Average Error: 32.2 → 0.0
Time: 402.0ms
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 r92675 = re;
        double r92676 = r92675 * r92675;
        double r92677 = im;
        double r92678 = r92677 * r92677;
        double r92679 = r92676 + r92678;
        double r92680 = sqrt(r92679);
        return r92680;
}
↓
double f(double re, double im) {
        double r92681 = re;
        double r92682 = im;
        double r92683 = hypot(r92681, r92682);
        return r92683;
}

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 32.2

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

  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 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))