Average Error: 0.0 → 0.0
Time: 8.4s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r335362 = re;
        double r335363 = r335362 * r335362;
        double r335364 = im;
        double r335365 = r335364 * r335364;
        double r335366 = r335363 - r335365;
        return r335366;
}
↓
double f(double re, double im) {
        double r335367 = im;
        double r335368 = re;
        double r335369 = r335367 + r335368;
        double r335370 = r335368 - r335367;
        double r335371 = r335369 * r335370;
        return r335371;
}

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 0.0

    \[re \cdot re - im \cdot im\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(re + im\right) \cdot \left(re - im\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(im + re\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019146 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))