Average Error: 30.9 → 0.0
Time: 4.6s
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 r54588 = re;
        double r54589 = r54588 * r54588;
        double r54590 = im;
        double r54591 = r54590 * r54590;
        double r54592 = r54589 + r54591;
        double r54593 = sqrt(r54592);
        return r54593;
}
↓
double f(double re, double im) {
        double r54594 = re;
        double r54595 = im;
        double r54596 = hypot(r54594, r54595);
        return r54596;
}

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 30.9

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

  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 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))