Average Error: 31.2 → 0.0
Time: 5.9s
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 r44312 = re;
        double r44313 = r44312 * r44312;
        double r44314 = im;
        double r44315 = r44314 * r44314;
        double r44316 = r44313 + r44315;
        double r44317 = sqrt(r44316);
        return r44317;
}
↓
double f(double re, double im) {
        double r44318 = re;
        double r44319 = im;
        double r44320 = hypot(r44318, r44319);
        return r44320;
}

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 31.2

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

  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 2019303 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))