about these tests, but nevertheless I entered the sum on the HWPrime, in CAS, time() said 12.582s, the result is, approx() used, 1395.34628774. Without approx it returns that sum of exact values. Then I switched to home, here the same commands needed 15.702s, which is some overhead produced by time, with TEVAL() only 0.223s were used to get the result you had.
Arno 

12222017, 11:10 PM
(This post was last modified: 12222017 11:11 PM by pier4r.)
Post: #4




RE: Summation based test for calculators
(12222017 10:18 PM)Arno K Wrote: I ususally am not that enthusiastic about these tests Yes they are nothing special, but they give an idea and moreover it is the first time I see the possibility to compare with scientific calculators (at least the last generation). Plus the formula is pretty easy to type. I did it on the ti89 and nspire that I almost never touch. If I understood correctly, the 0.223s where obtained in the home using Teval(). Could you run with the same setup a test until 10k ? I hope someone with a new dm42 does the test too. As well as some casio devices. Wikis are great, Contribute :) 

12232017, 12:57 AM
Post: #5




RE: Summation based test for calculators
(12222017 09:41 PM)pier4r Wrote: I did not forget this post (nor the topic about common calculators). Casio fx115ES Plus: 1395.346288, time 8 minutes and 45 seconds 

12232017, 06:32 AM
(This post was last modified: 02032018 07:49 PM by brickviking.)
Post: #6




RE: Summation based test for calculators
On the HP50G, I entered the formula into the Equation writer, popped it to the stack and hit EVAL. I get about 28.2" in exact mode and about 25.5" in Approx mode, giving a result of 1395.3462877 in both cases. I'm assuming that's the way I'm meant to do it? I also duplicated these results using >NUM just to check, but got roughly the same measurements. EVAL in the equation editor also got a similar result to using EVAL on the stack entry.
It's interesting that my fx9750gII (upgraded with 9860gII OS 2.04) beats out the 50G. My fx9750gII gets about 22" for sum(1,1000) giving me 1395.346288 as a result. Then I tried it out on the fx9750g+ (earlier generation) and got 1' 39.5". Just for laughs, I "souped up" the 9750gII with the FTune application (speeds up the CPU and bus clock) and got four seconds for 1,1000. Wow. I wonder what I'd get if I'd newRPL'd the 50G? (Post 148) BrickEdit: added gII to last instance of 9750, as it wasn't clear which machine I souped up. Could be a laugh trying to "soup up" the G+. Regards, BrickViking HP50g Casio fx9750G+ Casio fx9750GII (SH4a) 

12232017, 07:56 AM
Post: #7




RE: Summation based test for calculators
You do realise that you are basically repeating the same calculation thousands of times?
The atan will quickly converge to pi/2 and so the summand to exp(1/3). 

12232017, 09:05 AM
Post: #8




RE: Summation based test for calculators
(12222017 11:10 PM)pier4r Wrote:(12222017 10:18 PM)Arno K Wrote: I ususally am not that enthusiastic about these tests 2.072s to get it to 10000. Arno 

12232017, 09:09 AM
Post: #9




RE: Summation based test for calculators
I've not tried this on the 34S and probably won't. The internal summation command will be slower than a short program that just adds the terms  it goes to some extra effort to Kahan sum the terms in reverse order (which isn't ideal in this case).
Pauli 

12232017, 09:59 AM
(This post was last modified: 12232017 10:28 AM by pier4r.)
Post: #10




RE: Summation based test for calculators
(12232017 07:56 AM)AlexFekken Wrote: You do realise that you are basically repeating the same calculation thousands of times? Yes, but the calculator should not know (although I am not sure what happens when x gets large and tan^1 may report always the same value). Moreover as I wrote, the formula is pretty arbitrary and is one picked quickly that does not converge but also does not explode with larger values. I was thinking about alternate series (using sin or cos) but at the end it would be similar. It is repeating thousands of times the same functions. At it is also what is wanted, so one gets an idea how those functions performs together, likely avoiding possible internal optimizations such as "a function and its inverse composed". What is interesting is that with the 50g, in userRPL, I was not yet able to get a program faster than the summation. And the faster value is a summation, that is an algebraic object that is notoriously slower than pure userRPL! Anyone with a 48 or other devices? Is it difficult to produce a RPN equivalent (for 41 and other systems) for the formula? @Pauli: is it difficult to run an internal program on the 34s for this summation? If not, could you try? edit: also newrpl should be interesting. Because the first second is done at 6 mhz and then the 50g switches to full 192 mhz according to what I read in the newRPL threads. Wikis are great, Contribute :) 

12232017, 11:38 AM
(This post was last modified: 12232017 11:43 AM by Gilles59.)
Post: #11




RE: Summation based test for calculators
NewRPL, precision 32 digits :
1000 Loop (FOR NEXT) : 8.2 sec result : 1395.346287743423 12 digits = 6.022 sec 128 digits = 29.4 sec 

12232017, 12:54 PM
(This post was last modified: 12232017 02:28 PM by pier4r.)
Post: #12




RE: Summation based test for calculators
Thanks gilles! Super neat.
Would be really nice to have the results (if possible with common entry mode and then in an optimized form, if it exists) for:  a 41 version  41 CL  dm41  dm42  hp 42s  35s  a 48 version  12C (recent)  15C  50g with hpgcc (but this may be highly time consuming and not really usable in all day operations)  71B  67  34S  Nspire CX  A ti 84 (if possible recent)  Casio primz  Casio classpad (if possible 300 and then newer versions)  casio 991ex  Some sharp EL graphing or PC  Also Nspire lua would be interesting (I can do it on the nspire handheld, although a CX should be better) but actually it would be very similar to a hpgcc version on the 50g, very unlikely to be used in all day operations since lua is clumsy to use on the nspire for actual math results. Wikis are great, Contribute :) 

12232017, 01:56 PM
Post: #13




RE: Summation based test for calculators
(12232017 09:59 AM)pier4r Wrote: I was thinking about alternate series (using sin or cos) but at the end it would be similar. It is repeating thousands of times the same functions. I did not just mean "calling the same functions", but "calling the same functions with almost exactly the same (perhaps even the same) argument". I would say that any proper benchmark should call whatever functions it calls with a decent spread of the inputs. Using atan for (mainly) large values and then passing the almost constant result into sin (near an extremum!) pretty much garantees the exact opposite of that. Just my 2c of course... 

12232017, 02:27 PM
(This post was last modified: 12232017 03:05 PM by pier4r.)
Post: #14




RE: Summation based test for calculators
(12232017 01:56 PM)AlexFekken Wrote: I did not just mean "calling the same functions", but "calling the same functions with almost exactly the same (perhaps even the same) argument". I would say that any proper benchmark should call whatever functions it calls with a decent spread of the inputs. Using atan for (mainly) large values and then passing the almost constant result into sin (near an extremum!) pretty much garantees the exact opposite of that. You also have a point. But for the objective of the test (not much accuracy, rather timing) I would suppose that whatever spread of the inputs would be more or less similar. If you have better compositions of functions (trig, exp/ln/, power, add/sub/mul/div ) let me know! It may be an interesting input to learn a thing or two. At first I was exploring the hyperbolic functions (also because I never used them) but those may (a) be not so commonly implemented and (b) less often used. Edit. Meanwhile I forced the sharp 506w to do a similar tasks like the summation using the integral calculation, although the result is off due to fixed coefficents. The integral calculator in the sharp el506w is done with the Simpson's rule: This means that with a careful choice of the input parameters I can hope that the function is evaluated almost exactly in the 1000 points of the summation written above. In particular: a = 1 b = 1000 n = 500 N = 1000 h = 0.999 (if someone finds better parameters, please tell me!) I do not know how the summation is done, but I assume that there are two internal registers for the sum of the "even" steps and the "odd" steps that then gets multiplied by 4 and 2. The computation is done in 4m 58s . Wikis are great, Contribute :) 

12232017, 05:35 PM
Post: #15




RE: Summation based test for calculators
Interesting report from reddit.
Quote:TI89 (Original, not Titanium) OS 2.09 I will have to check with my ti 89 Wikis are great, Contribute :) 

12232017, 07:21 PM
Post: #16




RE: Summation based test for calculators
summation test for n=1000
Casio fxCG50  approx 13.5s, 1395.346288 Casio fxCP400  approx. 6.5s, 1395.346288 Casio fx991CE X  approx 1m 48s, 1395.346288 TINspire CX CAS  after 47s resource exhaustion, cannot complete calculations, Sharp EL9950  approx. 38s, 1395.346288 

12232017, 08:48 PM
Post: #17




RE: Summation based test for calculators
Thanks for the answer!
Thanks to grsbanks that reported the first entry for the dm42. I asked him to check the results with the prime and 50g, because his devices are like 10x faster than the one reported by other users and by me. The dm42 is pretty fast! I mean for a product done by a small company (compared to hp, ti, casio, sharp) plus one external indivisual (T.Okken) is quite amazing! Wikis are great, Contribute :) 

12232017, 08:49 PM
Post: #18




RE: Summation based test for calculators
(12232017 07:21 PM)klesl Wrote: TINspire CX CAS  after 47s resource exhaustion, cannot complete calculations, Thanks for the contributions. For the nspire be sure you are in approximate mode (and no pretty print when possible), otherwise the nspire tries to solve it symbolically. Like the ti89 as well. Wikis are great, Contribute :) 

12232017, 09:58 PM
(This post was last modified: 12232017 11:36 PM by Gilles59.)
Post: #19




RE: Summation based test for calculators
Casio FX603P
100 : 17 sec HP15C LE 1000 : 29 sec NewRPL HP50g hdw , 12 digits 10'000 : 56,51 sec On the Prime 100'000 : 19,2 sec ( very fast ! ) 

12242017, 02:32 AM
(This post was last modified: 12242017 06:24 AM by AlexFekken.)
Post: #20




RE: Summation based test for calculators
(12232017 02:27 PM)pier4r Wrote: But for the objective of the test (not much accuracy, rather timing) I would suppose that whatever spread of the inputs would be more or less similar.Incredible. We don't even seem to use the word "spread" with the same meaning... :) Wrt Simpsons rule, as someone has already pointed out in another thread: Simpson's rule is for student's only. Any serious, integration algorithm would be adaptive rather than using points with a fixed interval spacing. But perhaps it explains your obsession (in this thread) with summations. My main personal suggestion for performance benchmarking, if you really, really feel that you have to create one, is that you do the exact opposite of what you are doing, i.e. the opposite of combining a bunch of ad hoc operations into a single benchmark and then hoping that your becnhmark becomes popular. I would instead define and standardise a multitude of microbenchmarks that test the simplest of operations in isolation (examples below). Then, on top of that, you can define your "Pier4r" aggregation benchmark(s), e.g. by taking some weighted average of the microbenchmarks. That way others can define their own aggregated benchmarks, more suitable to their own use cases. Perhaps more importantly, it might help detect the relative strong and weak areas of each implementation (which can direct the implementers to the areas where they should look at improving things, or tap themselves on the back). For example, to test the performance of loop summation I would simply write some code to calculate 1+1+1+1+1... etc, in a loop and another one to force noninteger arithmetic, e.g. sqrt(2)+sqrt(2)+sqrt(2)+sqrt(2)+ etc. I would experiment with, i.e. have different benchmarks for, getting the values out of variables versus using contstants as well. But I would certainly *avoid* calling transcendental functions (whose execution time would probably dominate the total execution time) and then suggest that I am testing the performance of a summation loop... Wrt testing the performance of the transcendental functions, I would test them all (i.e. the ones you are interested in) in as much isolation as possible (e.g. separately time the overhead of the loops to set up the arguments; do *not* sum the values unless optimization forces you). And the basic trig functions already show that you may want multiple functionspecific microbenchmarks for every single function. For example, as some initial suggestions for the sine: sin(x), x = 10..10 (0.001) in radians sin(x), x = 1E6..1E6 (1) in radians sin(x), x = 500..500 (sqrt(0.02)) in degress sin(x), x = 1E8..1E8 (sqrt(20)) in degress sin(x+iy), x = 10..10 (0.001), y = 10..10 (0.001) in radians etc EDIT: it might be a good idea to adjust the numbers above so as to have the same number of function evaluations per microbenchmark. And to keep that number the same for the other functions. Some of the thoughts (and correct or incorrect assumptions about implementations) behind the reason for having these different microbenchmarks:  Test a decent spread of unrelated (from the function's perspective) inputs  Calculations for small and large arguments may perform very differently and not everyone may care about (very) large arguments (in this case) for their personalised aggregated benchmark  Calculations in radians and degress may perform very differently (especially if the implementation has been careful to deal with rounding appropriately in each mode) and, again, people may only care about one of these modes  Distinguish between real and complex calculations because the performance may be very different (perhaps predictably so for simple trig and exponential functions, but probably not for others, e.g. Gamma) and, again, not everyone will care about complex calculations. Lots of words, encouraging you to do lots of work, by someone who isn't going to do that work. But wellintended nevertheless.... 

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