Average Error: 31.6 → 0.3
Time: 25.5s
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 r2915309 = im;
        double r2915310 = re;
        double r2915311 = atan2(r2915309, r2915310);
        double r2915312 = base;
        double r2915313 = log(r2915312);
        double r2915314 = r2915311 * r2915313;
        double r2915315 = r2915310 * r2915310;
        double r2915316 = r2915309 * r2915309;
        double r2915317 = r2915315 + r2915316;
        double r2915318 = sqrt(r2915317);
        double r2915319 = log(r2915318);
        double r2915320 = 0.0;
        double r2915321 = r2915319 * r2915320;
        double r2915322 = r2915314 - r2915321;
        double r2915323 = r2915313 * r2915313;
        double r2915324 = r2915320 * r2915320;
        double r2915325 = r2915323 + r2915324;
        double r2915326 = r2915322 / r2915325;
        return r2915326;
}
↓
double f(double re, double im, double base) {
        double r2915327 = im;
        double r2915328 = re;
        double r2915329 = atan2(r2915327, r2915328);
        double r2915330 = base;
        double r2915331 = log(r2915330);
        double r2915332 = r2915329 / r2915331;
        return r2915332;
}

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))))