Average Error: 31.5 → 0.0
Time: 397.0ms
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 r55474 = re;
        double r55475 = r55474 * r55474;
        double r55476 = im;
        double r55477 = r55476 * r55476;
        double r55478 = r55475 + r55477;
        double r55479 = sqrt(r55478);
        return r55479;
}
↓
double f(double re, double im) {
        double r55480 = re;
        double r55481 = im;
        double r55482 = hypot(r55480, r55481);
        return r55482;
}

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 31.5

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

  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 2020042 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))