Average Error: 31.1 → 0.0
Time: 2.1s
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 r90202 = re;
        double r90203 = r90202 * r90202;
        double r90204 = im;
        double r90205 = r90204 * r90204;
        double r90206 = r90203 + r90205;
        double r90207 = sqrt(r90206);
        return r90207;
}
↓
double f(double re, double im) {
        double r90208 = re;
        double r90209 = im;
        double r90210 = hypot(r90208, r90209);
        return r90210;
}

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 31.1

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

  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 2019352 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))