Average Error: 31.3 → 0.0
Time: 9.5s
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 r4125134 = re;
        double r4125135 = r4125134 * r4125134;
        double r4125136 = im;
        double r4125137 = r4125136 * r4125136;
        double r4125138 = r4125135 + r4125137;
        double r4125139 = sqrt(r4125138);
        return r4125139;
}
↓
double f(double re, double im) {
        double r4125140 = re;
        double r4125141 = im;
        double r4125142 = hypot(r4125140, r4125141);
        return r4125142;
}

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 31.3

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

  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 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))