Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

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

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

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 2: 62.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+92} \lor \neg \left(y \leq 6.7 \cdot 10^{+162}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6e+14)
   (* x y)
   (if (<= y -3e-31)
     y
     (if (<= y 1.0)
       (- x)
       (if (or (<= y 7.6e+92) (not (<= y 6.7e+162))) (* x y) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6e+14) {
		tmp = x * y;
	} else if (y <= -3e-31) {
		tmp = y;
	} else if (y <= 1.0) {
		tmp = -x;
	} else if ((y <= 7.6e+92) || !(y <= 6.7e+162)) {
		tmp = x * y;
	} 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 <= (-6d+14)) then
        tmp = x * y
    else if (y <= (-3d-31)) then
        tmp = y
    else if (y <= 1.0d0) then
        tmp = -x
    else if ((y <= 7.6d+92) .or. (.not. (y <= 6.7d+162))) then
        tmp = x * y
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6e+14) {
		tmp = x * y;
	} else if (y <= -3e-31) {
		tmp = y;
	} else if (y <= 1.0) {
		tmp = -x;
	} else if ((y <= 7.6e+92) || !(y <= 6.7e+162)) {
		tmp = x * y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6e+14:
		tmp = x * y
	elif y <= -3e-31:
		tmp = y
	elif y <= 1.0:
		tmp = -x
	elif (y <= 7.6e+92) or not (y <= 6.7e+162):
		tmp = x * y
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6e+14)
		tmp = Float64(x * y);
	elseif (y <= -3e-31)
		tmp = y;
	elseif (y <= 1.0)
		tmp = Float64(-x);
	elseif ((y <= 7.6e+92) || !(y <= 6.7e+162))
		tmp = Float64(x * y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6e+14)
		tmp = x * y;
	elseif (y <= -3e-31)
		tmp = y;
	elseif (y <= 1.0)
		tmp = -x;
	elseif ((y <= 7.6e+92) || ~((y <= 6.7e+162)))
		tmp = x * y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6e+14], N[(x * y), $MachinePrecision], If[LessEqual[y, -3e-31], y, If[LessEqual[y, 1.0], (-x), If[Or[LessEqual[y, 7.6e+92], N[Not[LessEqual[y, 6.7e+162]], $MachinePrecision]], N[(x * y), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e14 or 1 < y < 7.6000000000000001e92 or 6.6999999999999999e162 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. *-commutative 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around inf 63.0%

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

   if -6e14 < y < -2.99999999999999981e-31 or 7.6000000000000001e92 < y < 6.6999999999999999e162

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 73.6%

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

   if -2.99999999999999981e-31 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.1%

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

      1. neg-mul-1 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+14}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-31}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+92} \lor \neg \left(y \leq 6.7 \cdot 10^{+162}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-22} \lor \neg \left(x \leq 2.9 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.4e-22) (not (<= x 2.9e-58))) (* x (+ y -1.0)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.4e-22) || !(x <= 2.9e-58)) {
		tmp = x * (y + -1.0);
	} 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 ((x <= (-4.4d-22)) .or. (.not. (x <= 2.9d-58))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.4e-22) || !(x <= 2.9e-58)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.4e-22) or not (x <= 2.9e-58):
		tmp = x * (y + -1.0)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.4e-22) || !(x <= 2.9e-58))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.4e-22) || ~((x <= 2.9e-58)))
		tmp = x * (y + -1.0);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.4e-22], N[Not[LessEqual[x, 2.9e-58]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -4.4000000000000001e-22 or 2.8999999999999999e-58 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 95.7%

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

   if -4.4000000000000001e-22 < x < 2.8999999999999999e-58

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-22} \lor \neg \left(x \leq 2.9 \cdot 10^{-58}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-30} \lor \neg \left(y \leq 6700000000\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9e-30) (not (<= y 6700000000.0)))
   (* y (+ x 1.0))
   (* x (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9e-30) || !(y <= 6700000000.0)) {
		tmp = y * (x + 1.0);
	} 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 ((y <= (-9d-30)) .or. (.not. (y <= 6700000000.0d0))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = x * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -9e-30) || !(y <= 6700000000.0)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9e-30) or not (y <= 6700000000.0):
		tmp = y * (x + 1.0)
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9e-30) || !(y <= 6700000000.0))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(x * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -9e-30) || ~((y <= 6700000000.0)))
		tmp = y * (x + 1.0);
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9e-30], N[Not[LessEqual[y, 6700000000.0]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999935e-30 or 6.7e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 97.7%

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

   if -8.99999999999999935e-30 < y < 6.7e9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-30} \lor \neg \left(y \leq 6700000000\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-40}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1e-29) y (if (<= y 2.2e-40) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1e-29) {
		tmp = y;
	} else if (y <= 2.2e-40) {
		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 <= (-1d-29)) then
        tmp = y
    else if (y <= 2.2d-40) 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 <= -1e-29) {
		tmp = y;
	} else if (y <= 2.2e-40) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1e-29:
		tmp = y
	elif y <= 2.2e-40:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1e-29)
		tmp = y;
	elseif (y <= 2.2e-40)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1e-29)
		tmp = y;
	elseif (y <= 2.2e-40)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1e-29], y, If[LessEqual[y, 2.2e-40], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999943e-30 or 2.20000000000000009e-40 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 42.3%

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

   if -9.99999999999999943e-30 < y < 2.20000000000000009e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.5%

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

      1. neg-mul-1 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-29}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-40}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 39.1% 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 31.9%

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

4. Final simplification 31.9%

   \[\leadsto y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))