Average Error: 0.0 → 0.0
Time: 13.5s
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 r267861 = re;
        double r267862 = r267861 * r267861;
        double r267863 = im;
        double r267864 = r267863 * r267863;
        double r267865 = r267862 - r267864;
        return r267865;
}
↓
double f(double re, double im) {
        double r267866 = re;
        double r267867 = im;
        double r267868 = r267866 + r267867;
        double r267869 = r267866 - r267867;
        double r267870 = r267868 * r267869;
        return r267870;
}

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 2019132 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))