Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re + im\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(re + im\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r267873 = re;
        double r267874 = r267873 * r267873;
        double r267875 = im;
        double r267876 = r267875 * r267875;
        double r267877 = r267874 - r267876;
        return r267877;
}
↓
double f(double re, double im) {
        double r267878 = re;
        double r267879 = im;
        double r267880 = r267878 + r267879;
        double r267881 = r267878 - r267879;
        double r267882 = r267880 * r267881;
        return r267882;
}

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. Taylor expanded around -inf 0.0

    \[\leadsto \color{blue}{{re}^{2} - {im}^{2}}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))