Average Error: 31.8 → 0
Time: 3.4s
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 r80516 = re;
        double r80517 = r80516 * r80516;
        double r80518 = im;
        double r80519 = r80518 * r80518;
        double r80520 = r80517 + r80519;
        double r80521 = sqrt(r80520);
        double r80522 = log(r80521);
        return r80522;
}
↓
double f(double re, double im) {
        double r80523 = re;
        double r80524 = im;
        double r80525 = hypot(r80523, r80524);
        double r80526 = log(r80525);
        return r80526;
}

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 31.8

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))