Average Error: 0.9 → 1.0
Time: 11.1s
Precision: 64
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\frac{1}{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\]
\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}
↓
\frac{1}{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}
double f(double re, double im) {
        double r34655 = im;
        double r34656 = re;
        double r34657 = atan2(r34655, r34656);
        double r34658 = 10.0;
        double r34659 = log(r34658);
        double r34660 = r34657 / r34659;
        return r34660;
}
↓
double f(double re, double im) {
        double r34661 = 1.0;
        double r34662 = 10.0;
        double r34663 = log(r34662);
        double r34664 = im;
        double r34665 = re;
        double r34666 = atan2(r34664, r34665);
        double r34667 = r34663 / r34666;
        double r34668 = r34661 / r34667;
        return r34668;
}

Error

Bits error versus re

Bits error versus im

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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. Using strategy rm

  9. Applied add-sqr-sqrt0.8

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

  10. Applied associate-*r*0.8

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

  12. Applied add-sqr-sqrt0.8

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

  13. Applied sqrt-prod0.1

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

  14. Applied associate-*r*0.1

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

  15. Final simplification1.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  :precision binary64
  (/ (atan2 im re) (log 10)))