Average Error: 31.1 → 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 r36352 = re;
        double r36353 = r36352 * r36352;
        double r36354 = im;
        double r36355 = r36354 * r36354;
        double r36356 = r36353 + r36355;
        double r36357 = sqrt(r36356);
        return r36357;
}
↓
double f(double re, double im) {
        double r36358 = re;
        double r36359 = im;
        double r36360 = hypot(r36358, r36359);
        return r36360;
}

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 2020064 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))