Average Error: 0.0 → 0.0
Time: 15.3s
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 r304398 = re;
        double r304399 = r304398 * r304398;
        double r304400 = im;
        double r304401 = r304400 * r304400;
        double r304402 = r304399 - r304401;
        return r304402;
}
↓
double f(double re, double im) {
        double r304403 = im;
        double r304404 = re;
        double r304405 = r304403 + r304404;
        double r304406 = r304404 - r304403;
        double r304407 = r304405 * r304406;
        return r304407;
}

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 2019146 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))