Average Error: 31.5 → 0.0
Time: 4.1s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\mathsf{hypot}\left(re, im\right)\]
\sqrt{re \cdot re + im \cdot im}
↓
\mathsf{hypot}\left(re, im\right)
double f(double re, double im) {
        double r43735 = re;
        double r43736 = r43735 * r43735;
        double r43737 = im;
        double r43738 = r43737 * r43737;
        double r43739 = r43736 + r43738;
        double r43740 = sqrt(r43739);
        return r43740;
}
↓
double f(double re, double im) {
        double r43741 = re;
        double r43742 = im;
        double r43743 = hypot(r43741, r43742);
        return r43743;
}

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

    \[\sqrt{re \cdot re + im \cdot im}\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))