Average Error: 31.2 → 0.0
Time: 2.6s
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 r35229 = re;
        double r35230 = r35229 * r35229;
        double r35231 = im;
        double r35232 = r35231 * r35231;
        double r35233 = r35230 + r35232;
        double r35234 = sqrt(r35233);
        return r35234;
}
↓
double f(double re, double im) {
        double r35235 = re;
        double r35236 = im;
        double r35237 = hypot(r35235, r35236);
        return r35237;
}

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 31.2

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

  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 2019195 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))