Average Error: 31.9 → 0.0
Time: 702.0ms
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 r41557 = re;
        double r41558 = r41557 * r41557;
        double r41559 = im;
        double r41560 = r41559 * r41559;
        double r41561 = r41558 + r41560;
        double r41562 = sqrt(r41561);
        double r41563 = log(r41562);
        return r41563;
}
↓
double f(double re, double im) {
        double r41564 = re;
        double r41565 = im;
        double r41566 = hypot(r41564, r41565);
        double r41567 = log(r41566);
        return r41567;
}

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 31.9

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied hypot-def0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))