Average Error: 30.8 → 0
Time: 2.1s
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 r1005641 = re;
        double r1005642 = r1005641 * r1005641;
        double r1005643 = im;
        double r1005644 = r1005643 * r1005643;
        double r1005645 = r1005642 + r1005644;
        double r1005646 = sqrt(r1005645);
        double r1005647 = log(r1005646);
        return r1005647;
}
↓
double f(double re, double im) {
        double r1005648 = re;
        double r1005649 = im;
        double r1005650 = hypot(r1005648, r1005649);
        double r1005651 = log(r1005650);
        return r1005651;
}

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 30.8

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

  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 2019156 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))