Average Error: 0.0 → 0.0
Time: 4.4s
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 r8711 = re;
        double r8712 = r8711 * r8711;
        double r8713 = im;
        double r8714 = r8713 * r8713;
        double r8715 = r8712 - r8714;
        return r8715;
}
↓
double f(double re, double im) {
        double r8716 = im;
        double r8717 = re;
        double r8718 = r8716 + r8717;
        double r8719 = r8717 - r8716;
        double r8720 = r8718 * r8719;
        return r8720;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019294 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))