Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x + 1.0d0) * y) - x
end function

Java

public static double code(double x, double y) {
	return ((x + 1.0) * y) - x;
}

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

function code(x, y)
	return Float64(Float64(Float64(x + 1.0) * y) - x)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x + 1.0) * y) - x;
end

Wolfram

code[x_, y_] := N[(N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision] - x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Final simplification 100.0%

   \[\leadsto \left(x + 1\right) \cdot y - x \]

Alternative 2: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+73}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+261}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.6e+25)
   (* x y)
   (if (<= x 1.5e+73) (- y x) (if (<= x 2.5e+261) (* x y) (- x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.6e+25) {
		tmp = x * y;
	} else if (x <= 1.5e+73) {
		tmp = y - x;
	} else if (x <= 2.5e+261) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.6d+25)) then
        tmp = x * y
    else if (x <= 1.5d+73) then
        tmp = y - x
    else if (x <= 2.5d+261) then
        tmp = x * y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.6e+25) {
		tmp = x * y;
	} else if (x <= 1.5e+73) {
		tmp = y - x;
	} else if (x <= 2.5e+261) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.6e+25:
		tmp = x * y
	elif x <= 1.5e+73:
		tmp = y - x
	elif x <= 2.5e+261:
		tmp = x * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.6e+25)
		tmp = Float64(x * y);
	elseif (x <= 1.5e+73)
		tmp = Float64(y - x);
	elseif (x <= 2.5e+261)
		tmp = Float64(x * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.6e+25)
		tmp = x * y;
	elseif (x <= 1.5e+73)
		tmp = y - x;
	elseif (x <= 2.5e+261)
		tmp = x * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.6e+25], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.5e+73], N[(y - x), $MachinePrecision], If[LessEqual[x, 2.5e+261], N[(x * y), $MachinePrecision], (-x)]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.60000000000000015e25 or 1.50000000000000005e73 < x < 2.5e261

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x \cdot y} - x \]
   3. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot x} - x \]

   4. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot x} - x \]

   5. Taylor expanded in y around inf 61.7%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -3.60000000000000015e25 < x < 1.50000000000000005e73

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 95.0%

      \[\leadsto \color{blue}{y} - x \]

   if 2.5e261 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x \cdot y} - x \]
   3. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot x} - x \]

   4. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot x} - x \]

   5. Taylor expanded in y around 0 79.0%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   6. Step-by-step derivation

      1. neg-mul-1 79.0%

         \[\leadsto \color{blue}{-x} \]

   7. Simplified 79.0%

      \[\leadsto \color{blue}{-x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+73}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+261}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -45000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -45000.0) (not (<= x 1.0))) (- (* x y) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -45000.0) || !(x <= 1.0)) {
		tmp = (x * y) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-45000.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (x * y) - x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -45000.0) || !(x <= 1.0)) {
		tmp = (x * y) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -45000.0) or not (x <= 1.0):
		tmp = (x * y) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -45000.0) || !(x <= 1.0))
		tmp = Float64(Float64(x * y) - x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -45000.0) || ~((x <= 1.0)))
		tmp = (x * y) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -45000.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -45000 or 1 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x \cdot y} - x \]
   3. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot x} - x \]

   4. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot x} - x \]

   if -45000 < x < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 99.3%

      \[\leadsto \color{blue}{y} - x \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -45000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 4: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* x y) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = x * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(x * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = x * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 56.0%

      \[\leadsto \color{blue}{x \cdot y} - x \]
   3. Step-by-step derivation

      1. *-commutative 56.0%

         \[\leadsto \color{blue}{y \cdot x} - x \]

   4. Simplified 56.0%

      \[\leadsto \color{blue}{y \cdot x} - x \]

   5. Taylor expanded in y around inf 55.1%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -1 < y < 1

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 71.0%

      \[\leadsto \color{blue}{x \cdot y} - x \]
   3. Step-by-step derivation

      1. *-commutative 71.0%

         \[\leadsto \color{blue}{y \cdot x} - x \]

   4. Simplified 71.0%

      \[\leadsto \color{blue}{y \cdot x} - x \]

   5. Taylor expanded in y around 0 69.3%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   6. Step-by-step derivation

      1. neg-mul-1 69.3%

         \[\leadsto \color{blue}{-x} \]

   7. Simplified 69.3%

      \[\leadsto \color{blue}{-x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 38.0% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -x

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := (-x)

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around inf 63.3%

   \[\leadsto \color{blue}{x \cdot y} - x \]
3. Step-by-step derivation

   1. *-commutative 63.3%

      \[\leadsto \color{blue}{y \cdot x} - x \]

4. Simplified 63.3%

   \[\leadsto \color{blue}{y \cdot x} - x \]

5. Taylor expanded in y around 0 35.1%

   \[\leadsto \color{blue}{-1 \cdot x} \]
6. Step-by-step derivation

   1. neg-mul-1 35.1%

      \[\leadsto \color{blue}{-x} \]

7. Simplified 35.1%

   \[\leadsto \color{blue}{-x} \]

8. Final simplification 35.1%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))