Average Error: 32.3 → 0.0
Time: 2.3s
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 r98769 = re;
        double r98770 = r98769 * r98769;
        double r98771 = im;
        double r98772 = r98771 * r98771;
        double r98773 = r98770 + r98772;
        double r98774 = sqrt(r98773);
        return r98774;
}
↓
double f(double re, double im) {
        double r98775 = re;
        double r98776 = im;
        double r98777 = hypot(r98775, r98776);
        return r98777;
}

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 32.3

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

  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 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))