Average Error: 31.3 → 0
Time: 3.2s
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 r26163 = re;
        double r26164 = r26163 * r26163;
        double r26165 = im;
        double r26166 = r26165 * r26165;
        double r26167 = r26164 + r26166;
        double r26168 = sqrt(r26167);
        double r26169 = log(r26168);
        return r26169;
}
↓
double f(double re, double im) {
        double r26170 = re;
        double r26171 = im;
        double r26172 = hypot(r26170, r26171);
        double r26173 = log(r26172);
        return r26173;
}

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 31.3

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

  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 2019303 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))