Average Error: 29.3 → 0.0
Time: 1.3s
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 r742540 = re;
        double r742541 = r742540 * r742540;
        double r742542 = im;
        double r742543 = r742542 * r742542;
        double r742544 = r742541 + r742543;
        double r742545 = sqrt(r742544);
        return r742545;
}
↓
double f(double re, double im) {
        double r742546 = re;
        double r742547 = im;
        double r742548 = hypot(r742546, r742547);
        return r742548;
}

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 29.3

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

  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 2019152 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))