Average Error: 32.2 → 0.0
Time: 410.0ms
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 r99702 = re;
        double r99703 = r99702 * r99702;
        double r99704 = im;
        double r99705 = r99704 * r99704;
        double r99706 = r99703 + r99705;
        double r99707 = sqrt(r99706);
        return r99707;
}
↓
double f(double re, double im) {
        double r99708 = re;
        double r99709 = im;
        double r99710 = hypot(r99708, r99709);
        return r99710;
}

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 32.2

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

  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 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))