Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

Alternatives: 6

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot x - x\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00012:\\ \;\;\;\;1 \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y x) x)))
   (if (<= x -1.0) t_0 (if (<= x 0.00012) (- (* 1.0 y) x) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * x) - x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 0.00012) {
		tmp = (1.0 * y) - 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 = (y * x) - x
    if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= 0.00012d0) then
        tmp = (1.0d0 * y) - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * x) - x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 0.00012) {
		tmp = (1.0 * y) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * x) - x
	tmp = 0
	if x <= -1.0:
		tmp = t_0
	elif x <= 0.00012:
		tmp = (1.0 * y) - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * x) - x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 0.00012)
		tmp = Float64(Float64(1.0 * y) - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * x) - x;
	tmp = 0.0;
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 0.00012)
		tmp = (1.0 * y) - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 0.00012], N[(N[(1.0 * y), $MachinePrecision] - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.20000000000000003e-4 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 98.7

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

   5. Applied rewrites 98.7%

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

   if -1 < x < 1.20000000000000003e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{1} \cdot y - x \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;y \cdot x - x\\ \mathbf{elif}\;x \leq 0.00012:\\ \;\;\;\;1 \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(x, y, y\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-5}:\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.3e-71) (fma x y y) (if (<= y 9.8e-5) (- (* y x) x) (fma x y y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.3e-71) {
		tmp = fma(x, y, y);
	} else if (y <= 9.8e-5) {
		tmp = (y * x) - x;
	} else {
		tmp = fma(x, y, y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.3e-71)
		tmp = fma(x, y, y);
	elseif (y <= 9.8e-5)
		tmp = Float64(Float64(y * x) - x);
	else
		tmp = fma(x, y, y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.3e-71], N[(x * y + y), $MachinePrecision], If[LessEqual[y, 9.8e-5], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], N[(x * y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999998e-71 or 9.8e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 + x\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. lower-fma.f64 97.3

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

   5. Applied rewrites 97.3%

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

   if -2.2999999999999998e-71 < y < 9.8e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 75.8

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

   5. Applied rewrites 75.8%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(x, y, y\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-5}:\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-71}:\\ \;\;\;\;\mathsf{fma}\left(x, y, y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-20}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.3e-71) (fma x y y) (if (<= y 1.1e-20) (- x) (fma x y y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.3e-71) {
		tmp = fma(x, y, y);
	} else if (y <= 1.1e-20) {
		tmp = -x;
	} else {
		tmp = fma(x, y, y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.3e-71)
		tmp = fma(x, y, y);
	elseif (y <= 1.1e-20)
		tmp = Float64(-x);
	else
		tmp = fma(x, y, y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.3e-71], N[(x * y + y), $MachinePrecision], If[LessEqual[y, 1.1e-20], (-x), N[(x * y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2999999999999998e-71 or 1.09999999999999995e-20 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 + x\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. lower-fma.f64 95.4

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

   5. Applied rewrites 95.4%

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

   if -2.2999999999999998e-71 < y < 1.09999999999999995e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

      2. lower-neg.f64 77.1

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

   5. Applied rewrites 77.1%

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

Alternative 5: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+26}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 0.55:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.9e+26) (* y x) (if (<= y 0.55) (- x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.9e+26) {
		tmp = y * x;
	} else if (y <= 0.55) {
		tmp = -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 (y <= (-2.9d+26)) then
        tmp = y * x
    else if (y <= 0.55d0) then
        tmp = -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.9e+26) {
		tmp = y * x;
	} else if (y <= 0.55) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.9e+26:
		tmp = y * x
	elif y <= 0.55:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.9e+26)
		tmp = Float64(y * x);
	elseif (y <= 0.55)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.9e+26)
		tmp = y * x;
	elseif (y <= 0.55)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.9e+26], N[(y * x), $MachinePrecision], If[LessEqual[y, 0.55], (-x), N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e26 or 0.55000000000000004 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 + x\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. lower-fma.f64 99.1

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 53.4%

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

   if -2.9e26 < y < 0.55000000000000004

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

      2. lower-neg.f64 68.5

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

   5. Applied rewrites 68.5%

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

Alternative 6: 37.8% accurate, 4.0× 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

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

   2. lower-neg.f64 35.4

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

5. Applied rewrites 35.4%

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

Reproduce

herbie shell --seed 2024243 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))