Average Error: 31.8 → 0.0
Time: 702.0ms
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 r86655 = re;
        double r86656 = r86655 * r86655;
        double r86657 = im;
        double r86658 = r86657 * r86657;
        double r86659 = r86656 + r86658;
        double r86660 = sqrt(r86659);
        double r86661 = log(r86660);
        return r86661;
}
↓
double f(double re, double im) {
        double r86662 = re;
        double r86663 = im;
        double r86664 = hypot(r86662, r86663);
        double r86665 = log(r86664);
        return r86665;
}

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 31.8

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied hypot-def0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))