Average Error: 0.0 → 0.0
Time: 15.8s
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 r304466 = re;
        double r304467 = r304466 * r304466;
        double r304468 = im;
        double r304469 = r304468 * r304468;
        double r304470 = r304467 - r304469;
        return r304470;
}
↓
double f(double re, double im) {
        double r304471 = re;
        double r304472 = im;
        double r304473 = r304471 + r304472;
        double r304474 = r304471 - r304472;
        double r304475 = r304473 * r304474;
        return r304475;
}

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 2019149 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))