Average Error: 31.8 → 0.0
Time: 6.9s
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 r2774811 = re;
        double r2774812 = r2774811 * r2774811;
        double r2774813 = im;
        double r2774814 = r2774813 * r2774813;
        double r2774815 = r2774812 + r2774814;
        double r2774816 = sqrt(r2774815);
        return r2774816;
}
↓
double f(double re, double im) {
        double r2774817 = re;
        double r2774818 = im;
        double r2774819 = hypot(r2774817, r2774818);
        return r2774819;
}

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 31.8

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

  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 2019169 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))