Average Error: 0.9 → 0.9
Time: 5.0s
Precision: 64
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\frac{1}{\log 10} \cdot \tan^{-1}_* \frac{im}{re}\]
\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}
↓
\frac{1}{\log 10} \cdot \tan^{-1}_* \frac{im}{re}
double f(double re, double im) {
        double r33018 = im;
        double r33019 = re;
        double r33020 = atan2(r33018, r33019);
        double r33021 = 10.0;
        double r33022 = log(r33021);
        double r33023 = r33020 / r33022;
        return r33023;
}
↓
double f(double re, double im) {
        double r33024 = 1.0;
        double r33025 = 10.0;
        double r33026 = log(r33025);
        double r33027 = r33024 / r33026;
        double r33028 = im;
        double r33029 = re;
        double r33030 = atan2(r33028, r33029);
        double r33031 = r33027 * r33030;
        return r33031;
}

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 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. Final simplification0.9

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

Reproduce

herbie shell --seed 2019308 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  :precision binary64
  (/ (atan2 im re) (log 10)))