Average Error: 31.3 → 0.0
Time: 8.0s
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 r42755 = re;
        double r42756 = r42755 * r42755;
        double r42757 = im;
        double r42758 = r42757 * r42757;
        double r42759 = r42756 + r42758;
        double r42760 = sqrt(r42759);
        return r42760;
}
↓
double f(double re, double im) {
        double r42761 = re;
        double r42762 = im;
        double r42763 = hypot(r42761, r42762);
        return r42763;
}

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 31.3

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

  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 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))