Average Error: 31.9 → 0.0
Time: 783.0ms
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 r44419 = re;
        double r44420 = r44419 * r44419;
        double r44421 = im;
        double r44422 = r44421 * r44421;
        double r44423 = r44420 + r44422;
        double r44424 = sqrt(r44423);
        return r44424;
}
↓
double f(double re, double im) {
        double r44425 = re;
        double r44426 = im;
        double r44427 = hypot(r44425, r44426);
        return r44427;
}

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 31.9

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

  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 2019212 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))