Average Error: 32.5 → 0.0
Time: 1.0s
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 r113427 = re;
        double r113428 = r113427 * r113427;
        double r113429 = im;
        double r113430 = r113429 * r113429;
        double r113431 = r113428 + r113430;
        double r113432 = sqrt(r113431);
        return r113432;
}
↓
double f(double re, double im) {
        double r113433 = re;
        double r113434 = im;
        double r113435 = hypot(r113433, r113434);
        return r113435;
}

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 32.5

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

  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 2020002 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))