Average Error: 31.2 → 0.0
Time: 6.6s
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 r26694 = re;
        double r26695 = r26694 * r26694;
        double r26696 = im;
        double r26697 = r26696 * r26696;
        double r26698 = r26695 + r26697;
        double r26699 = sqrt(r26698);
        return r26699;
}
↓
double f(double re, double im) {
        double r26700 = re;
        double r26701 = im;
        double r26702 = hypot(r26700, r26701);
        return r26702;
}

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))))