Average Error: 31.8 → 0
Time: 14.3s
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 r1616220 = re;
        double r1616221 = r1616220 * r1616220;
        double r1616222 = im;
        double r1616223 = r1616222 * r1616222;
        double r1616224 = r1616221 + r1616223;
        double r1616225 = sqrt(r1616224);
        double r1616226 = log(r1616225);
        return r1616226;
}
↓
double f(double re, double im) {
        double r1616227 = re;
        double r1616228 = im;
        double r1616229 = hypot(r1616227, r1616228);
        double r1616230 = log(r1616229);
        return r1616230;
}

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 2019168 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))