Average Error: 29.9 → 0.0
Time: 10.3s
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 r2044268 = re;
        double r2044269 = r2044268 * r2044268;
        double r2044270 = im;
        double r2044271 = r2044270 * r2044270;
        double r2044272 = r2044269 + r2044271;
        double r2044273 = sqrt(r2044272);
        return r2044273;
}
↓
double f(double re, double im) {
        double r2044274 = re;
        double r2044275 = im;
        double r2044276 = hypot(r2044274, r2044275);
        return r2044276;
}

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 29.9

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

  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 2019135 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))