Average Error: 31.6 → 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 r22654 = re;
        double r22655 = r22654 * r22654;
        double r22656 = im;
        double r22657 = r22656 * r22656;
        double r22658 = r22655 + r22657;
        double r22659 = sqrt(r22658);
        double r22660 = log(r22659);
        return r22660;
}
↓
double f(double re, double im) {
        double r22661 = re;
        double r22662 = im;
        double r22663 = hypot(r22661, r22662);
        double r22664 = log(r22663);
        return r22664;
}

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 31.6

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

  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 2019196 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))