Average Error: 31.6 → 0.3
Time: 23.7s
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 r2434202 = im;
        double r2434203 = re;
        double r2434204 = atan2(r2434202, r2434203);
        double r2434205 = base;
        double r2434206 = log(r2434205);
        double r2434207 = r2434204 * r2434206;
        double r2434208 = r2434203 * r2434203;
        double r2434209 = r2434202 * r2434202;
        double r2434210 = r2434208 + r2434209;
        double r2434211 = sqrt(r2434210);
        double r2434212 = log(r2434211);
        double r2434213 = 0.0;
        double r2434214 = r2434212 * r2434213;
        double r2434215 = r2434207 - r2434214;
        double r2434216 = r2434206 * r2434206;
        double r2434217 = r2434213 * r2434213;
        double r2434218 = r2434216 + r2434217;
        double r2434219 = r2434215 / r2434218;
        return r2434219;
}
↓
double f(double re, double im, double base) {
        double r2434220 = im;
        double r2434221 = re;
        double r2434222 = atan2(r2434220, r2434221);
        double r2434223 = base;
        double r2434224 = log(r2434223);
        double r2434225 = r2434222 / r2434224;
        return r2434225;
}

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))))