Average Error: 32.3 → 0.0
Time: 593.0ms
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 r46908 = re;
        double r46909 = r46908 * r46908;
        double r46910 = im;
        double r46911 = r46910 * r46910;
        double r46912 = r46909 + r46911;
        double r46913 = sqrt(r46912);
        return r46913;
}
↓
double f(double re, double im) {
        double r46914 = re;
        double r46915 = im;
        double r46916 = hypot(r46914, r46915);
        return r46916;
}

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 32.3

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

  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 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))