Average Error: 0.0 → 0.0
Time: 9.7s
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 r9355 = re;
        double r9356 = r9355 * r9355;
        double r9357 = im;
        double r9358 = r9357 * r9357;
        double r9359 = r9356 - r9358;
        return r9359;
}
↓
double f(double re, double im) {
        double r9360 = im;
        double r9361 = re;
        double r9362 = r9360 + r9361;
        double r9363 = r9361 - r9360;
        double r9364 = r9362 * r9363;
        return r9364;
}

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 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))