Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 8

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-143}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9e-22) y (if (<= y 3e-143) (- x) (if (<= y 3.8e+49) y (* y x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9e-22) {
		tmp = y;
	} else if (y <= 3e-143) {
		tmp = -x;
	} else if (y <= 3.8e+49) {
		tmp = y;
	} 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 <= (-9d-22)) then
        tmp = y
    else if (y <= 3d-143) then
        tmp = -x
    else if (y <= 3.8d+49) then
        tmp = y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -9e-22) {
		tmp = y;
	} else if (y <= 3e-143) {
		tmp = -x;
	} else if (y <= 3.8e+49) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9e-22:
		tmp = y
	elif y <= 3e-143:
		tmp = -x
	elif y <= 3.8e+49:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9e-22)
		tmp = y;
	elseif (y <= 3e-143)
		tmp = Float64(-x);
	elseif (y <= 3.8e+49)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9e-22)
		tmp = y;
	elseif (y <= 3e-143)
		tmp = -x;
	elseif (y <= 3.8e+49)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9e-22], y, If[LessEqual[y, 3e-143], (-x), If[LessEqual[y, 3.8e+49], y, N[(y * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999973e-22 or 2.99999999999999985e-143 < y < 3.7999999999999999e49

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.8%

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

   4. Taylor expanded in y around inf 61.8%

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

   if -8.99999999999999973e-22 < y < 2.99999999999999985e-143

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.2%

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

      1. neg-mul-1 89.2%

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

   5. Simplified 89.2%

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

   if 3.7999999999999999e49 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in y around inf 65.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-143}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -68 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -68.0) (not (<= x 1.0))) (- (* y x) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -68.0) || !(x <= 1.0)) {
		tmp = (y * x) - 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 <= (-68.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (y * x) - x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -68.0) || !(x <= 1.0)) {
		tmp = (y * x) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -68.0) or not (x <= 1.0):
		tmp = (y * x) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -68.0) || !(x <= 1.0))
		tmp = Float64(Float64(y * x) - x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -68.0) || ~((x <= 1.0)))
		tmp = (y * x) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -68.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -68 or 1 < x

   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 -68 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -68 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;y \cdot x - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-143}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.05e-21) y (if (<= y 3e-143) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.05e-21) {
		tmp = y;
	} else if (y <= 3e-143) {
		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 <= (-1.05d-21)) then
        tmp = y
    else if (y <= 3d-143) 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 <= -1.05e-21) {
		tmp = y;
	} else if (y <= 3e-143) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.05e-21:
		tmp = y
	elif y <= 3e-143:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.05e-21)
		tmp = y;
	elseif (y <= 3e-143)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.05e-21)
		tmp = y;
	elseif (y <= 3e-143)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.05e-21], y, If[LessEqual[y, 3e-143], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000006e-21 or 2.99999999999999985e-143 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 63.3%

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

   4. Taylor expanded in y around inf 53.9%

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

   if -1.05000000000000006e-21 < y < 2.99999999999999985e-143

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.2%

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

      1. neg-mul-1 89.2%

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

   5. Simplified 89.2%

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

Alternative 5: 74.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2e+47) (- y x) (* y x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2e+47) {
		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) :: tmp
    if (y <= 2d+47) then
        tmp = y - 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+47) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2e+47:
		tmp = y - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2e+47)
		tmp = Float64(y - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2e+47)
		tmp = y - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2e+47], N[(y - x), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.0000000000000001e47

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 87.1%

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

   if 2.0000000000000001e47 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in y around inf 65.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 7: 38.0% accurate, 7.0× 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 77.1%

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

4. Taylor expanded in y around inf 38.5%

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

Alternative 8: 2.6% accurate, 7.0× 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 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 41.1%

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

   1. neg-mul-1 41.1%

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

5. Simplified 41.1%

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

   1. neg-sub0 41.1%

      \[\leadsto \color{blue}{0 - x} \]

   2. sub-neg 41.1%

      \[\leadsto \color{blue}{0 + \left(-x\right)} \]

   3. add-sqr-sqrt 21.8%

      \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   4. sqrt-unprod 21.2%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   5. sqr-neg 21.2%

      \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   6. sqrt-unprod 1.4%

      \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   7. add-sqr-sqrt 2.7%

      \[\leadsto 0 + \color{blue}{x} \]

7. Applied egg-rr 2.7%

   \[\leadsto \color{blue}{0 + x} \]
8. Step-by-step derivation

   1. +-lft-identity 2.7%

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

9. Simplified 2.7%

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

Reproduce

herbie shell --seed 2024116 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))