Average Error: 30.8 → 0
Time: 1.1s
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 r1232908 = re;
        double r1232909 = r1232908 * r1232908;
        double r1232910 = im;
        double r1232911 = r1232910 * r1232910;
        double r1232912 = r1232909 + r1232911;
        double r1232913 = sqrt(r1232912);
        double r1232914 = log(r1232913);
        return r1232914;
}
↓
double f(double re, double im) {
        double r1232915 = re;
        double r1232916 = im;
        double r1232917 = hypot(r1232915, r1232916);
        double r1232918 = log(r1232917);
        return r1232918;
}

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 30.8

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))