Linear.Matrix:fromQuaternion from linear-1.19.1.3, A

Percentage Accurate: 95.2% → 100.0%

Time: 6.5s

Alternatives: 5

Speedup: 1.3×

• 28.3% 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: 95.2% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot x - x \cdot y\right)}\right) \]

   2. distribute-lft-out-- N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{\left(x - y\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{\left(x - y\right)}\right)\right) \]

   4. --lowering--.f64 100.0%

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x - y\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-*r* N/A

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

   2. *-commutative N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(x - y\right), \color{blue}{\left(2 \cdot x\right)}\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), \left(\color{blue}{2} \cdot x\right)\right) \]

   5. *-lowering-*.f64 100.0%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \color{blue}{x}\right)\right) \]

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

   \[\leadsto \left(x - y\right) \cdot \left(x \cdot 2\right) \]
8. Add Preprocessing

Alternative 2: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* -2.0 (* x y))))
   (if (<= y -1.05e+40) t_0 (if (<= y 1.95e-53) (* x (* x 2.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = -2.0 * (x * y);
	double tmp;
	if (y <= -1.05e+40) {
		tmp = t_0;
	} else if (y <= 1.95e-53) {
		tmp = x * (x * 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-2.0d0) * (x * y)
    if (y <= (-1.05d+40)) then
        tmp = t_0
    else if (y <= 1.95d-53) then
        tmp = x * (x * 2.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -2.0 * (x * y);
	double tmp;
	if (y <= -1.05e+40) {
		tmp = t_0;
	} else if (y <= 1.95e-53) {
		tmp = x * (x * 2.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -2.0 * (x * y)
	tmp = 0
	if y <= -1.05e+40:
		tmp = t_0
	elif y <= 1.95e-53:
		tmp = x * (x * 2.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -1.05e+40)
		tmp = t_0;
	elseif (y <= 1.95e-53)
		tmp = Float64(x * Float64(x * 2.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -2.0 * (x * y);
	tmp = 0.0;
	if (y <= -1.05e+40)
		tmp = t_0;
	elseif (y <= 1.95e-53)
		tmp = x * (x * 2.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+40], t$95$0, If[LessEqual[y, 1.95e-53], N[(x * N[(x * 2.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000005e40 or 1.9500000000000001e-53 < y

   1. Initial program 92.7%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot x - x \cdot y\right)}\right) \]

      2. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{\left(x - y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{\left(x - y\right)}\right)\right) \]

      4. --lowering--.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-2 \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-2, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 84.0%

         \[\leadsto \mathsf{*.f64}\left(-2, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 84.0%

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

   if -1.05000000000000005e40 < y < 1.9500000000000001e-53

   1. Initial program 99.1%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot x - x \cdot y\right)}\right) \]

      2. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{\left(x - y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{\left(x - y\right)}\right)\right) \]

      4. --lowering--.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot {x}^{2}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left({x}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{x}\right)\right) \]

      3. *-lowering-*.f64 87.7%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right) \]

   7. Simplified 87.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot x\right)} \]
   8. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot x\right), \color{blue}{x}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(x \cdot 2\right), x\right) \]

      4. *-lowering-*.f64 87.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, 2\right), x\right) \]

   9. Applied egg-rr 87.7%

      \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;-2 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \left(x \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-54}:\\ \;\;\;\;2 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* -2.0 (* x y))))
   (if (<= y -4.4e+39) t_0 (if (<= y 9e-54) (* 2.0 (* x x)) t_0))))

C

double code(double x, double y) {
	double t_0 = -2.0 * (x * y);
	double tmp;
	if (y <= -4.4e+39) {
		tmp = t_0;
	} else if (y <= 9e-54) {
		tmp = 2.0 * (x * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-2.0d0) * (x * y)
    if (y <= (-4.4d+39)) then
        tmp = t_0
    else if (y <= 9d-54) then
        tmp = 2.0d0 * (x * x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -2.0 * (x * y);
	double tmp;
	if (y <= -4.4e+39) {
		tmp = t_0;
	} else if (y <= 9e-54) {
		tmp = 2.0 * (x * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -2.0 * (x * y)
	tmp = 0
	if y <= -4.4e+39:
		tmp = t_0
	elif y <= 9e-54:
		tmp = 2.0 * (x * x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-2.0 * Float64(x * y))
	tmp = 0.0
	if (y <= -4.4e+39)
		tmp = t_0;
	elseif (y <= 9e-54)
		tmp = Float64(2.0 * Float64(x * x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -2.0 * (x * y);
	tmp = 0.0;
	if (y <= -4.4e+39)
		tmp = t_0;
	elseif (y <= 9e-54)
		tmp = 2.0 * (x * x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-2.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+39], t$95$0, If[LessEqual[y, 9e-54], N[(2.0 * N[(x * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4000000000000003e39 or 8.9999999999999997e-54 < y

   1. Initial program 92.7%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot x - x \cdot y\right)}\right) \]

      2. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{\left(x - y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{\left(x - y\right)}\right)\right) \]

      4. --lowering--.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-2 \cdot \left(x \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-2, \color{blue}{\left(x \cdot y\right)}\right) \]

      2. *-lowering-*.f64 84.0%

         \[\leadsto \mathsf{*.f64}\left(-2, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 84.0%

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

   if -4.4000000000000003e39 < y < 8.9999999999999997e-54

   1. Initial program 99.1%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot x - x \cdot y\right)}\right) \]

      2. distribute-lft-out-- N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{\left(x - y\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{\left(x - y\right)}\right)\right) \]

      4. --lowering--.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot {x}^{2}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left({x}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{x}\right)\right) \]

      3. *-lowering-*.f64 87.7%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{x}\right)\right) \]

   7. Simplified 87.7%

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot x - x \cdot y\right)}\right) \]

   2. distribute-lft-out-- N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{\left(x - y\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{\left(x - y\right)}\right)\right) \]

   4. --lowering--.f64 100.0%

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x - y\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 5: 57.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(x \cdot x - x \cdot y\right)}\right) \]

   2. distribute-lft-out-- N/A

      \[\leadsto \mathsf{*.f64}\left(2, \left(x \cdot \color{blue}{\left(x - y\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \color{blue}{\left(x - y\right)}\right)\right) \]

   4. --lowering--.f64 100.0%

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-2 \cdot \left(x \cdot y\right)} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(-2, \color{blue}{\left(x \cdot y\right)}\right) \]

   2. *-lowering-*.f64 57.6%

      \[\leadsto \mathsf{*.f64}\left(-2, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

7. Simplified 57.6%

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

Developer Target 1: 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 2024155 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (* (* x 2) (- x y)))

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