Average Error: 0.0 → 0.0
Time: 14.5s
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 r304269 = re;
        double r304270 = r304269 * r304269;
        double r304271 = im;
        double r304272 = r304271 * r304271;
        double r304273 = r304270 - r304272;
        return r304273;
}
↓
double f(double re, double im) {
        double r304274 = re;
        double r304275 = im;
        double r304276 = r304274 + r304275;
        double r304277 = r304274 - r304275;
        double r304278 = r304276 * r304277;
        return r304278;
}

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 2019152 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))