Average Error: 30.7 → 0.0
Time: 939.0ms
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r2742904 = re;
        double r2742905 = r2742904 * r2742904;
        double r2742906 = im;
        double r2742907 = r2742906 * r2742906;
        double r2742908 = r2742905 + r2742907;
        double r2742909 = sqrt(r2742908);
        double r2742910 = log(r2742909);
        return r2742910;
}
↓
double f(double re, double im) {
        double r2742911 = re;
        double r2742912 = im;
        double r2742913 = hypot(r2742911, r2742912);
        double r2742914 = log(r2742913);
        return r2742914;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.7

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))