Average Error: 31.7 → 0.0
Time: 395.0ms
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 r43051 = re;
        double r43052 = r43051 * r43051;
        double r43053 = im;
        double r43054 = r43053 * r43053;
        double r43055 = r43052 + r43054;
        double r43056 = sqrt(r43055);
        return r43056;
}
↓
double f(double re, double im) {
        double r43057 = re;
        double r43058 = im;
        double r43059 = hypot(r43057, r43058);
        return r43059;
}

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 31.7

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

  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 2020060 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))