Average Error: 0.0 → 0.0
Time: 5.0s
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 r103698 = re;
        double r103699 = r103698 * r103698;
        double r103700 = im;
        double r103701 = r103700 * r103700;
        double r103702 = r103699 - r103701;
        return r103702;
}
↓
double f(double re, double im) {
        double r103703 = re;
        double r103704 = im;
        double r103705 = r103703 + r103704;
        double r103706 = r103703 - r103704;
        double r103707 = r103705 * r103706;
        return r103707;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{re}^{2} - {im}^{2}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\left(im + re\right) \cdot \left(re - im\right)}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))