Average Error: 0.0 → 0.0
Time: 2.6s
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 r37723 = re;
        double r37724 = r37723 * r37723;
        double r37725 = im;
        double r37726 = r37725 * r37725;
        double r37727 = r37724 - r37726;
        return r37727;
}
↓
double f(double re, double im) {
        double r37728 = im;
        double r37729 = re;
        double r37730 = r37728 + r37729;
        double r37731 = r37729 - r37728;
        double r37732 = r37730 * r37731;
        return r37732;
}

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 2019119 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))