Average Error: 0.9 → 0.8
Time: 11.3s
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 r560471 = im;
        double r560472 = re;
        double r560473 = atan2(r560471, r560472);
        double r560474 = 10.0;
        double r560475 = log(r560474);
        double r560476 = r560473 / r560475;
        return r560476;
}
↓
double f(double re, double im) {
        double r560477 = 1.0;
        double r560478 = 10.0;
        double r560479 = log(r560478);
        double r560480 = sqrt(r560479);
        double r560481 = r560477 / r560480;
        double r560482 = im;
        double r560483 = re;
        double r560484 = atan2(r560482, r560483);
        double r560485 = r560484 * r560481;
        double r560486 = r560481 * r560485;
        return r560486;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.9

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

  4. Applied *-un-lft-identity0.9

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

  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. Applied associate-*r*0.8

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

  9. 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 2019153 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))