Average Error: 30.8 → 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 r1298543 = re;
        double r1298544 = r1298543 * r1298543;
        double r1298545 = im;
        double r1298546 = r1298545 * r1298545;
        double r1298547 = r1298544 + r1298546;
        double r1298548 = sqrt(r1298547);
        double r1298549 = log(r1298548);
        return r1298549;
}
↓
double f(double re, double im) {
        double r1298550 = re;
        double r1298551 = im;
        double r1298552 = hypot(r1298550, r1298551);
        double r1298553 = log(r1298552);
        return r1298553;
}

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 30.8

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

  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 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))