Average Error: 29.1 → 0.0
Time: 9.7s
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 r1364750 = re;
        double r1364751 = r1364750 * r1364750;
        double r1364752 = im;
        double r1364753 = r1364752 * r1364752;
        double r1364754 = r1364751 + r1364753;
        double r1364755 = sqrt(r1364754);
        return r1364755;
}
↓
double f(double re, double im) {
        double r1364756 = re;
        double r1364757 = im;
        double r1364758 = hypot(r1364756, r1364757);
        return r1364758;
}

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 29.1

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

  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 2019138 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))