Average Error: 31.1 → 0.0
Time: 1.3s
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 r867662 = re;
        double r867663 = r867662 * r867662;
        double r867664 = im;
        double r867665 = r867664 * r867664;
        double r867666 = r867663 + r867665;
        double r867667 = sqrt(r867666);
        double r867668 = log(r867667);
        return r867668;
}
↓
double f(double re, double im) {
        double r867669 = re;
        double r867670 = im;
        double r867671 = hypot(r867669, r867670);
        double r867672 = log(r867671);
        return r867672;
}

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)))))