Average Error: 31.1 → 0.0
Time: 888.0ms
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 r43312 = re;
        double r43313 = r43312 * r43312;
        double r43314 = im;
        double r43315 = r43314 * r43314;
        double r43316 = r43313 + r43315;
        double r43317 = sqrt(r43316);
        return r43317;
}
↓
double f(double re, double im) {
        double r43318 = re;
        double r43319 = im;
        double r43320 = hypot(r43318, r43319);
        return r43320;
}

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 31.1

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

  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 2019209 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))