Average Error: 0.0 → 0.0
Time: 6.9s
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 r9237 = re;
        double r9238 = r9237 * r9237;
        double r9239 = im;
        double r9240 = r9239 * r9239;
        double r9241 = r9238 - r9240;
        return r9241;
}
↓
double f(double re, double im) {
        double r9242 = im;
        double r9243 = re;
        double r9244 = r9242 + r9243;
        double r9245 = r9243 - r9242;
        double r9246 = r9244 * r9245;
        return r9246;
}

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