Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
double f(double re, double im) {
        double r37730 = re;
        double r37731 = r37730 * r37730;
        double r37732 = im;
        double r37733 = r37732 * r37732;
        double r37734 = r37731 - r37733;
        return r37734;
}
↓
double f(double re, double im) {
        double r37735 = im;
        double r37736 = re;
        double r37737 = r37735 + r37736;
        double r37738 = r37736 - r37735;
        double r37739 = r37737 * r37738;
        return r37739;
}


re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)

Error

Bits error versus re

Bits error versus im

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 2019102 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))