Average Error: 30.7 → 0.0
Time: 1.4s
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 r1201312 = re;
        double r1201313 = r1201312 * r1201312;
        double r1201314 = im;
        double r1201315 = r1201314 * r1201314;
        double r1201316 = r1201313 + r1201315;
        double r1201317 = sqrt(r1201316);
        double r1201318 = log(r1201317);
        return r1201318;
}
↓
double f(double re, double im) {
        double r1201319 = re;
        double r1201320 = im;
        double r1201321 = hypot(r1201319, r1201320);
        double r1201322 = log(r1201321);
        return r1201322;
}

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 30.7

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

  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 2019162 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))