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 r37114 = re;
        double r37115 = r37114 * r37114;
        double r37116 = im;
        double r37117 = r37116 * r37116;
        double r37118 = r37115 + r37117;
        double r37119 = sqrt(r37118);
        double r37120 = log(r37119);
        return r37120;
}
↓
double f(double re, double im) {
        double r37121 = re;
        double r37122 = im;
        double r37123 = hypot(r37121, r37122);
        double r37124 = log(r37123);
        return r37124;
}

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)))))