Average Error: 31.9 → 0.0
Time: 569.0ms
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 r42440 = re;
        double r42441 = r42440 * r42440;
        double r42442 = im;
        double r42443 = r42442 * r42442;
        double r42444 = r42441 + r42443;
        double r42445 = sqrt(r42444);
        return r42445;
}
↓
double f(double re, double im) {
        double r42446 = re;
        double r42447 = im;
        double r42448 = hypot(r42446, r42447);
        return r42448;
}

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 31.9

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

  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 2020083 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))