Average Error: 31.3 → 0
Time: 7.4s
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 r1523689 = re;
        double r1523690 = r1523689 * r1523689;
        double r1523691 = im;
        double r1523692 = r1523691 * r1523691;
        double r1523693 = r1523690 + r1523692;
        double r1523694 = sqrt(r1523693);
        double r1523695 = log(r1523694);
        return r1523695;
}
↓
double f(double re, double im) {
        double r1523696 = re;
        double r1523697 = im;
        double r1523698 = hypot(r1523696, r1523697);
        double r1523699 = log(r1523698);
        return r1523699;
}

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 31.3

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

  2. Simplified0

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)}\]

  3. Final simplification0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))