Average Error: 29.5 → 0.0
Time: 1.1s
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 r790795 = re;
        double r790796 = r790795 * r790795;
        double r790797 = im;
        double r790798 = r790797 * r790797;
        double r790799 = r790796 + r790798;
        double r790800 = sqrt(r790799);
        return r790800;
}
↓
double f(double re, double im) {
        double r790801 = re;
        double r790802 = im;
        double r790803 = hypot(r790801, r790802);
        return r790803;
}

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 29.5

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

  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 2019139 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))