Average Error: 0.0 → 0.0
Time: 7.7s
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 r228431 = re;
        double r228432 = r228431 * r228431;
        double r228433 = im;
        double r228434 = r228433 * r228433;
        double r228435 = r228432 - r228434;
        return r228435;
}
↓
double f(double re, double im) {
        double r228436 = re;
        double r228437 = im;
        double r228438 = r228436 + r228437;
        double r228439 = r228436 - r228437;
        double r228440 = r228438 * r228439;
        return r228440;
}

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 -inf 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 2019132 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))