Average Error: 31.5 → 0.0
Time: 6.3s
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 r51122 = re;
        double r51123 = r51122 * r51122;
        double r51124 = im;
        double r51125 = r51124 * r51124;
        double r51126 = r51123 + r51125;
        double r51127 = sqrt(r51126);
        return r51127;
}
↓
double f(double re, double im) {
        double r51128 = re;
        double r51129 = im;
        double r51130 = hypot(r51128, r51129);
        return r51130;
}

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 31.5

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

  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 2019306 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))