Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 6

Speedup: 1.2×

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, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-+.f64 N/A

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

   5. +-commutative N/A

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

   6. distribute-rgt-in N/A

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

   7. *-lft-identity N/A

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

   8. *-commutative N/A

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

   9. +-commutative N/A

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

   10. associate--l+ N/A

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

   11. lower-fma.f64 N/A

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

   12. lower--.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot x - x\\ \mathbf{if}\;x \leq -59:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.00028:\\ \;\;\;\;y \cdot 1 - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y x) x)))
   (if (<= x -59.0) t_0 (if (<= x 0.00028) (- (* y 1.0) x) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * x) - x;
	double tmp;
	if (x <= -59.0) {
		tmp = t_0;
	} else if (x <= 0.00028) {
		tmp = (y * 1.0) - 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 <= (-59.0d0)) then
        tmp = t_0
    else if (x <= 0.00028d0) then
        tmp = (y * 1.0d0) - 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 <= -59.0) {
		tmp = t_0;
	} else if (x <= 0.00028) {
		tmp = (y * 1.0) - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * x) - x
	tmp = 0
	if x <= -59.0:
		tmp = t_0
	elif x <= 0.00028:
		tmp = (y * 1.0) - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * x) - x)
	tmp = 0.0
	if (x <= -59.0)
		tmp = t_0;
	elseif (x <= 0.00028)
		tmp = Float64(Float64(y * 1.0) - 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 <= -59.0)
		tmp = t_0;
	elseif (x <= 0.00028)
		tmp = (y * 1.0) - 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, -59.0], t$95$0, If[LessEqual[x, 0.00028], N[(N[(y * 1.0), $MachinePrecision] - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -59 or 2.7999999999999998e-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. *-commutative N/A

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

      2. lower-*.f64 99.6

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

   5. Applied rewrites 99.6%

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

   if -59 < x < 2.7999999999999998e-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 98.2%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -59:\\ \;\;\;\;y \cdot x - x\\ \mathbf{elif}\;x \leq 0.00028:\\ \;\;\;\;y \cdot 1 - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot x - x\\ \mathbf{if}\;x \leq -0.00043:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y x) x)))
   (if (<= x -0.00043) t_0 (if (<= x 6.6e-65) (fma y x y) t_0))))

C

double code(double x, double y) {
	double t_0 = (y * x) - x;
	double tmp;
	if (x <= -0.00043) {
		tmp = t_0;
	} else if (x <= 6.6e-65) {
		tmp = fma(y, x, y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(y * x) - x)
	tmp = 0.0
	if (x <= -0.00043)
		tmp = t_0;
	elseif (x <= 6.6e-65)
		tmp = fma(y, x, y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, -0.00043], t$95$0, If[LessEqual[x, 6.6e-65], N[(y * x + y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.29999999999999989e-4 or 6.6000000000000002e-65 < 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. *-commutative N/A

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

      2. lower-*.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if -4.29999999999999989e-4 < x < 6.6000000000000002e-65

   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

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

      2. distribute-lft-in N/A

         \[\leadsto \color{blue}{y \cdot x + y \cdot 1} \]

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 79.1

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

   5. Applied rewrites 79.1%

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

Alternative 4: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-54}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-105}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.5e-54) (fma y x y) (if (<= y 5.4e-105) (- x) (fma y x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.5e-54) {
		tmp = fma(y, x, y);
	} else if (y <= 5.4e-105) {
		tmp = -x;
	} else {
		tmp = fma(y, x, y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.5e-54)
		tmp = fma(y, x, y);
	elseif (y <= 5.4e-105)
		tmp = Float64(-x);
	else
		tmp = fma(y, x, y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.5e-54], N[(y * x + y), $MachinePrecision], If[LessEqual[y, 5.4e-105], (-x), N[(y * x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000005e-54 or 5.39999999999999985e-105 < 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

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

      2. distribute-lft-in N/A

         \[\leadsto \color{blue}{y \cdot x + y \cdot 1} \]

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 89.3

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

   5. Applied rewrites 89.3%

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

   if -1.50000000000000005e-54 < y < 5.39999999999999985e-105

   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 85.6

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

   5. Applied rewrites 85.6%

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

Alternative 5: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5000:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2e-6) (* y x) (if (<= y 5000.0) (- x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2e-6) {
		tmp = y * x;
	} else if (y <= 5000.0) {
		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 <= (-2d-6)) then
        tmp = y * x
    else if (y <= 5000.0d0) 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 <= -2e-6) {
		tmp = y * x;
	} else if (y <= 5000.0) {
		tmp = -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2e-6:
		tmp = y * x
	elif y <= 5000.0:
		tmp = -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2e-6)
		tmp = Float64(y * x);
	elseif (y <= 5000.0)
		tmp = Float64(-x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2e-6)
		tmp = y * x;
	elseif (y <= 5000.0)
		tmp = -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2e-6], N[(y * x), $MachinePrecision], If[LessEqual[y, 5000.0], (-x), N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999991e-6 or 5e3 < 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

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

      2. distribute-lft-in N/A

         \[\leadsto \color{blue}{y \cdot x + y \cdot 1} \]

      3. *-rgt-identity N/A

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

      4. lower-fma.f64 98.8

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

   5. Applied rewrites 98.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 52.5%

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

   if -1.99999999999999991e-6 < y < 5e3

   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 69.8

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

   5. Applied rewrites 69.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 5000:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.6% 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 39.7

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

5. Applied rewrites 39.7%

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

Reproduce

herbie shell --seed 2024219 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))