Average Error: 0.0 → 0.0
Time: 859.0ms
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(y + \left|x\right|\right) \cdot \left(\left|x\right| - y\right)\]
x \cdot x - y \cdot y
↓
\left(y + \left|x\right|\right) \cdot \left(\left|x\right| - y\right)
double code(double x, double y) {
	return ((x * x) - (y * y));
}
↓
double code(double x, double y) {
	return ((y + fabs(x)) * (fabs(x) - y));
}

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 add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{x \cdot x} \cdot \sqrt{x \cdot x}} - y \cdot y\]

  4. Applied difference-of-squares0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))