Average Error: 31.5 → 0
Time: 3.7s
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 r24892 = re;
        double r24893 = r24892 * r24892;
        double r24894 = im;
        double r24895 = r24894 * r24894;
        double r24896 = r24893 + r24895;
        double r24897 = sqrt(r24896);
        double r24898 = log(r24897);
        return r24898;
}
↓
double f(double re, double im) {
        double r24899 = re;
        double r24900 = im;
        double r24901 = hypot(r24899, r24900);
        double r24902 = log(r24901);
        return r24902;
}

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 31.5

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

  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 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))