Average Error: 31.4 → 0.0
Time: 1.3s
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 r1682805 = re;
        double r1682806 = r1682805 * r1682805;
        double r1682807 = im;
        double r1682808 = r1682807 * r1682807;
        double r1682809 = r1682806 + r1682808;
        double r1682810 = sqrt(r1682809);
        return r1682810;
}
↓
double f(double re, double im) {
        double r1682811 = re;
        double r1682812 = im;
        double r1682813 = hypot(r1682811, r1682812);
        return r1682813;
}

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 31.4

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

  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 2019192 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))