Average Error: 31.8 → 0.0
Time: 10.1s
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 r40600 = re;
        double r40601 = r40600 * r40600;
        double r40602 = im;
        double r40603 = r40602 * r40602;
        double r40604 = r40601 + r40603;
        double r40605 = sqrt(r40604);
        return r40605;
}
↓
double f(double re, double im) {
        double r40606 = re;
        double r40607 = im;
        double r40608 = hypot(r40606, r40607);
        return r40608;
}

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 31.8

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

  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 2019347 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))