Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

Alternatives: 7

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 87.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0025 \lor \neg \left(y \leq 5.4 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.0025) (not (<= y 5.4e-6)))
   (/ y (+ y 1.0))
   (+ x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.0025) || !(y <= 5.4e-6)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x + (y * (1.0 - 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 <= (-0.0025d0)) .or. (.not. (y <= 5.4d-6))) then
        tmp = y / (y + 1.0d0)
    else
        tmp = x + (y * (1.0d0 - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -0.0025) || !(y <= 5.4e-6)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x + (y * (1.0 - x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.0025) or not (y <= 5.4e-6):
		tmp = y / (y + 1.0)
	else:
		tmp = x + (y * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.0025) || !(y <= 5.4e-6))
		tmp = Float64(y / Float64(y + 1.0));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.0025) || ~((y <= 5.4e-6)))
		tmp = y / (y + 1.0);
	else
		tmp = x + (y * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.0025], N[Not[LessEqual[y, 5.4e-6]], $MachinePrecision]], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00250000000000000005 or 5.39999999999999997e-6 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.2%

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

      1. +-commutative 72.2%

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

   5. Simplified 72.2%

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

   if -0.00250000000000000005 < y < 5.39999999999999997e-6

   1. Initial program 99.9%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0025 \lor \neg \left(y \leq 5.4 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+59} \lor \neg \left(x \leq 2.1 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.5e+59) (not (<= x 2.1e+19)))
   (/ x (+ y 1.0))
   (/ y (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+59) || !(x <= 2.1e+19)) {
		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 ((x <= (-1.5d+59)) .or. (.not. (x <= 2.1d+19))) 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 ((x <= -1.5e+59) || !(x <= 2.1e+19)) {
		tmp = x / (y + 1.0);
	} else {
		tmp = y / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.5e+59) or not (x <= 2.1e+19):
		tmp = x / (y + 1.0)
	else:
		tmp = y / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.5e+59) || !(x <= 2.1e+19))
		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 ((x <= -1.5e+59) || ~((x <= 2.1e+19)))
		tmp = x / (y + 1.0);
	else
		tmp = y / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.5e+59], N[Not[LessEqual[x, 2.1e+19]], $MachinePrecision]], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e59 or 2.1e19 < x

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.8%

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

      1. +-commutative 79.8%

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

   5. Simplified 79.8%

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

   if -1.5e59 < x < 2.1e19

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.8%

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

      1. +-commutative 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+59} \lor \neg \left(x \leq 2.1 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 150000000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.2e+97) 1.0 (if (<= y 150000000000.0) (/ x (+ y 1.0)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.2e+97) {
		tmp = 1.0;
	} else if (y <= 150000000000.0) {
		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 <= (-5.2d+97)) then
        tmp = 1.0d0
    else if (y <= 150000000000.0d0) 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 <= -5.2e+97) {
		tmp = 1.0;
	} else if (y <= 150000000000.0) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.2e+97:
		tmp = 1.0
	elif y <= 150000000000.0:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.2e+97)
		tmp = 1.0;
	elseif (y <= 150000000000.0)
		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 <= -5.2e+97)
		tmp = 1.0;
	elseif (y <= 150000000000.0)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.2e+97], 1.0, If[LessEqual[y, 150000000000.0], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e97 or 1.5e11 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.9%

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

   if -5.2e97 < y < 1.5e11

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 73.2%

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

      1. +-commutative 73.2%

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

   5. Simplified 73.2%

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

Alternative 5: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.000165:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 0.000165) (* x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.000165) {
		tmp = x * (1.0 - y);
	} 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 <= 0.000165d0) then
        tmp = x * (1.0d0 - y)
    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 <= 0.000165) {
		tmp = x * (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 0.000165:
		tmp = x * (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 0.000165)
		tmp = Float64(x * Float64(1.0 - y));
	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 <= 0.000165)
		tmp = x * (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 0.000165], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.65e-4 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.8%

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

   if -1 < y < 1.65e-4

   1. Initial program 99.9%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.2%

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

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in y around 0 76.7%

      \[\leadsto \color{blue}{x + -1 \cdot \left(x \cdot y\right)} \]
   7. Step-by-step derivation

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. remove-double-neg 76.7%

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

      4. distribute-neg-out 76.7%

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

      5. neg-mul-1 76.7%

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

      6. *-commutative 76.7%

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

      7. distribute-lft-in 76.7%

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

      8. distribute-rgt-neg-in 76.7%

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

      9. sub0-neg 76.7%

         \[\leadsto x \cdot \color{blue}{\left(0 - \left(y + -1\right)\right)} \]

      10. metadata-eval 76.7%

          \[\leadsto x \cdot \left(0 - \left(y + \color{blue}{\left(-1\right)}\right)\right) \]

      11. sub-neg 76.7%

          \[\leadsto x \cdot \left(0 - \color{blue}{\left(y - 1\right)}\right) \]

      12. associate-+l- 76.7%

          \[\leadsto x \cdot \color{blue}{\left(\left(0 - y\right) + 1\right)} \]

      13. neg-sub0 76.7%

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

      14. +-commutative 76.7%

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

      15. unsub-neg 76.7%

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

   8. Simplified 76.7%

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

Alternative 6: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.000165:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 0.000165) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.000165) {
		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 <= 0.000165d0) 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 <= 0.000165) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 0.000165:
		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 <= 0.000165)
		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 <= 0.000165)
		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, 0.000165], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.65e-4 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.8%

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

   if -1 < y < 1.65e-4

   1. Initial program 99.9%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.4%

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

Alternative 7: 37.9% 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. Add Preprocessing

3. Taylor expanded in y around inf 37.2%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Reproduce

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