Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r469287 = re;
        double r469288 = r469287 * r469287;
        double r469289 = im;
        double r469290 = r469289 * r469289;
        double r469291 = r469288 - r469290;
        return r469291;
}
↓
double f(double re, double im) {
        double r469292 = im;
        double r469293 = re;
        double r469294 = r469292 + r469293;
        double r469295 = r469293 - r469292;
        double r469296 = r469294 * r469295;
        return r469296;
}

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. Using strategy rm

  3. Applied difference-of-squares0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019143 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))