Average Error: 29.5 → 0.0
Time: 10.9s
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 r1734653 = re;
        double r1734654 = r1734653 * r1734653;
        double r1734655 = im;
        double r1734656 = r1734655 * r1734655;
        double r1734657 = r1734654 + r1734656;
        double r1734658 = sqrt(r1734657);
        return r1734658;
}
↓
double f(double re, double im) {
        double r1734659 = re;
        double r1734660 = im;
        double r1734661 = hypot(r1734659, r1734660);
        return r1734661;
}

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 29.5

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

  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 2019149 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))