Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re + im\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(re + im\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r2834 = re;
        double r2835 = r2834 * r2834;
        double r2836 = im;
        double r2837 = r2836 * r2836;
        double r2838 = r2835 - r2837;
        return r2838;
}
↓
double f(double re, double im) {
        double r2839 = re;
        double r2840 = im;
        double r2841 = r2839 + r2840;
        double r2842 = r2839 - r2840;
        double r2843 = r2841 * r2842;
        return r2843;
}

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

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))