Examples.Basics.BasicTests:f2 from sbv-4.4

Average Accuracy: 100.0% → 100.0%

Time: 1.7s

Precision: binary64

Cost: 448

Math

\[x \cdot x - y \cdot y \]

↓

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

FPCore

(FPCore (x y) :precision binary64 (- (* x x) (* y y)))

↓

(FPCore (x y) :precision binary64 (* (- x y) (+ x y)))

C

double code(double x, double y) {
	return (x * x) - (y * y);
}

↓

double code(double x, double y) {
	return (x - y) * (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * x) - (y * y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) * (x + y)
end function

Java

public static double code(double x, double y) {
	return (x * x) - (y * y);
}

↓

public static double code(double x, double y) {
	return (x - y) * (x + y);
}

Python

def code(x, y):
	return (x * x) - (y * y)

↓

def code(x, y):
	return (x - y) * (x + y)

Julia

function code(x, y)
	return Float64(Float64(x * x) - Float64(y * y))
end

↓

function code(x, y)
	return Float64(Float64(x - y) * Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * x) - (y * y);
end

↓

function tmp = code(x, y)
	tmp = (x - y) * (x + y);
end

Wolfram

code[x_, y_] := N[(N[(x * x), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := N[(N[(x - y), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot x - y \cdot y \]

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ x \cdot x - y \cdot y \]
   difference-of-squares [=>] 100.0	\[ \color{blue}{\left(x + y\right) \cdot \left(x - y\right)} \]
   *-commutative [=>] 100.0	\[ \color{blue}{\left(x - y\right) \cdot \left(x + y\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	79.2%
Cost	521

\[\begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-125} \lor \neg \left(y \leq 1.05 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Accuracy	56.0%
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 2023137 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))