Average Error: 31.1 → 0.0
Time: 866.0ms
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 r43266 = re;
        double r43267 = r43266 * r43266;
        double r43268 = im;
        double r43269 = r43268 * r43268;
        double r43270 = r43267 + r43269;
        double r43271 = sqrt(r43270);
        return r43271;
}
↓
double f(double re, double im) {
        double r43272 = re;
        double r43273 = im;
        double r43274 = hypot(r43272, r43273);
        return r43274;
}

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 2020035 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))