Average Error: 29.6 → 0.0
Time: 727.0ms
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 r1233308 = re;
        double r1233309 = r1233308 * r1233308;
        double r1233310 = im;
        double r1233311 = r1233310 * r1233310;
        double r1233312 = r1233309 + r1233311;
        double r1233313 = sqrt(r1233312);
        return r1233313;
}
↓
double f(double re, double im) {
        double r1233314 = re;
        double r1233315 = im;
        double r1233316 = hypot(r1233314, r1233315);
        return r1233316;
}

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 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))