Average Error: 0.9 → 0.9
Time: 1.1s
Precision: 64
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}
↓
\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}
double code(double re, double im) {
	return (atan2(im, re) / log(10.0));
}
↓
double code(double re, double im) {
	return (atan2(im, re) / log(10.0));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.9

    \[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]

  2. Final simplification0.9

    \[\leadsto \frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]

Reproduce

herbie shell --seed 2020071 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  :precision binary64
  (/ (atan2 im re) (log 10)))