Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (y + 1.0)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (y + 1.0)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (y + 1.0)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{y + 1} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x + y}{y + 1} \]

Alternative 2: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -30000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -30000000000.0)
     t_0
     (if (<= y -2.9e-69) (/ y (+ y 1.0)) (if (<= y 5.6e-24) x t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -30000000000.0) {
		tmp = t_0;
	} else if (y <= -2.9e-69) {
		tmp = y / (y + 1.0);
	} else if (y <= 5.6e-24) {
		tmp = 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 = 1.0d0 + (x / y)
    if (y <= (-30000000000.0d0)) then
        tmp = t_0
    else if (y <= (-2.9d-69)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 5.6d-24) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -30000000000.0) {
		tmp = t_0;
	} else if (y <= -2.9e-69) {
		tmp = y / (y + 1.0);
	} else if (y <= 5.6e-24) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if y <= -30000000000.0:
		tmp = t_0
	elif y <= -2.9e-69:
		tmp = y / (y + 1.0)
	elif y <= 5.6e-24:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -30000000000.0)
		tmp = t_0;
	elseif (y <= -2.9e-69)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 5.6e-24)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	tmp = 0.0;
	if (y <= -30000000000.0)
		tmp = t_0;
	elseif (y <= -2.9e-69)
		tmp = y / (y + 1.0);
	elseif (y <= 5.6e-24)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -30000000000.0], t$95$0, If[LessEqual[y, -2.9e-69], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-24], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3e10 or 5.6000000000000003e-24 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around -inf 97.0%

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

      1. mul-1-neg 97.0%

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

      2. unsub-neg 97.0%

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

      3. mul-1-neg 97.0%

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

      4. sub-neg 97.0%

         \[\leadsto 1 - \frac{\color{blue}{1 - x}}{y} \]

   4. Simplified 97.0%

      \[\leadsto \color{blue}{1 - \frac{1 - x}{y}} \]

   5. Taylor expanded in x around inf 97.1%

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

      1. neg-mul-1 97.1%

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

      2. distribute-neg-frac 97.1%

         \[\leadsto 1 - \color{blue}{\frac{-x}{y}} \]

   7. Simplified 97.1%

      \[\leadsto 1 - \color{blue}{\frac{-x}{y}} \]

   if -3e10 < y < -2.8999999999999998e-69

   1. Initial program 99.9%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 77.1%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 77.1%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 77.1%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   if -2.8999999999999998e-69 < y < 5.6000000000000003e-24

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0 78.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -30000000000:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \]

Alternative 3: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-69} \lor \neg \left(y \leq 4.5 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.7e-69) (not (<= y 4.5e-44))) (/ y (+ y 1.0)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.7e-69) || !(y <= 4.5e-44)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = 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 <= (-2.7d-69)) .or. (.not. (y <= 4.5d-44))) then
        tmp = y / (y + 1.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.7e-69) || !(y <= 4.5e-44)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.7e-69) or not (y <= 4.5e-44):
		tmp = y / (y + 1.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.7e-69) || !(y <= 4.5e-44))
		tmp = Float64(y / Float64(y + 1.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.7e-69) || ~((y <= 4.5e-44)))
		tmp = y / (y + 1.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.7e-69], N[Not[LessEqual[y, 4.5e-44]], $MachinePrecision]], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999997e-69 or 4.4999999999999999e-44 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 72.7%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 72.7%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   if -2.6999999999999997e-69 < y < 4.4999999999999999e-44

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0 80.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-69} \lor \neg \left(y \leq 4.5 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-69}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y -3.3e-69) y (if (<= y 5.6e-24) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -3.3e-69) {
		tmp = y;
	} else if (y <= 5.6e-24) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= (-3.3d-69)) then
        tmp = y
    else if (y <= 5.6d-24) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -3.3e-69) {
		tmp = y;
	} else if (y <= 5.6e-24) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= -3.3e-69:
		tmp = y
	elif y <= 5.6e-24:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= -3.3e-69)
		tmp = y;
	elseif (y <= 5.6e-24)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= -3.3e-69)
		tmp = y;
	elseif (y <= 5.6e-24)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, -3.3e-69], y, If[LessEqual[y, 5.6e-24], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 5.6000000000000003e-24 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf 70.0%

      \[\leadsto \color{blue}{1} \]

   if -1 < y < -3.3e-69

   1. Initial program 99.9%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 75.7%

         \[\leadsto \frac{y}{\color{blue}{y + 1}} \]

   4. Simplified 75.7%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]

   5. Taylor expanded in y around 0 58.6%

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

   if -3.3e-69 < y < 5.6000000000000003e-24

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0 78.7%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-69}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 72.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 5.6e-24) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 5.6e-24) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 5.6d-24) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 5.6e-24) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 5.6e-24:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 5.6e-24)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 5.6e-24)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 5.6e-24], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 5.6000000000000003e-24 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around inf 70.0%

      \[\leadsto \color{blue}{1} \]

   if -1 < y < 5.6000000000000003e-24

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]

   2. Taylor expanded in y around 0 72.6%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 38.6% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{y + 1} \]

2. Taylor expanded in y around inf 35.5%

   \[\leadsto \color{blue}{1} \]

3. Final simplification 35.5%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023185 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))