Average Error: 29.5 → 0.0
Time: 862.0ms
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 r705392 = re;
        double r705393 = r705392 * r705392;
        double r705394 = im;
        double r705395 = r705394 * r705394;
        double r705396 = r705393 + r705395;
        double r705397 = sqrt(r705396);
        return r705397;
}
↓
double f(double re, double im) {
        double r705398 = re;
        double r705399 = im;
        double r705400 = hypot(r705398, r705399);
        return r705400;
}

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 29.5

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

  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 2019154 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))