Average Error: 0.0 → 0.0
Time: 5.4s
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(y + x\right) \cdot \left(x - y\right)\]
x \cdot x - y \cdot y
↓
\left(y + x\right) \cdot \left(x - y\right)
double f(double x, double y) {
        double r8258943 = x;
        double r8258944 = r8258943 * r8258943;
        double r8258945 = y;
        double r8258946 = r8258945 * r8258945;
        double r8258947 = r8258944 - r8258946;
        return r8258947;
}
↓
double f(double x, double y) {
        double r8258948 = y;
        double r8258949 = x;
        double r8258950 = r8258948 + r8258949;
        double r8258951 = r8258949 - r8258948;
        double r8258952 = r8258950 * r8258951;
        return r8258952;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot x - y \cdot y\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(x - y\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(y + x\right) \cdot \left(x - y\right)\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))