Average Error: 29.9 → 0.0
Time: 1.0s
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 r529352 = re;
        double r529353 = r529352 * r529352;
        double r529354 = im;
        double r529355 = r529354 * r529354;
        double r529356 = r529353 + r529355;
        double r529357 = sqrt(r529356);
        return r529357;
}
↓
double f(double re, double im) {
        double r529358 = re;
        double r529359 = im;
        double r529360 = hypot(r529358, r529359);
        return r529360;
}

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 29.9

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

  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 2019153 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))