Average Error: 31.1 → 0.0
Time: 1.2s
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 r625761 = re;
        double r625762 = r625761 * r625761;
        double r625763 = im;
        double r625764 = r625763 * r625763;
        double r625765 = r625762 + r625764;
        double r625766 = sqrt(r625765);
        double r625767 = log(r625766);
        return r625767;
}
↓
double f(double re, double im) {
        double r625768 = re;
        double r625769 = im;
        double r625770 = hypot(r625768, r625769);
        double r625771 = log(r625770);
        return r625771;
}

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 31.1

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

  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 2019153 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))