Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r37736 = re;
        double r37737 = r37736 * r37736;
        double r37738 = im;
        double r37739 = r37738 * r37738;
        double r37740 = r37737 - r37739;
        return r37740;
}
↓
double f(double re, double im) {
        double r37741 = im;
        double r37742 = re;
        double r37743 = r37741 + r37742;
        double r37744 = r37742 - r37741;
        double r37745 = r37743 * r37744;
        return r37745;
}

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 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))