Average Error: 29.3 → 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 r733666 = re;
        double r733667 = r733666 * r733666;
        double r733668 = im;
        double r733669 = r733668 * r733668;
        double r733670 = r733667 + r733669;
        double r733671 = sqrt(r733670);
        return r733671;
}
↓
double f(double re, double im) {
        double r733672 = re;
        double r733673 = im;
        double r733674 = hypot(r733672, r733673);
        return r733674;
}

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))))