Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 8

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. Final simplification 100.0%

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

Alternative 2: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+65}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= y -4.9e+65)
     1.0
     (if (<= y 1.55e-75)
       t_0
       (if (<= y 5.3e-33) y (if (<= y 2.2e+19) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -4.9e+65) {
		tmp = 1.0;
	} else if (y <= 1.55e-75) {
		tmp = t_0;
	} else if (y <= 5.3e-33) {
		tmp = y;
	} else if (y <= 2.2e+19) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (y + 1.0d0)
    if (y <= (-4.9d+65)) then
        tmp = 1.0d0
    else if (y <= 1.55d-75) then
        tmp = t_0
    else if (y <= 5.3d-33) then
        tmp = y
    else if (y <= 2.2d+19) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -4.9e+65) {
		tmp = 1.0;
	} else if (y <= 1.55e-75) {
		tmp = t_0;
	} else if (y <= 5.3e-33) {
		tmp = y;
	} else if (y <= 2.2e+19) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if y <= -4.9e+65:
		tmp = 1.0
	elif y <= 1.55e-75:
		tmp = t_0
	elif y <= 5.3e-33:
		tmp = y
	elif y <= 2.2e+19:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -4.9e+65)
		tmp = 1.0;
	elseif (y <= 1.55e-75)
		tmp = t_0;
	elseif (y <= 5.3e-33)
		tmp = y;
	elseif (y <= 2.2e+19)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -4.9e+65)
		tmp = 1.0;
	elseif (y <= 1.55e-75)
		tmp = t_0;
	elseif (y <= 5.3e-33)
		tmp = y;
	elseif (y <= 2.2e+19)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.9e+65], 1.0, If[LessEqual[y, 1.55e-75], t$95$0, If[LessEqual[y, 5.3e-33], y, If[LessEqual[y, 2.2e+19], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.89999999999999956e65 or 2.2e19 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.6%

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

   if -4.89999999999999956e65 < y < 1.55000000000000003e-75 or 5.29999999999999968e-33 < y < 2.2e19

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.2%

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

      1. +-commutative 78.2%

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

   5. Simplified 78.2%

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

   if 1.55000000000000003e-75 < y < 5.29999999999999968e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.2%

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

      1. +-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in y around 0 70.2%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+65}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-33}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+66}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+101}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6e+66)
   1.0
   (if (<= y 4.2e-76)
     (/ x (+ y 1.0))
     (if (<= y 5.6e+101) (/ y (+ y 1.0)) (if (<= y 1.15e+142) (/ x y) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6e+66) {
		tmp = 1.0;
	} else if (y <= 4.2e-76) {
		tmp = x / (y + 1.0);
	} else if (y <= 5.6e+101) {
		tmp = y / (y + 1.0);
	} else if (y <= 1.15e+142) {
		tmp = x / 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 <= (-6d+66)) then
        tmp = 1.0d0
    else if (y <= 4.2d-76) then
        tmp = x / (y + 1.0d0)
    else if (y <= 5.6d+101) then
        tmp = y / (y + 1.0d0)
    else if (y <= 1.15d+142) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6e+66) {
		tmp = 1.0;
	} else if (y <= 4.2e-76) {
		tmp = x / (y + 1.0);
	} else if (y <= 5.6e+101) {
		tmp = y / (y + 1.0);
	} else if (y <= 1.15e+142) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6e+66:
		tmp = 1.0
	elif y <= 4.2e-76:
		tmp = x / (y + 1.0)
	elif y <= 5.6e+101:
		tmp = y / (y + 1.0)
	elif y <= 1.15e+142:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6e+66)
		tmp = 1.0;
	elseif (y <= 4.2e-76)
		tmp = Float64(x / Float64(y + 1.0));
	elseif (y <= 5.6e+101)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 1.15e+142)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6e+66)
		tmp = 1.0;
	elseif (y <= 4.2e-76)
		tmp = x / (y + 1.0);
	elseif (y <= 5.6e+101)
		tmp = y / (y + 1.0);
	elseif (y <= 1.15e+142)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6e+66], 1.0, If[LessEqual[y, 4.2e-76], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+101], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+142], N[(x / y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.00000000000000005e66 or 1.15000000000000001e142 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.2%

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

   if -6.00000000000000005e66 < y < 4.19999999999999985e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.6%

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

      1. +-commutative 79.6%

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

   5. Simplified 79.6%

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

   if 4.19999999999999985e-76 < y < 5.59999999999999962e101

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.0%

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

      1. +-commutative 70.0%

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

   5. Simplified 70.0%

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

   if 5.59999999999999962e101 < y < 1.15000000000000001e142

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.9%

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

      1. +-commutative 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in y around inf 79.9%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+66}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+101}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.000185:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y 1.0))))
   (if (<= y -3.9e-5)
     t_0
     (if (<= y 0.000185)
       (+ x (* y (- 1.0 x)))
       (if (<= y 4.7e+101) t_0 (if (<= y 1.15e+142) (/ x y) 1.0))))))

C

double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	double tmp;
	if (y <= -3.9e-5) {
		tmp = t_0;
	} else if (y <= 0.000185) {
		tmp = x + (y * (1.0 - x));
	} else if (y <= 4.7e+101) {
		tmp = t_0;
	} else if (y <= 1.15e+142) {
		tmp = x / 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) :: t_0
    real(8) :: tmp
    t_0 = y / (y + 1.0d0)
    if (y <= (-3.9d-5)) then
        tmp = t_0
    else if (y <= 0.000185d0) then
        tmp = x + (y * (1.0d0 - x))
    else if (y <= 4.7d+101) then
        tmp = t_0
    else if (y <= 1.15d+142) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	double tmp;
	if (y <= -3.9e-5) {
		tmp = t_0;
	} else if (y <= 0.000185) {
		tmp = x + (y * (1.0 - x));
	} else if (y <= 4.7e+101) {
		tmp = t_0;
	} else if (y <= 1.15e+142) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + 1.0)
	tmp = 0
	if y <= -3.9e-5:
		tmp = t_0
	elif y <= 0.000185:
		tmp = x + (y * (1.0 - x))
	elif y <= 4.7e+101:
		tmp = t_0
	elif y <= 1.15e+142:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -3.9e-5)
		tmp = t_0;
	elseif (y <= 0.000185)
		tmp = Float64(x + Float64(y * Float64(1.0 - x)));
	elseif (y <= 4.7e+101)
		tmp = t_0;
	elseif (y <= 1.15e+142)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + 1.0);
	tmp = 0.0;
	if (y <= -3.9e-5)
		tmp = t_0;
	elseif (y <= 0.000185)
		tmp = x + (y * (1.0 - x));
	elseif (y <= 4.7e+101)
		tmp = t_0;
	elseif (y <= 1.15e+142)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e-5], t$95$0, If[LessEqual[y, 0.000185], N[(x + N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+101], t$95$0, If[LessEqual[y, 1.15e+142], N[(x / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8999999999999999e-5 or 1.85e-4 < y < 4.69999999999999971e101

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -3.8999999999999999e-5 < y < 1.85e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   if 4.69999999999999971e101 < y < 1.15000000000000001e142

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.9%

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

      1. +-commutative 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in y around inf 79.9%

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

   if 1.15000000000000001e142 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 0.000185:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+101}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+142}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 6.5e-76) x (if (<= y 1.22e-12) y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 6.5e-76) {
		tmp = x;
	} else if (y <= 1.22e-12) {
		tmp = 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 <= 6.5d-76) then
        tmp = x
    else if (y <= 1.22d-12) then
        tmp = 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 <= 6.5e-76) {
		tmp = x;
	} else if (y <= 1.22e-12) {
		tmp = y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 6.5e-76:
		tmp = x
	elif y <= 1.22e-12:
		tmp = y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 6.5e-76)
		tmp = x;
	elseif (y <= 1.22e-12)
		tmp = 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 <= 6.5e-76)
		tmp = x;
	elseif (y <= 1.22e-12)
		tmp = y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 6.5e-76], x, If[LessEqual[y, 1.22e-12], y, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.2200000000000001e-12 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.0%

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

   if -1 < y < 6.5e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.6%

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

   if 6.5e-76 < y < 1.2200000000000001e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.2%

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

      1. +-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in y around 0 70.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y 1.45e-75) (* x (- 1.0 y)) (if (<= y 1.22e-12) y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 1.45e-75) {
		tmp = x * (1.0 - y);
	} else if (y <= 1.22e-12) {
		tmp = 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 <= 1.45d-75) then
        tmp = x * (1.0d0 - y)
    else if (y <= 1.22d-12) then
        tmp = 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 <= 1.45e-75) {
		tmp = x * (1.0 - y);
	} else if (y <= 1.22e-12) {
		tmp = y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 1.45e-75:
		tmp = x * (1.0 - y)
	elif y <= 1.22e-12:
		tmp = y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 1.45e-75)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (y <= 1.22e-12)
		tmp = 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 <= 1.45e-75)
		tmp = x * (1.0 - y);
	elseif (y <= 1.22e-12)
		tmp = y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 1.45e-75], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e-12], y, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.2200000000000001e-12 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.0%

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

   if -1 < y < 1.4500000000000001e-75

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.9%

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

      1. +-commutative 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in y around 0 82.9%

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

      1. +-commutative 82.9%

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

      2. mul-1-neg 82.9%

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

      3. remove-double-neg 82.9%

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

      4. distribute-neg-out 82.9%

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

      5. neg-mul-1 82.9%

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

      6. *-commutative 82.9%

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

      7. distribute-lft-in 82.9%

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

      8. distribute-rgt-neg-in 82.9%

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

      9. sub0-neg 82.9%

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

      10. metadata-eval 82.9%

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

      11. sub-neg 82.9%

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

      12. associate-+l- 82.9%

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

      13. neg-sub0 82.9%

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

      14. +-commutative 82.9%

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

      15. unsub-neg 82.9%

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

   8. Simplified 82.9%

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

   if 1.4500000000000001e-75 < y < 1.2200000000000001e-12

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.2%

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

      1. +-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in y around 0 70.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.027:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 0.027) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.027) {
		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 <= 0.027d0) 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 <= 0.027) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 0.027:
		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 <= 0.027)
		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 <= 0.027)
		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, 0.027], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.0269999999999999997 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.5%

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

   if -1 < y < 0.0269999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.027:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.4% 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 36.6%

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

4. Final simplification 36.6%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))