Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

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: 87.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -25000 \lor \neg \left(y \leq 12500000\right):\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -25000.0) (not (<= y 12500000.0)))
   (- 1.0 (/ (- 1.0 x) y))
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -25000.0) || !(y <= 12500000.0)) {
		tmp = 1.0 - ((1.0 - x) / y);
	} 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 <= (-25000.0d0)) .or. (.not. (y <= 12500000.0d0))) then
        tmp = 1.0d0 - ((1.0d0 - x) / y)
    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 <= -25000.0) || !(y <= 12500000.0)) {
		tmp = 1.0 - ((1.0 - x) / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -25000.0) or not (y <= 12500000.0):
		tmp = 1.0 - ((1.0 - x) / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -25000.0) || !(y <= 12500000.0))
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -25000.0) || ~((y <= 12500000.0)))
		tmp = 1.0 - ((1.0 - x) / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -25000.0], N[Not[LessEqual[y, 12500000.0]], $MachinePrecision]], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -25000 or 1.25e7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   if -25000 < y < 1.25e7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.4%

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

      1. +-commutative 76.4%

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

   4. Simplified 76.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -25000 \lor \neg \left(y \leq 12500000\right):\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 3: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 122000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.4e+80) 1.0 (if (<= y 122000000.0) (/ x (+ y 1.0)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.4e+80) {
		tmp = 1.0;
	} else if (y <= 122000000.0) {
		tmp = x / (y + 1.0);
	} 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 <= (-2.4d+80)) then
        tmp = 1.0d0
    else if (y <= 122000000.0d0) then
        tmp = x / (y + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.4e+80) {
		tmp = 1.0;
	} else if (y <= 122000000.0) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.4e+80:
		tmp = 1.0
	elif y <= 122000000.0:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.4e+80)
		tmp = 1.0;
	elseif (y <= 122000000.0)
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.4e+80)
		tmp = 1.0;
	elseif (y <= 122000000.0)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.4e+80], 1.0, If[LessEqual[y, 122000000.0], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999979e80 or 1.22e8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 80.2%

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

   if -2.39999999999999979e80 < y < 1.22e8

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.3%

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

      1. +-commutative 74.3%

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

   4. Simplified 74.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 122000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-37}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.02e+80) 1.0 (if (<= y 1e-37) (/ x (+ y 1.0)) (/ y (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.02e+80) {
		tmp = 1.0;
	} else if (y <= 1e-37) {
		tmp = x / (y + 1.0);
	} else {
		tmp = y / (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 <= (-1.02d+80)) then
        tmp = 1.0d0
    else if (y <= 1d-37) then
        tmp = x / (y + 1.0d0)
    else
        tmp = y / (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.02e+80) {
		tmp = 1.0;
	} else if (y <= 1e-37) {
		tmp = x / (y + 1.0);
	} else {
		tmp = y / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.02e+80:
		tmp = 1.0
	elif y <= 1e-37:
		tmp = x / (y + 1.0)
	else:
		tmp = y / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.02e+80)
		tmp = 1.0;
	elseif (y <= 1e-37)
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = Float64(y / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.02e+80)
		tmp = 1.0;
	elseif (y <= 1e-37)
		tmp = x / (y + 1.0);
	else
		tmp = y / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.02e+80], 1.0, If[LessEqual[y, 1e-37], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02e80

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.5%

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

   if -1.02e80 < y < 1.00000000000000007e-37

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.1%

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

      1. +-commutative 76.1%

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

   4. Simplified 76.1%

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

   if 1.00000000000000007e-37 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. +-commutative 77.8%

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

   4. Simplified 77.8%

      \[\leadsto \color{blue}{\frac{y}{y + 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-37}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \]

Alternative 5: 72.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 3.3e-37) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 3.3e-37) {
		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-37) 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-37) {
		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-37:
		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-37)
		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-37)
		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-37], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3.29999999999999982e-37 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 71.5%

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

   if -1 < y < 3.29999999999999982e-37

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 39.1% 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 42.8%

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

3. Final simplification 42.8%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))