Average Error: 0.0 → 0.0
Time: 911.0ms
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(\left|y\right| + x\right) \cdot \left(x - \left|y\right|\right)\]
x \cdot x - y \cdot y
↓
\left(\left|y\right| + x\right) \cdot \left(x - \left|y\right|\right)
double code(double x, double y) {
	return ((double) (((double) (x * x)) - ((double) (y * y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) fabs(y)) + x)) * ((double) (x - ((double) fabs(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

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

  4. Applied difference-of-squares0.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))