Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

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. *-commutative N/A

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

   2. +-commutative N/A

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

   3. distribute-rgt-in N/A

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

   4. *-lft-identity N/A

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

   5. *-commutative N/A

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

   6. +-commutative N/A

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

   7. associate--l+ N/A

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

   8. accelerator-lowering-fma.f64 N/A

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

   9. --lowering--.f64 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 86.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + 1\right) - x\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+299}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+294}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (* y (+ x 1.0)) x)))
   (if (<= t_0 -2e+299) (* y x) (if (<= t_0 2e+294) (- y x) (* y x)))))

C

double code(double x, double y) {
	double t_0 = (y * (x + 1.0)) - x;
	double tmp;
	if (t_0 <= -2e+299) {
		tmp = y * x;
	} else if (t_0 <= 2e+294) {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = (y * (x + 1.0d0)) - x
    if (t_0 <= (-2d+299)) then
        tmp = y * x
    else if (t_0 <= 2d+294) then
        tmp = y - x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (x + 1.0)) - x;
	double tmp;
	if (t_0 <= -2e+299) {
		tmp = y * x;
	} else if (t_0 <= 2e+294) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (x + 1.0)) - x
	tmp = 0
	if t_0 <= -2e+299:
		tmp = y * x
	elif t_0 <= 2e+294:
		tmp = y - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(x + 1.0)) - x)
	tmp = 0.0
	if (t_0 <= -2e+299)
		tmp = Float64(y * x);
	elseif (t_0 <= 2e+294)
		tmp = Float64(y - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (x + 1.0)) - x;
	tmp = 0.0;
	if (t_0 <= -2e+299)
		tmp = y * x;
	elseif (t_0 <= 2e+294)
		tmp = y - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+299], N[(y * x), $MachinePrecision], If[LessEqual[t$95$0, 2e+294], N[(y - x), $MachinePrecision], N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x) < -2.0000000000000001e299 or 2.00000000000000013e294 < (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x)

   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. accelerator-lowering-fma.f64 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 93.4

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

   8. Simplified 93.4%

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

   if -2.0000000000000001e299 < (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) y) x) < 2.00000000000000013e294

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 88.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(x + 1\right) - x \leq -2 \cdot 10^{+299}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot \left(x + 1\right) - x \leq 2 \cdot 10^{+294}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.65:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.65) (fma y x y) (if (<= y 1.7e-7) (- y x) (fma y x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.65) {
		tmp = fma(y, x, y);
	} else if (y <= 1.7e-7) {
		tmp = y - x;
	} else {
		tmp = fma(y, x, y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.65)
		tmp = fma(y, x, y);
	elseif (y <= 1.7e-7)
		tmp = Float64(y - x);
	else
		tmp = fma(y, x, y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.65], N[(y * x + y), $MachinePrecision], If[LessEqual[y, 1.7e-7], N[(y - x), $MachinePrecision], N[(y * x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.64999999999999991 or 1.69999999999999987e-7 < y

   1. Initial program 99.9%

      \[\left(x + 1\right) \cdot y - x \]
   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. accelerator-lowering-fma.f64 99.2

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

   5. Simplified 99.2%

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

   if -3.64999999999999991 < y < 1.69999999999999987e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 98.8%

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

Alternative 4: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00032:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-25}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.00032) y (if (<= y 1.4e-25) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.00032) {
		tmp = y;
	} else if (y <= 1.4e-25) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.00032d0)) then
        tmp = y
    else if (y <= 1.4d-25) then
        tmp = -x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.00032) {
		tmp = y;
	} else if (y <= 1.4e-25) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.00032:
		tmp = y
	elif y <= 1.4e-25:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.00032)
		tmp = y;
	elseif (y <= 1.4e-25)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.00032)
		tmp = y;
	elseif (y <= 1.4e-25)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.00032], y, If[LessEqual[y, 1.4e-25], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000026e-4 or 1.39999999999999994e-25 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Simplified 52.2%

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

   if -3.20000000000000026e-4 < y < 1.39999999999999994e-25

   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. neg-lowering-neg.f64 82.9

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

   5. Simplified 82.9%

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

Alternative 5: 75.0% accurate, 3.0× 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

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

5. Simplified 76.0%

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

Alternative 6: 38.5% accurate, 12.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

5. Simplified 35.4%

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

Reproduce

herbie shell --seed 2024198 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))