Average Error: 30.5 → 0.0
Time: 3.0s
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 r1359995 = re;
        double r1359996 = r1359995 * r1359995;
        double r1359997 = im;
        double r1359998 = r1359997 * r1359997;
        double r1359999 = r1359996 + r1359998;
        double r1360000 = sqrt(r1359999);
        double r1360001 = log(r1360000);
        return r1360001;
}
↓
double f(double re, double im) {
        double r1360002 = re;
        double r1360003 = im;
        double r1360004 = hypot(r1360002, r1360003);
        double r1360005 = log(r1360004);
        return r1360005;
}

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 2019165 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))