Average Error: 32.0 → 0
Time: 816.0ms
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 r85466 = re;
        double r85467 = r85466 * r85466;
        double r85468 = im;
        double r85469 = r85468 * r85468;
        double r85470 = r85467 + r85469;
        double r85471 = sqrt(r85470);
        double r85472 = log(r85471);
        return r85472;
}
↓
double f(double re, double im) {
        double r85473 = re;
        double r85474 = im;
        double r85475 = hypot(r85473, r85474);
        double r85476 = log(r85475);
        return r85476;
}

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. Using strategy rm

  3. Applied hypot-def0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))