Average Error: 30.6 → 0.0
Time: 2.5s
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 r821372 = re;
        double r821373 = r821372 * r821372;
        double r821374 = im;
        double r821375 = r821374 * r821374;
        double r821376 = r821373 + r821375;
        double r821377 = sqrt(r821376);
        double r821378 = log(r821377);
        return r821378;
}
↓
double f(double re, double im) {
        double r821379 = re;
        double r821380 = im;
        double r821381 = hypot(r821379, r821380);
        double r821382 = log(r821381);
        return r821382;
}

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 30.6

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))