Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

Alternatives: 7

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. *-commutative 100.0%

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

   3. +-commutative 100.0%

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

   4. distribute-lft-in 100.0%

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

   5. *-rgt-identity 100.0%

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

   6. associate-+l+ 100.0%

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

   7. *-commutative 100.0%

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

   8. +-commutative 100.0%

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

   9. *-commutative 100.0%

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

   10. neg-mul-1 100.0%

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

   11. distribute-rgt-out 100.0%

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

   12. fma-define 100.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + -1, y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -300 \lor \neg \left(x \leq 0.95\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -300.0) (not (<= x 0.95))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -300.0) || !(x <= 0.95)) {
		tmp = x * (y + -1.0);
	} 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 <= (-300.0d0)) .or. (.not. (x <= 0.95d0))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -300.0) || !(x <= 0.95)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -300.0) or not (x <= 0.95):
		tmp = x * (y + -1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -300.0) || !(x <= 0.95))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -300.0) || ~((x <= 0.95)))
		tmp = x * (y + -1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -300.0], N[Not[LessEqual[x, 0.95]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -300 or 0.94999999999999996 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.4%

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

   if -300 < x < 0.94999999999999996

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -300 \lor \neg \left(x \leq 0.95\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -300:\\ \;\;\;\;x \cdot y - x\\ \mathbf{elif}\;x \leq 0.95:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -300.0) (- (* x y) x) (if (<= x 0.95) (- y x) (* x (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -300.0) {
		tmp = (x * y) - x;
	} else if (x <= 0.95) {
		tmp = y - x;
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-300.0d0)) then
        tmp = (x * y) - x
    else if (x <= 0.95d0) then
        tmp = y - x
    else
        tmp = x * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -300.0) {
		tmp = (x * y) - x;
	} else if (x <= 0.95) {
		tmp = y - x;
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -300.0:
		tmp = (x * y) - x
	elif x <= 0.95:
		tmp = y - x
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -300.0)
		tmp = Float64(Float64(x * y) - x);
	elseif (x <= 0.95)
		tmp = Float64(y - x);
	else
		tmp = Float64(x * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -300.0)
		tmp = (x * y) - x;
	elseif (x <= 0.95)
		tmp = y - x;
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -300.0], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[x, 0.95], N[(y - x), $MachinePrecision], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -300

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   if -300 < x < 0.94999999999999996

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.2%

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

   if 0.94999999999999996 < x

   1. Initial program 99.9%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 95.2%

      \[\leadsto \color{blue}{x \cdot \left(y - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -300:\\ \;\;\;\;x \cdot y - x\\ \mathbf{elif}\;x \leq 0.95:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \left(y + x \cdot y\right) - x \]
6. Add Preprocessing

Alternative 5: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto y \cdot \left(x + 1\right) - x \]
4. Add Preprocessing

Alternative 6: 75.4% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing

3. Taylor expanded in x around 0 77.4%

   \[\leadsto \color{blue}{y} - x \]
4. Add Preprocessing

Alternative 7: 38.4% 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. Add Preprocessing

3. Taylor expanded in y around 0 40.9%

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

   1. neg-mul-1 40.9%

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

5. Simplified 40.9%

   \[\leadsto \color{blue}{-x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024086 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))