Average Error: 30.1 → 0.0
Time: 23.0s
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 r2450765 = re;
        double r2450766 = r2450765 * r2450765;
        double r2450767 = im;
        double r2450768 = r2450767 * r2450767;
        double r2450769 = r2450766 + r2450768;
        double r2450770 = sqrt(r2450769);
        return r2450770;
}
↓
double f(double re, double im) {
        double r2450771 = re;
        double r2450772 = im;
        double r2450773 = hypot(r2450771, r2450772);
        return r2450773;
}

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 30.1

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

  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 2019143 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))