Average Error: 0.0 → 0.0
Time: 2.5s
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 r37731 = re;
        double r37732 = r37731 * r37731;
        double r37733 = im;
        double r37734 = r37733 * r37733;
        double r37735 = r37732 - r37734;
        return r37735;
}
↓
double f(double re, double im) {
        double r37736 = im;
        double r37737 = re;
        double r37738 = r37736 + r37737;
        double r37739 = r37737 - r37736;
        double r37740 = r37738 * r37739;
        return r37740;
}

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)))