Average Error: 31.6 → 0.3
Time: 23.5s
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 r2879508 = im;
        double r2879509 = re;
        double r2879510 = atan2(r2879508, r2879509);
        double r2879511 = base;
        double r2879512 = log(r2879511);
        double r2879513 = r2879510 * r2879512;
        double r2879514 = r2879509 * r2879509;
        double r2879515 = r2879508 * r2879508;
        double r2879516 = r2879514 + r2879515;
        double r2879517 = sqrt(r2879516);
        double r2879518 = log(r2879517);
        double r2879519 = 0.0;
        double r2879520 = r2879518 * r2879519;
        double r2879521 = r2879513 - r2879520;
        double r2879522 = r2879512 * r2879512;
        double r2879523 = r2879519 * r2879519;
        double r2879524 = r2879522 + r2879523;
        double r2879525 = r2879521 / r2879524;
        return r2879525;
}
↓
double f(double re, double im, double base) {
        double r2879526 = im;
        double r2879527 = re;
        double r2879528 = atan2(r2879526, r2879527);
        double r2879529 = base;
        double r2879530 = log(r2879529);
        double r2879531 = r2879528 / r2879530;
        return r2879531;
}

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 31.6

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

  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 2019163 
(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))))