Average Error: 32.0 → 0.0
Time: 3.7s
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 r26638 = re;
        double r26639 = r26638 * r26638;
        double r26640 = im;
        double r26641 = r26640 * r26640;
        double r26642 = r26639 + r26641;
        double r26643 = sqrt(r26642);
        double r26644 = log(r26643);
        return r26644;
}
↓
double f(double re, double im) {
        double r26645 = re;
        double r26646 = im;
        double r26647 = hypot(r26645, r26646);
        double r26648 = log(r26647);
        return r26648;
}

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 2019304 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))