Average Error: 0.0 → 0.0
Time: 6.5s
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 r337284 = re;
        double r337285 = r337284 * r337284;
        double r337286 = im;
        double r337287 = r337286 * r337286;
        double r337288 = r337285 - r337287;
        return r337288;
}
↓
double f(double re, double im) {
        double r337289 = im;
        double r337290 = re;
        double r337291 = r337289 + r337290;
        double r337292 = r337290 - r337289;
        double r337293 = r337291 * r337292;
        return r337293;
}

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 2019104 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))