Average Error: 31.8 → 0
Time: 3.4s
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 r37076 = re;
        double r37077 = r37076 * r37076;
        double r37078 = im;
        double r37079 = r37078 * r37078;
        double r37080 = r37077 + r37079;
        double r37081 = sqrt(r37080);
        double r37082 = log(r37081);
        return r37082;
}
↓
double f(double re, double im) {
        double r37083 = re;
        double r37084 = im;
        double r37085 = hypot(r37083, r37084);
        double r37086 = log(r37085);
        return r37086;
}

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 31.8

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

  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 2019323 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))