Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 7.2s

Alternatives: 11

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 99.9%

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

Alternative 2: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+47}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75:\\ \;\;\;\;y \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.4e+47)
   1.0
   (if (<= y -1.0)
     (/ x y)
     (if (<= y 2.15e-23) x (if (<= y 1.75) (* y (- 1.0 y)) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.4e+47) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / y;
	} else if (y <= 2.15e-23) {
		tmp = x;
	} else if (y <= 1.75) {
		tmp = y * (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 <= (-1.4d+47)) then
        tmp = 1.0d0
    else if (y <= (-1.0d0)) then
        tmp = x / y
    else if (y <= 2.15d-23) then
        tmp = x
    else if (y <= 1.75d0) then
        tmp = y * (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 <= -1.4e+47) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / y;
	} else if (y <= 2.15e-23) {
		tmp = x;
	} else if (y <= 1.75) {
		tmp = y * (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.4e+47:
		tmp = 1.0
	elif y <= -1.0:
		tmp = x / y
	elif y <= 2.15e-23:
		tmp = x
	elif y <= 1.75:
		tmp = y * (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.4e+47)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = Float64(x / y);
	elseif (y <= 2.15e-23)
		tmp = x;
	elseif (y <= 1.75)
		tmp = Float64(y * Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.4e+47)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = x / y;
	elseif (y <= 2.15e-23)
		tmp = x;
	elseif (y <= 1.75)
		tmp = y * (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.4e+47], 1.0, If[LessEqual[y, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[y, 2.15e-23], x, If[LessEqual[y, 1.75], N[(y * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.39999999999999994e47 or 1.75 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.0%

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

   if -1.39999999999999994e47 < y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. +-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in y around inf 58.8%

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

   if -1 < y < 2.15000000000000001e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.0%

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

   if 2.15000000000000001e-23 < y < 1.75

   1. Initial program 98.9%

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

   3. Taylor expanded in y around inf 99.1%

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

   4. Taylor expanded in x around 0 85.6%

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

   5. Taylor expanded in y around 0 68.2%

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

      1. neg-mul-1 68.2%

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

      2. sub-neg 68.2%

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

   7. Simplified 68.2%

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

Alternative 3: 85.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -540000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 2400000:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -540000000000.0)
     t_0
     (if (<= y 1.2e-20)
       (/ x (+ y 1.0))
       (if (<= y 2400000.0) (/ y (+ y 1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -540000000000.0) {
		tmp = t_0;
	} else if (y <= 1.2e-20) {
		tmp = x / (y + 1.0);
	} else if (y <= 2400000.0) {
		tmp = y / (y + 1.0);
	} 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 <= (-540000000000.0d0)) then
        tmp = t_0
    else if (y <= 1.2d-20) then
        tmp = x / (y + 1.0d0)
    else if (y <= 2400000.0d0) then
        tmp = y / (y + 1.0d0)
    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 <= -540000000000.0) {
		tmp = t_0;
	} else if (y <= 1.2e-20) {
		tmp = x / (y + 1.0);
	} else if (y <= 2400000.0) {
		tmp = y / (y + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if y <= -540000000000.0:
		tmp = t_0
	elif y <= 1.2e-20:
		tmp = x / (y + 1.0)
	elif y <= 2400000.0:
		tmp = y / (y + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -540000000000.0)
		tmp = t_0;
	elseif (y <= 1.2e-20)
		tmp = Float64(x / Float64(y + 1.0));
	elseif (y <= 2400000.0)
		tmp = Float64(y / Float64(y + 1.0));
	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 <= -540000000000.0)
		tmp = t_0;
	elseif (y <= 1.2e-20)
		tmp = x / (y + 1.0);
	elseif (y <= 2400000.0)
		tmp = y / (y + 1.0);
	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, -540000000000.0], t$95$0, If[LessEqual[y, 1.2e-20], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2400000.0], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4e11 or 2.4e6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around inf 99.0%

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

   5. Taylor expanded in x around 0 99.0%

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

   if -5.4e11 < y < 1.19999999999999996e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.8%

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

      1. +-commutative 77.8%

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

   5. Simplified 77.8%

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

   if 1.19999999999999996e-20 < y < 2.4e6

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 78.2%

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

      1. +-commutative 78.2%

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

   5. Simplified 78.2%

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

Alternative 4: 85.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-24}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;y \leq 0.031:\\ \;\;\;\;y \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -1.0)
     t_0
     (if (<= y 3.05e-24)
       (- x (* x y))
       (if (<= y 0.031) (* y (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 3.05e-24) {
		tmp = x - (x * y);
	} else if (y <= 0.031) {
		tmp = y * (1.0 - y);
	} 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 <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 3.05d-24) then
        tmp = x - (x * y)
    else if (y <= 0.031d0) then
        tmp = y * (1.0d0 - y)
    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 <= -1.0) {
		tmp = t_0;
	} else if (y <= 3.05e-24) {
		tmp = x - (x * y);
	} else if (y <= 0.031) {
		tmp = y * (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 3.05e-24:
		tmp = x - (x * y)
	elif y <= 0.031:
		tmp = y * (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 3.05e-24)
		tmp = Float64(x - Float64(x * y));
	elseif (y <= 0.031)
		tmp = Float64(y * Float64(1.0 - y));
	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 <= -1.0)
		tmp = t_0;
	elseif (y <= 3.05e-24)
		tmp = x - (x * y);
	elseif (y <= 0.031)
		tmp = y * (1.0 - y);
	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, -1.0], t$95$0, If[LessEqual[y, 3.05e-24], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.031], N[(y * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.031 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around inf 96.0%

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

   5. Taylor expanded in x around 0 96.0%

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

   if -1 < y < 3.05000000000000018e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.5%

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

      1. +-commutative 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in y around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. unsub-neg 77.8%

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

      3. *-commutative 77.8%

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

   8. Simplified 77.8%

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

   if 3.05000000000000018e-24 < y < 0.031

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 99.0%

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

   4. Taylor expanded in x around 0 99.7%

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

   5. Taylor expanded in y around 0 78.8%

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

      1. neg-mul-1 78.8%

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

      2. sub-neg 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-24}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;y \leq 0.031:\\ \;\;\;\;y \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.02:\\ \;\;\;\;y \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -1.0)
     t_0
     (if (<= y 4.9e-20) x (if (<= y 0.02) (* y (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 4.9e-20) {
		tmp = x;
	} else if (y <= 0.02) {
		tmp = y * (1.0 - y);
	} 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 <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 4.9d-20) then
        tmp = x
    else if (y <= 0.02d0) then
        tmp = y * (1.0d0 - y)
    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 <= -1.0) {
		tmp = t_0;
	} else if (y <= 4.9e-20) {
		tmp = x;
	} else if (y <= 0.02) {
		tmp = y * (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 4.9e-20:
		tmp = x
	elif y <= 0.02:
		tmp = y * (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 4.9e-20)
		tmp = x;
	elseif (y <= 0.02)
		tmp = Float64(y * Float64(1.0 - y));
	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 <= -1.0)
		tmp = t_0;
	elseif (y <= 4.9e-20)
		tmp = x;
	elseif (y <= 0.02)
		tmp = y * (1.0 - y);
	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, -1.0], t$95$0, If[LessEqual[y, 4.9e-20], x, If[LessEqual[y, 0.02], N[(y * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.0200000000000000004 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around inf 96.0%

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

   5. Taylor expanded in x around 0 96.0%

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

   if -1 < y < 4.9000000000000002e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.0%

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

   if 4.9000000000000002e-20 < y < 0.0200000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 99.0%

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

   4. Taylor expanded in x around 0 99.7%

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

   5. Taylor expanded in y around 0 78.8%

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

      1. neg-mul-1 78.8%

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

      2. sub-neg 78.8%

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

   7. Simplified 78.8%

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

Alternative 6: 98.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 96.8%

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

      1. associate--l+ 96.8%

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

      2. div-sub 96.8%

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

      3. sub-neg 96.8%

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

      4. metadata-eval 96.8%

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

   5. Simplified 96.8%

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

   if -1 < y < 1

   1. Initial program 99.9%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 98.2%

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

      1. neg-mul-1 98.2%

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

      2. sub-neg 98.2%

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

   7. Simplified 98.2%

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

4. Final simplification 97.5%

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

Alternative 7: 98.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.76\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.76))) (+ 1.0 (/ x y)) (* (+ x y) (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.76)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = (x + y) * (1.0 - 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 <= (-1.0d0)) .or. (.not. (y <= 0.76d0))) then
        tmp = 1.0d0 + (x / y)
    else
        tmp = (x + y) * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.76)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = (x + y) * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.76):
		tmp = 1.0 + (x / y)
	else:
		tmp = (x + y) * (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.76))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = Float64(Float64(x + y) * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.76)))
		tmp = 1.0 + (x / y);
	else
		tmp = (x + y) * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.76]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.76000000000000001 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around inf 96.0%

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

   5. Taylor expanded in x around 0 96.0%

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

   if -1 < y < 0.76000000000000001

   1. Initial program 99.9%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 99.7%

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

      2. associate-/r/ 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 98.2%

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

      1. neg-mul-1 98.2%

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

      2. sub-neg 98.2%

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

   7. Simplified 98.2%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.76\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.4e+46) 1.0 (if (<= y -1.0) (/ x y) (if (<= y 7.2e-20) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.4e+46) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / y;
	} else if (y <= 7.2e-20) {
		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 <= (-2.4d+46)) then
        tmp = 1.0d0
    else if (y <= (-1.0d0)) then
        tmp = x / y
    else if (y <= 7.2d-20) 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 <= -2.4e+46) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / y;
	} else if (y <= 7.2e-20) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.4e+46:
		tmp = 1.0
	elif y <= -1.0:
		tmp = x / y
	elif y <= 7.2e-20:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.4e+46)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = Float64(x / y);
	elseif (y <= 7.2e-20)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.4e+46)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = x / y;
	elseif (y <= 7.2e-20)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.4e+46], 1.0, If[LessEqual[y, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[y, 7.2e-20], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000008e46 or 7.19999999999999948e-20 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.5%

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

   if -2.40000000000000008e46 < y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.2%

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

      1. +-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in y around inf 58.8%

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

   if -1 < y < 7.19999999999999948e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.0%

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

Alternative 9: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -540000000000 \lor \neg \left(y \leq 106000000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -540000000000.0) (not (<= y 106000000.0)))
   (+ 1.0 (/ x y))
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -540000000000.0) || !(y <= 106000000.0)) {
		tmp = 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 <= (-540000000000.0d0)) .or. (.not. (y <= 106000000.0d0))) then
        tmp = 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 <= -540000000000.0) || !(y <= 106000000.0)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -540000000000.0) or not (y <= 106000000.0):
		tmp = 1.0 + (x / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -540000000000.0) || !(y <= 106000000.0))
		tmp = Float64(1.0 + Float64(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 <= -540000000000.0) || ~((y <= 106000000.0)))
		tmp = 1.0 + (x / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -540000000000.0], N[Not[LessEqual[y, 106000000.0]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4e11 or 1.06e8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in y around inf 99.3%

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

   5. Taylor expanded in x around 0 99.4%

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

   if -5.4e11 < y < 1.06e8

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.1%

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

      1. +-commutative 74.1%

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

   5. Simplified 74.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -540000000000 \lor \neg \left(y \leq 106000000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 7.2e-20) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 7.2e-20) {
		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 <= 7.2d-20) 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 <= 7.2e-20) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 7.2e-20:
		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 <= 7.2e-20)
		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 <= 7.2e-20)
		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, 7.2e-20], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 7.19999999999999948e-20 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 66.8%

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

   if -1 < y < 7.19999999999999948e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.0%

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

Alternative 11: 38.7% 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 99.9%

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

3. Taylor expanded in y around inf 39.4%

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

Reproduce

herbie shell --seed 2024172 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))