Average Error: 0.8 → 0.2
Time: 19.3s
Precision: 64
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\left(\sqrt[3]{\sqrt{\frac{1}{\sqrt{\log 10}}}} \cdot \sqrt[3]{\sqrt{\frac{1}{\sqrt{\log 10}}}}\right) \cdot \left(\left(\sqrt{\frac{1}{\sqrt{\log 10}}} \cdot \left(\frac{1}{\sqrt{\log 10}} \cdot \tan^{-1}_* \frac{im}{re}\right)\right) \cdot \sqrt[3]{\sqrt{\frac{1}{\sqrt{\log 10}}}}\right)\]
\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}
↓
\left(\sqrt[3]{\sqrt{\frac{1}{\sqrt{\log 10}}}} \cdot \sqrt[3]{\sqrt{\frac{1}{\sqrt{\log 10}}}}\right) \cdot \left(\left(\sqrt{\frac{1}{\sqrt{\log 10}}} \cdot \left(\frac{1}{\sqrt{\log 10}} \cdot \tan^{-1}_* \frac{im}{re}\right)\right) \cdot \sqrt[3]{\sqrt{\frac{1}{\sqrt{\log 10}}}}\right)
double f(double re, double im) {
        double r1413673 = im;
        double r1413674 = re;
        double r1413675 = atan2(r1413673, r1413674);
        double r1413676 = 10.0;
        double r1413677 = log(r1413676);
        double r1413678 = r1413675 / r1413677;
        return r1413678;
}
↓
double f(double re, double im) {
        double r1413679 = 1.0;
        double r1413680 = 10.0;
        double r1413681 = log(r1413680);
        double r1413682 = sqrt(r1413681);
        double r1413683 = r1413679 / r1413682;
        double r1413684 = sqrt(r1413683);
        double r1413685 = cbrt(r1413684);
        double r1413686 = r1413685 * r1413685;
        double r1413687 = im;
        double r1413688 = re;
        double r1413689 = atan2(r1413687, r1413688);
        double r1413690 = r1413683 * r1413689;
        double r1413691 = r1413684 * r1413690;
        double r1413692 = r1413691 * r1413685;
        double r1413693 = r1413686 * r1413692;
        return r1413693;
}

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. Using strategy rm

  9. Applied add-sqr-sqrt0.8

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

  10. Applied associate-*l*0.8

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

  12. Applied add-cube-cbrt0.1

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

  13. Applied associate-*l*0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10.0)))