Average Error: 0.8 → 1.0
Time: 4.1s
Precision: binary64
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\frac{1}{\log 10 \cdot \frac{1}{\tan^{-1}_* \frac{im}{re}}}\]
\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}
↓
\frac{1}{\log 10 \cdot \frac{1}{\tan^{-1}_* \frac{im}{re}}}
(FPCore (re im) :precision binary64 (/ (atan2 im re) (log 10.0)))
↓
(FPCore (re im)
 :precision binary64
 (/ 1.0 (* (log 10.0) (/ 1.0 (atan2 im re)))))
double code(double re, double im) {
	return atan2(im, re) / log(10.0);
}
↓
double code(double re, double im) {
	return 1.0 / (log(10.0) * (1.0 / atan2(im, re)));
}

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 0.8

    \[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
  2. Using strategy rm

  3. Applied clear-num_binary64_761.0

    \[\leadsto \color{blue}{\frac{1}{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}\]
  4. Using strategy rm

  5. Applied div-inv_binary64_741.0

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

  6. Final simplification1.0

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

Reproduce

herbie shell --seed 2020281 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  :precision binary64
  (/ (atan2 im re) (log 10.0)))