Average Error: 30.6 → 0.0
Time: 7.8s
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 r1340416 = re;
        double r1340417 = r1340416 * r1340416;
        double r1340418 = im;
        double r1340419 = r1340418 * r1340418;
        double r1340420 = r1340417 + r1340419;
        double r1340421 = sqrt(r1340420);
        double r1340422 = log(r1340421);
        return r1340422;
}
↓
double f(double re, double im) {
        double r1340423 = re;
        double r1340424 = im;
        double r1340425 = hypot(r1340423, r1340424);
        double r1340426 = log(r1340425);
        return r1340426;
}

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 2019149 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))