Average Error: 30.5 → 0.0
Time: 2.8s
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 r597023 = re;
        double r597024 = r597023 * r597023;
        double r597025 = im;
        double r597026 = r597025 * r597025;
        double r597027 = r597024 + r597026;
        double r597028 = sqrt(r597027);
        double r597029 = log(r597028);
        return r597029;
}
↓
double f(double re, double im) {
        double r597030 = re;
        double r597031 = im;
        double r597032 = hypot(r597030, r597031);
        double r597033 = log(r597032);
        return r597033;
}

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 30.5

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

  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 2019132 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))