Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

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. Final simplification 100.0%

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

Alternative 2: 87.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00011 \lor \neg \left(y \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.00011) (not (<= y 2e-5)))
   (/ y (+ y 1.0))
   (+ x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.00011) || !(y <= 2e-5)) {
		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 <= (-0.00011d0)) .or. (.not. (y <= 2d-5))) 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 <= -0.00011) || !(y <= 2e-5)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x + (y * (1.0 - x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.00011) or not (y <= 2e-5):
		tmp = y / (y + 1.0)
	else:
		tmp = x + (y * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.00011) || !(y <= 2e-5))
		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 <= -0.00011) || ~((y <= 2e-5)))
		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, -0.00011], N[Not[LessEqual[y, 2e-5]], $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 < -1.10000000000000004e-4 or 2.00000000000000016e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.9%

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

      1. +-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -1.10000000000000004e-4 < y < 2.00000000000000016e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 98.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00011 \lor \neg \left(y \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-61}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.0096:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.25e-6) 1.0 (if (<= y -3e-61) y (if (<= y 0.0096) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.25e-6) {
		tmp = 1.0;
	} else if (y <= -3e-61) {
		tmp = y;
	} else if (y <= 0.0096) {
		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 <= (-1.25d-6)) then
        tmp = 1.0d0
    else if (y <= (-3d-61)) then
        tmp = y
    else if (y <= 0.0096d0) 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 <= -1.25e-6) {
		tmp = 1.0;
	} else if (y <= -3e-61) {
		tmp = y;
	} else if (y <= 0.0096) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.25e-6:
		tmp = 1.0
	elif y <= -3e-61:
		tmp = y
	elif y <= 0.0096:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.25e-6)
		tmp = 1.0;
	elseif (y <= -3e-61)
		tmp = y;
	elseif (y <= 0.0096)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.25e-6)
		tmp = 1.0;
	elseif (y <= -3e-61)
		tmp = y;
	elseif (y <= 0.0096)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.25e-6], 1.0, If[LessEqual[y, -3e-61], y, If[LessEqual[y, 0.0096], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2500000000000001e-6 or 0.00959999999999999916 < 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 -1.2500000000000001e-6 < y < -3.00000000000000012e-61

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 69.9%

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

      1. +-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in y around 0 64.6%

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

   if -3.00000000000000012e-61 < y < 0.00959999999999999916

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 73.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-61}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.0096:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00022 \lor \neg \left(y \leq 6 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.00022) (not (<= y 6e-5))) (/ y (+ y 1.0)) (+ x y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.00022) || !(y <= 6e-5)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x + 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 <= (-0.00022d0)) .or. (.not. (y <= 6d-5))) then
        tmp = y / (y + 1.0d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -0.00022) || !(y <= 6e-5)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.00022) or not (y <= 6e-5):
		tmp = y / (y + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.00022) || !(y <= 6e-5))
		tmp = Float64(y / Float64(y + 1.0));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.00022) || ~((y <= 6e-5)))
		tmp = y / (y + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.00022], N[Not[LessEqual[y, 6e-5]], $MachinePrecision]], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.20000000000000008e-4 or 6.00000000000000015e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.9%

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

      1. +-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -2.20000000000000008e-4 < y < 6.00000000000000015e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.8%

      \[\leadsto \color{blue}{x + \left(y \cdot \left(1 - x\right) + {y}^{2} \cdot \left(x - 1\right)\right)} \]
   4. Step-by-step derivation

      1. unpow2 99.8%

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

      2. associate-*l* 99.8%

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

      3. distribute-lft-out 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 97.9%

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

      1. neg-mul-1 97.9%

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

      2. sub-neg 97.9%

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

   8. Simplified 97.9%

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

   9. Taylor expanded in y around 0 97.3%

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

       1. +-commutative 97.3%

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

   11. Simplified 97.3%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00022 \lor \neg \left(y \leq 6 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 13500000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 13500000.0) (+ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 13500000.0) {
		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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 13500000.0d0) 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 <= -1.0) {
		tmp = 1.0;
	} else if (y <= 13500000.0) {
		tmp = x + y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 13500000.0:
		tmp = x + y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 13500000.0)
		tmp = Float64(x + 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 <= 13500000.0)
		tmp = x + y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 13500000.0], N[(x + y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.35e7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 76.3%

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

   if -1 < y < 1.35e7

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 97.2%

      \[\leadsto \color{blue}{x + \left(y \cdot \left(1 - x\right) + {y}^{2} \cdot \left(x - 1\right)\right)} \]
   4. Step-by-step derivation

      1. unpow2 97.2%

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

      2. associate-*l* 97.2%

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

      3. distribute-lft-out 97.2%

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

      4. sub-neg 97.2%

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

      5. metadata-eval 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in x around 0 95.5%

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

      1. neg-mul-1 95.5%

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

      2. sub-neg 95.5%

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

   8. Simplified 95.5%

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

   9. Taylor expanded in y around 0 94.7%

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

       1. +-commutative 94.7%

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

   11. Simplified 94.7%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 13500000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.0118:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 0.0118) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.0118) {
		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 <= 0.0118d0) 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 <= 0.0118) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 0.0118:
		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 <= 0.0118)
		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 <= 0.0118)
		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, 0.0118], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.0117999999999999997 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 74.4%

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

   if -1 < y < 0.0117999999999999997

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.1%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.0118:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.0% 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 42.0%

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

4. Final simplification 42.0%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))