Average Error: 0.0 → 0.0
Time: 21.6s
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 r317620 = re;
        double r317621 = r317620 * r317620;
        double r317622 = im;
        double r317623 = r317622 * r317622;
        double r317624 = r317621 - r317623;
        return r317624;
}
↓
double f(double re, double im) {
        double r317625 = im;
        double r317626 = re;
        double r317627 = r317625 + r317626;
        double r317628 = r317626 - r317625;
        double r317629 = r317627 * r317628;
        return r317629;
}

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 2019165 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))