Average Error: 31.6 → 0.0
Time: 412.0ms
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 r95472 = re;
        double r95473 = r95472 * r95472;
        double r95474 = im;
        double r95475 = r95474 * r95474;
        double r95476 = r95473 + r95475;
        double r95477 = sqrt(r95476);
        return r95477;
}
↓
double f(double re, double im) {
        double r95478 = re;
        double r95479 = im;
        double r95480 = hypot(r95478, r95479);
        return r95480;
}

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 31.6

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

  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 2020057 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))