Average Error: 31.4 → 0.0
Time: 3.0s
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 r24624 = re;
        double r24625 = r24624 * r24624;
        double r24626 = im;
        double r24627 = r24626 * r24626;
        double r24628 = r24625 + r24627;
        double r24629 = sqrt(r24628);
        double r24630 = log(r24629);
        return r24630;
}
↓
double f(double re, double im) {
        double r24631 = re;
        double r24632 = im;
        double r24633 = hypot(r24631, r24632);
        double r24634 = log(r24633);
        return r24634;
}

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 31.4

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

  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 2019195 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))