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 r867664 = re;
        double r867665 = r867664 * r867664;
        double r867666 = im;
        double r867667 = r867666 * r867666;
        double r867668 = r867665 + r867667;
        double r867669 = sqrt(r867668);
        double r867670 = log(r867669);
        return r867670;
}
↓
double f(double re, double im) {
        double r867671 = re;
        double r867672 = im;
        double r867673 = hypot(r867671, r867672);
        double r867674 = log(r867673);
        return r867674;
}

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)))))