Average Error: 31.4 → 0.3
Time: 22.9s
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 r1959236 = im;
        double r1959237 = re;
        double r1959238 = atan2(r1959236, r1959237);
        double r1959239 = base;
        double r1959240 = log(r1959239);
        double r1959241 = r1959238 * r1959240;
        double r1959242 = r1959237 * r1959237;
        double r1959243 = r1959236 * r1959236;
        double r1959244 = r1959242 + r1959243;
        double r1959245 = sqrt(r1959244);
        double r1959246 = log(r1959245);
        double r1959247 = 0.0;
        double r1959248 = r1959246 * r1959247;
        double r1959249 = r1959241 - r1959248;
        double r1959250 = r1959240 * r1959240;
        double r1959251 = r1959247 * r1959247;
        double r1959252 = r1959250 + r1959251;
        double r1959253 = r1959249 / r1959252;
        return r1959253;
}
↓
double f(double re, double im, double base) {
        double r1959254 = im;
        double r1959255 = re;
        double r1959256 = atan2(r1959254, r1959255);
        double r1959257 = base;
        double r1959258 = log(r1959257);
        double r1959259 = r1959256 / r1959258;
        return r1959259;
}

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 31.4

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

  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 2019164 
(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))))