Average Error: 30.8 → 0.0
Time: 8.3s
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 r649912 = re;
        double r649913 = r649912 * r649912;
        double r649914 = im;
        double r649915 = r649914 * r649914;
        double r649916 = r649913 + r649915;
        double r649917 = sqrt(r649916);
        double r649918 = log(r649917);
        return r649918;
}
↓
double f(double re, double im) {
        double r649919 = re;
        double r649920 = im;
        double r649921 = hypot(r649919, r649920);
        double r649922 = log(r649921);
        return r649922;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))