Average Error: 30.7 → 0.3
Time: 23.2s
Precision: 64
\[\frac{\tan^{-1}_* \frac{im}{re} \cdot \log base - \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
↓
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log base}\]
\frac{\tan^{-1}_* \frac{im}{re} \cdot \log base - \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot 0}{\log base \cdot \log base + 0 \cdot 0}
↓
\frac{\tan^{-1}_* \frac{im}{re}}{\log base}
double f(double re, double im, double base) {
        double r2059837 = im;
        double r2059838 = re;
        double r2059839 = atan2(r2059837, r2059838);
        double r2059840 = base;
        double r2059841 = log(r2059840);
        double r2059842 = r2059839 * r2059841;
        double r2059843 = r2059838 * r2059838;
        double r2059844 = r2059837 * r2059837;
        double r2059845 = r2059843 + r2059844;
        double r2059846 = sqrt(r2059845);
        double r2059847 = log(r2059846);
        double r2059848 = 0.0;
        double r2059849 = r2059847 * r2059848;
        double r2059850 = r2059842 - r2059849;
        double r2059851 = r2059841 * r2059841;
        double r2059852 = r2059848 * r2059848;
        double r2059853 = r2059851 + r2059852;
        double r2059854 = r2059850 / r2059853;
        return r2059854;
}
↓
double f(double re, double im, double base) {
        double r2059855 = im;
        double r2059856 = re;
        double r2059857 = atan2(r2059855, r2059856);
        double r2059858 = base;
        double r2059859 = log(r2059858);
        double r2059860 = r2059857 / r2059859;
        return r2059860;
}

Error

Bits error versus re

Bits error versus im

Bits error versus base

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.7

    \[\frac{\tan^{-1}_* \frac{im}{re} \cdot \log base - \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

  2. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019158 
(FPCore (re im base)
  :name "math.log/2 on complex, imaginary part"
  (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))))