Average Error: 29.6 → 0.0
Time: 1.1s
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 r1098236 = re;
        double r1098237 = r1098236 * r1098236;
        double r1098238 = im;
        double r1098239 = r1098238 * r1098238;
        double r1098240 = r1098237 + r1098239;
        double r1098241 = sqrt(r1098240);
        return r1098241;
}
↓
double f(double re, double im) {
        double r1098242 = re;
        double r1098243 = im;
        double r1098244 = hypot(r1098242, r1098243);
        return r1098244;
}

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 29.6

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

  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 2019124 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))