Average Error: 31.2 → 0.0
Time: 2.4s
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 r27233 = re;
        double r27234 = r27233 * r27233;
        double r27235 = im;
        double r27236 = r27235 * r27235;
        double r27237 = r27234 + r27236;
        double r27238 = sqrt(r27237);
        return r27238;
}
↓
double f(double re, double im) {
        double r27239 = re;
        double r27240 = im;
        double r27241 = hypot(r27239, r27240);
        return r27241;
}

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))))