Average Error: 0.0 → 0.0
Time: 4.5s
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 r108734 = re;
        double r108735 = r108734 * r108734;
        double r108736 = im;
        double r108737 = r108736 * r108736;
        double r108738 = r108735 - r108737;
        return r108738;
}
↓
double f(double re, double im) {
        double r108739 = re;
        double r108740 = im;
        double r108741 = r108739 + r108740;
        double r108742 = r108739 - r108740;
        double r108743 = r108741 * r108742;
        return r108743;
}

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 0 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 2019156 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))