Average Error: 31.7 → 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 r30881 = re;
        double r30882 = r30881 * r30881;
        double r30883 = im;
        double r30884 = r30883 * r30883;
        double r30885 = r30882 + r30884;
        double r30886 = sqrt(r30885);
        double r30887 = log(r30886);
        return r30887;
}
↓
double f(double re, double im) {
        double r30888 = re;
        double r30889 = im;
        double r30890 = hypot(r30888, r30889);
        double r30891 = log(r30890);
        return r30891;
}

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 31.7

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied hypot-def0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))