Average Error: 0.8 → 0.5
Time: 19.6s
Precision: 64
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\frac{1}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}} \cdot \sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}}\right)\right)\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right)}\]
\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}
↓
\frac{1}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}} \cdot \sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}}\right)\right)\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right)}
double f(double re, double im) {
        double r950610 = im;
        double r950611 = re;
        double r950612 = atan2(r950610, r950611);
        double r950613 = 10.0;
        double r950614 = log(r950613);
        double r950615 = r950612 / r950614;
        return r950615;
}
↓
double f(double re, double im) {
        double r950616 = 1.0;
        double r950617 = 10.0;
        double r950618 = log(r950617);
        double r950619 = im;
        double r950620 = re;
        double r950621 = atan2(r950619, r950620);
        double r950622 = r950618 / r950621;
        double r950623 = cbrt(r950622);
        double r950624 = cbrt(r950618);
        double r950625 = r950624 * r950624;
        double r950626 = cbrt(r950625);
        double r950627 = r950624 / r950621;
        double r950628 = cbrt(r950627);
        double r950629 = cbrt(r950628);
        double r950630 = r950629 * r950629;
        double r950631 = r950629 * r950630;
        double r950632 = r950626 * r950631;
        double r950633 = r950632 * r950623;
        double r950634 = r950623 * r950633;
        double r950635 = r950616 / r950634;
        return r950635;
}

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-num1.0

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

  5. Applied add-cube-cbrt0.8

    \[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}}\]
  6. Using strategy rm

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

    \[\leadsto \frac{1}{\left(\sqrt[3]{\frac{\log 10}{\color{blue}{1 \cdot \tan^{-1}_* \frac{im}{re}}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}\]

  8. Applied add-cube-cbrt1.2

    \[\leadsto \frac{1}{\left(\sqrt[3]{\frac{\color{blue}{\left(\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}\right) \cdot \sqrt[3]{\log 10}}}{1 \cdot \tan^{-1}_* \frac{im}{re}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}\]

  9. Applied times-frac1.2

    \[\leadsto \frac{1}{\left(\sqrt[3]{\color{blue}{\frac{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}{1} \cdot \frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}\]

  10. Applied cbrt-prod0.8

    \[\leadsto \frac{1}{\left(\color{blue}{\left(\sqrt[3]{\frac{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}{1}} \cdot \sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}\right)} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}\]

  11. Simplified0.8

    \[\leadsto \frac{1}{\left(\left(\color{blue}{\sqrt[3]{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}\]
  12. Using strategy rm

  13. Applied add-cube-cbrt0.5

    \[\leadsto \frac{1}{\left(\left(\sqrt[3]{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}} \cdot \sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}}\right)}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}\]

  14. Final simplification0.5

    \[\leadsto \frac{1}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}} \cdot \sqrt[3]{\sqrt[3]{\frac{\sqrt[3]{\log 10}}{\tan^{-1}_* \frac{im}{re}}}}\right)\right)\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right)}\]

Reproduce

herbie shell --seed 2019146 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))