Average Error: 31.2 → 0.0
Time: 2.7s
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 r41584 = re;
        double r41585 = r41584 * r41584;
        double r41586 = im;
        double r41587 = r41586 * r41586;
        double r41588 = r41585 + r41587;
        double r41589 = sqrt(r41588);
        return r41589;
}
↓
double f(double re, double im) {
        double r41590 = re;
        double r41591 = im;
        double r41592 = hypot(r41590, r41591);
        return r41592;
}

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 31.2

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

  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 2019198 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))