Linear.Matrix:fromQuaternion from linear-1.19.1.3, A

Average Error: 0.0 → 0.0

Time: 17.9s

Precision: binary64

Cost: 448

Math

\[2 \cdot \left(x \cdot x - x \cdot y\right) \]

↓

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

FPCore

(FPCore (x y) :precision binary64 (* 2.0 (- (* x x) (* x y))))

↓

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

C

double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0 * ((x * x) - (x * y))
end function

↓

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

Java

public static double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}

↓

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

Python

def code(x, y):
	return 2.0 * ((x * x) - (x * y))

↓

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

Julia

function code(x, y)
	return Float64(2.0 * Float64(Float64(x * x) - Float64(x * y)))
end

↓

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

MATLAB

function tmp = code(x, y)
	tmp = 2.0 * ((x * x) - (x * y));
end

↓

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

Wolfram

code[x_, y_] := N[(2.0 * N[(N[(x * x), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(x \cdot 2\right) \cdot \left(x - y\right) \]

Derivation

1. Initial program 0.0

   \[2 \cdot \left(x \cdot x - x \cdot y\right) \]

2. Simplified 0.0

   \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x - y\right)\right)} \]
   Proof

   [Start] 0.0	\[ 2 \cdot \left(x \cdot x - x \cdot y\right) \]
   rational_best-simplify-62 [=>] 0.0	\[ 2 \cdot \color{blue}{\left(x \cdot \left(x - y\right)\right)} \]

3. Applied egg-rr 0.0

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

4. Simplified 0.0

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

   [Start] 0.0	\[ x \cdot \left(x - y\right) + x \cdot \left(x - y\right) \]
   rational_best-simplify-63 [=>] 0.0	\[ \color{blue}{\left(x - y\right) \cdot \left(x + x\right)} \]

5. Final simplification 0.0

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

Alternatives

Alternative 1
Error	7.7
Cost	584

\[\begin{array}{l} t_0 := -2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(x + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

\[2 \cdot \left(x \cdot \left(x - y\right)\right) \]

Alternative 3
Error	22.1
Cost	320

\[-2 \cdot \left(y \cdot x\right) \]

Reproduce

herbie shell --seed 2023099 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (* (* x 2.0) (- x y))

  (* 2.0 (- (* x x) (* x y))))