Average Error: 29.6 → 0.0
Time: 1.1s
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 r1451680 = re;
        double r1451681 = r1451680 * r1451680;
        double r1451682 = im;
        double r1451683 = r1451682 * r1451682;
        double r1451684 = r1451681 + r1451683;
        double r1451685 = sqrt(r1451684);
        return r1451685;
}
↓
double f(double re, double im) {
        double r1451686 = re;
        double r1451687 = im;
        double r1451688 = hypot(r1451686, r1451687);
        return r1451688;
}

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 29.6

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

  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 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))