Summation based benchmark for calculators

[jlind]

With the exception of the Nspire CX II CAS, these were done without trying to simplify or optimize anything. Used default settings. 1000 was long enough for the older calculators listed. The TI-85 and TI-86 don't have a sigma summation function per se. To do a summation with an equation, the Seq() function is used to generate the sequence of f(x) from 1 to n with an optional specified interval (default is 1 if not specified). The TI-85 and TI-86 results are consistent as they're both driven by a 6 MHz Zilog Z80 uP and their hardware architecture is nearly identical. The TI-86 has 4x the RAM.

Didn't see the 2018 TI Nspire CX II CAS listed, which has a significantly faster uP than the CX. It was near instantaneous when set to 1000. Ran it at 10k and then 100k with its default settings using "Ctrl-Enter" for numerical approximation. Taking about 10x longer with 10x the sum iterations was expected. Provided its H/W and O/S data. Other than some f(x) tweaks to simplify and optimize it, the Nspire was run as-is out of the box with default settings.

1000:

• HP-50g: ~25.5 seconds; RPN; Sum function; Std number format; ~Num key; 1395.3462877
• TI Voyage 200: ~57 seconds; Sum function; 12 digits; "Approx ="; 1395.34628774
• TI-86: ~138 seconds: nested Sum(Seq(f(x),x,1,1000,1)); Mode defaults; 1395.34628774
• TI-85: ~136 seconds: nested Sum(Seq(f(x),x,1,1000,1)); Mode defaults; 1395.34628774
  

10,000:

• TI Nspire CX II CAS: ~9.5 sec; 13955.8579044; Sum function; original f(x); HW Rev. M-0119AF; OS 5.1.0.177
  

100,000:

• TI Nspire CX II CAS: ~ 94 sec; 139560.976284; Sum function and cube root; HW Rev. M-0119AF; OS 5.1.0.177
• TI Nspire CX II CAS: ~ 54.5 sec; 139560.976284; Sum function and ^1/3 power instead of cube root
• TI Nspire CX II CAS: ~ 51.5 sec; 139560.976284; Sum function and CAS simplified f(x)
  f(x) = e^(x/(3*sqrt(x^2+1)))
  

Nspire Notes:
Tweaked things with the 100k summation. Found that changing from cube root to 1/3rd power cut time by over 1/3rd. It's apparent the nth root function isn't as efficient as using the equivalent fractional power. Reduced time by several seconds more by letting CAS simplify original f(x) to the equation shown, which goes further than simply replacing the trig functions.

Should have tried replacing cube root with 1/3rd power in the other calculators. ;-)

John