Linear.Matrix:fromQuaternion from linear-1.19.1.3, A

Average Error: 0.0 → 0.0

Time: 7.2s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return (y - x) * (-2.0 * 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 = (y - x) * ((-2.0d0) * 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 (y - x) * (-2.0 * x);
}

Python

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

↓

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

MATLAB

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

↓

function tmp = code(x, y)
	tmp = (y - x) * (-2.0 * 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[(y - x), $MachinePrecision] * N[(-2.0 * 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. Applied egg-rr 0.0

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

3. Simplified 0.0

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

   [Start] 0.0	\[ x \cdot \left(x - y\right) + x \cdot \left(x - y\right) \]
   rational.json-simplify-7 [<=] 0.0	\[ x \cdot \left(x - y\right) + \color{blue}{\frac{x \cdot \left(x - y\right)}{1}} \]
   rational.json-simplify-30 [<=] 0.0	\[ \color{blue}{\left(1 + 1\right) \cdot \frac{x \cdot \left(x - y\right)}{1}} \]
   metadata-eval [=>] 0.0	\[ \color{blue}{2} \cdot \frac{x \cdot \left(x - y\right)}{1} \]
   metadata-eval [<=] 0.0	\[ \color{blue}{\left(1 - -1\right)} \cdot \frac{x \cdot \left(x - y\right)}{1} \]
   rational.json-simplify-7 [=>] 0.0	\[ \left(1 - -1\right) \cdot \color{blue}{\left(x \cdot \left(x - y\right)\right)} \]
   rational.json-simplify-5 [<=] 0.0	\[ \left(1 - -1\right) \cdot \left(x \cdot \left(x - \color{blue}{\left(y - 0\right)}\right)\right) \]
   rational.json-simplify-45 [<=] 0.0	\[ \left(1 - -1\right) \cdot \left(x \cdot \color{blue}{\left(0 - \left(y - x\right)\right)}\right) \]
   rational.json-simplify-12 [<=] 0.0	\[ \left(1 - -1\right) \cdot \left(x \cdot \color{blue}{\left(-\left(y - x\right)\right)}\right) \]
   rational.json-simplify-10 [=>] 0.0	\[ \left(1 - -1\right) \cdot \left(x \cdot \color{blue}{\frac{y - x}{-1}}\right) \]
   rational.json-simplify-49 [<=] 0.0	\[ \left(1 - -1\right) \cdot \color{blue}{\frac{\left(y - x\right) \cdot x}{-1}} \]
   rational.json-simplify-2 [<=] 0.0	\[ \left(1 - -1\right) \cdot \frac{\color{blue}{x \cdot \left(y - x\right)}}{-1} \]
   rational.json-simplify-32 [=>] 0.0	\[ \color{blue}{\frac{x \cdot \left(y - x\right)}{-1} - x \cdot \left(y - x\right)} \]
   rational.json-simplify-49 [=>] 0.0	\[ \color{blue}{\left(y - x\right) \cdot \frac{x}{-1}} - x \cdot \left(y - x\right) \]
   rational.json-simplify-52 [=>] 0.0	\[ \color{blue}{\left(y - x\right) \cdot \left(\frac{x}{-1} - x\right)} \]
   rational.json-simplify-11 [=>] 0.0	\[ \left(y - x\right) \cdot \left(\color{blue}{\left(-x\right)} - x\right) \]
   rational.json-simplify-9 [<=] 0.0	\[ \left(y - x\right) \cdot \left(\color{blue}{x \cdot -1} - x\right) \]
   rational.json-simplify-6 [<=] 0.0	\[ \left(y - x\right) \cdot \left(x \cdot -1 - \color{blue}{1 \cdot x}\right) \]
   rational.json-simplify-52 [=>] 0.0	\[ \left(y - x\right) \cdot \color{blue}{\left(x \cdot \left(-1 - 1\right)\right)} \]
   metadata-eval [=>] 0.0	\[ \left(y - x\right) \cdot \left(x \cdot \color{blue}{-2}\right) \]
   rational.json-simplify-2 [=>] 0.0	\[ \left(y - x\right) \cdot \color{blue}{\left(-2 \cdot x\right)} \]

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	0.0
Cost	448

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

Alternative 2
Error	22.3
Cost	320

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

Reproduce

herbie shell --seed 2023064 
(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))))