Average Error: 31.3 → 0.0
Time: 9.2s
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 r2451521 = re;
        double r2451522 = r2451521 * r2451521;
        double r2451523 = im;
        double r2451524 = r2451523 * r2451523;
        double r2451525 = r2451522 + r2451524;
        double r2451526 = sqrt(r2451525);
        return r2451526;
}
↓
double f(double re, double im) {
        double r2451527 = re;
        double r2451528 = im;
        double r2451529 = hypot(r2451527, r2451528);
        return r2451529;
}

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 31.3

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

  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 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))