Average Error: 31.5 → 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 r2095132 = re;
        double r2095133 = r2095132 * r2095132;
        double r2095134 = im;
        double r2095135 = r2095134 * r2095134;
        double r2095136 = r2095133 + r2095135;
        double r2095137 = sqrt(r2095136);
        double r2095138 = log(r2095137);
        return r2095138;
}
↓
double f(double re, double im) {
        double r2095139 = re;
        double r2095140 = im;
        double r2095141 = hypot(r2095139, r2095140);
        double r2095142 = log(r2095141);
        return r2095142;
}

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 31.5

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

  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 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))