Average Error: 31.1 → 0.0
Time: 1.4s
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 r846682 = re;
        double r846683 = r846682 * r846682;
        double r846684 = im;
        double r846685 = r846684 * r846684;
        double r846686 = r846683 + r846685;
        double r846687 = sqrt(r846686);
        double r846688 = log(r846687);
        return r846688;
}
↓
double f(double re, double im) {
        double r846689 = re;
        double r846690 = im;
        double r846691 = hypot(r846689, r846690);
        double r846692 = log(r846691);
        return r846692;
}

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 31.1

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

  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 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))