Average Error: 31.6 → 0.0
Time: 15.8s
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 r1422876 = re;
        double r1422877 = r1422876 * r1422876;
        double r1422878 = im;
        double r1422879 = r1422878 * r1422878;
        double r1422880 = r1422877 + r1422879;
        double r1422881 = sqrt(r1422880);
        return r1422881;
}
↓
double f(double re, double im) {
        double r1422882 = re;
        double r1422883 = im;
        double r1422884 = hypot(r1422882, r1422883);
        return r1422884;
}

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 31.6

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

  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 2019200 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))