Average Error: 0.0 → 0.0
Time: 8.0s
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 r228438 = re;
        double r228439 = r228438 * r228438;
        double r228440 = im;
        double r228441 = r228440 * r228440;
        double r228442 = r228439 - r228441;
        return r228442;
}
↓
double f(double re, double im) {
        double r228443 = re;
        double r228444 = im;
        double r228445 = r228443 + r228444;
        double r228446 = r228443 - r228444;
        double r228447 = r228445 * r228446;
        return r228447;
}

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 2019133 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))