Average Error: 31.5 → 0
Time: 793.0ms
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 r31737 = re;
        double r31738 = r31737 * r31737;
        double r31739 = im;
        double r31740 = r31739 * r31739;
        double r31741 = r31738 + r31740;
        double r31742 = sqrt(r31741);
        double r31743 = log(r31742);
        return r31743;
}
↓
double f(double re, double im) {
        double r31744 = re;
        double r31745 = im;
        double r31746 = hypot(r31744, r31745);
        double r31747 = log(r31746);
        return r31747;
}

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 31.5

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

  3. Applied hypot-def0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))