Average Error: 0.0 → 0.0
Time: 5.3s
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 r245774 = re;
        double r245775 = r245774 * r245774;
        double r245776 = im;
        double r245777 = r245776 * r245776;
        double r245778 = r245775 - r245777;
        return r245778;
}
↓
double f(double re, double im) {
        double r245779 = im;
        double r245780 = re;
        double r245781 = r245779 + r245780;
        double r245782 = r245780 - r245779;
        double r245783 = r245781 * r245782;
        return r245783;
}

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