Linear.Matrix:fromQuaternion from linear-1.19.1.3, A

Percentage Accurate: 95.1% → 100.0%

Time: 2.0s

Alternatives: 1

Speedup: 1.3×

• 28.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \left(x \cdot x - x \cdot y\right) \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(x \cdot x - x \cdot y\right) \end{array} \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(-2 \cdot x\right) \cdot \left(y - x\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

   \[2 \cdot \left(x \cdot x - x \cdot y\right) \]
2. Step-by-step derivation

   1. distribute-lft-out-- 100.0%

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

   2. associate-*r* 100.0%

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

   3. sub-neg 100.0%

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

   4. remove-double-neg 100.0%

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

   5. distribute-neg-out 100.0%

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

   6. +-commutative 100.0%

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

   7. sub-neg 100.0%

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

   8. distribute-rgt-neg-out 100.0%

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

   9. distribute-lft-neg-out 100.0%

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

   10. distribute-rgt-neg-out 100.0%

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

   11. neg-mul-1 100.0%

       \[\leadsto \left(2 \cdot \color{blue}{\left(-1 \cdot x\right)}\right) \cdot \left(y - x\right) \]

   12. associate-*r* 100.0%

       \[\leadsto \color{blue}{\left(\left(2 \cdot -1\right) \cdot x\right)} \cdot \left(y - x\right) \]

   13. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Developer target: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 2\right) \cdot \left(x - y\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(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))))