Average Error: 30.5 → 0.0
Time: 1.4s
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 r838902 = re;
        double r838903 = r838902 * r838902;
        double r838904 = im;
        double r838905 = r838904 * r838904;
        double r838906 = r838903 + r838905;
        double r838907 = sqrt(r838906);
        double r838908 = log(r838907);
        return r838908;
}
↓
double f(double re, double im) {
        double r838909 = re;
        double r838910 = im;
        double r838911 = hypot(r838909, r838910);
        double r838912 = log(r838911);
        return r838912;
}

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 30.5

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

  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 2019152 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))