Average Error: 0.8 → 0.8
Time: 15.0s
Precision: 64
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\frac{1}{\sqrt{\log 10}} \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\sqrt{\log 10}}\right)\]
\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}
↓
\frac{1}{\sqrt{\log 10}} \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\sqrt{\log 10}}\right)
double f(double re, double im) {
        double r17378 = im;
        double r17379 = re;
        double r17380 = atan2(r17378, r17379);
        double r17381 = 10.0;
        double r17382 = log(r17381);
        double r17383 = r17380 / r17382;
        return r17383;
}
↓
double f(double re, double im) {
        double r17384 = 1.0;
        double r17385 = 10.0;
        double r17386 = log(r17385);
        double r17387 = sqrt(r17386);
        double r17388 = r17384 / r17387;
        double r17389 = im;
        double r17390 = re;
        double r17391 = atan2(r17389, r17390);
        double r17392 = r17391 * r17388;
        double r17393 = r17388 * r17392;
        return r17393;
}

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 add-sqr-sqrt0.8

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

  4. Applied *-un-lft-identity0.8

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

  5. Applied times-frac0.8

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

  7. Applied div-inv0.8

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

  8. Final simplification0.8

    \[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\sqrt{\log 10}}\right)\]

Reproduce

herbie shell --seed 2019196 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10.0)))