Average Error: 32.0 → 0.0
Time: 4.0s
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 r1343390 = re;
        double r1343391 = r1343390 * r1343390;
        double r1343392 = im;
        double r1343393 = r1343392 * r1343392;
        double r1343394 = r1343391 + r1343393;
        double r1343395 = sqrt(r1343394);
        double r1343396 = log(r1343395);
        return r1343396;
}
↓
double f(double re, double im) {
        double r1343397 = re;
        double r1343398 = im;
        double r1343399 = hypot(r1343397, r1343398);
        double r1343400 = log(r1343399);
        return r1343400;
}

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 32.0

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

  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 2019169 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))