Average Error: 31.6 → 0.0
Time: 571.0ms
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 r24602 = re;
        double r24603 = r24602 * r24602;
        double r24604 = im;
        double r24605 = r24604 * r24604;
        double r24606 = r24603 + r24605;
        double r24607 = sqrt(r24606);
        double r24608 = log(r24607);
        return r24608;
}
↓
double f(double re, double im) {
        double r24609 = re;
        double r24610 = im;
        double r24611 = hypot(r24609, r24610);
        double r24612 = log(r24611);
        return r24612;
}

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 31.6

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

  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 2019351 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))