Average Error: 29.4 → 0.0
Time: 825.0ms
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 r1462490 = re;
        double r1462491 = r1462490 * r1462490;
        double r1462492 = im;
        double r1462493 = r1462492 * r1462492;
        double r1462494 = r1462491 + r1462493;
        double r1462495 = sqrt(r1462494);
        return r1462495;
}
↓
double f(double re, double im) {
        double r1462496 = re;
        double r1462497 = im;
        double r1462498 = hypot(r1462496, r1462497);
        return r1462498;
}

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 29.4

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

  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 2019164 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))