Average Error: 32.4 → 0.0
Time: 531.0ms
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 r38873 = re;
        double r38874 = r38873 * r38873;
        double r38875 = im;
        double r38876 = r38875 * r38875;
        double r38877 = r38874 + r38876;
        double r38878 = sqrt(r38877);
        double r38879 = log(r38878);
        return r38879;
}
↓
double f(double re, double im) {
        double r38880 = re;
        double r38881 = im;
        double r38882 = hypot(r38880, r38881);
        double r38883 = log(r38882);
        return r38883;
}

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 32.4

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

  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 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))