Average Error: 31.9 → 0.0
Time: 551.0ms
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 r46592 = re;
        double r46593 = r46592 * r46592;
        double r46594 = im;
        double r46595 = r46594 * r46594;
        double r46596 = r46593 + r46595;
        double r46597 = sqrt(r46596);
        return r46597;
}
↓
double f(double re, double im) {
        double r46598 = re;
        double r46599 = im;
        double r46600 = hypot(r46598, r46599);
        return r46600;
}

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 31.9

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

  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 2020025 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))