Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 8.2s

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, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{y}{y + 1} + \frac{x}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (/ y (+ y 1.0)) (/ x (+ y 1.0))))

C

double code(double x, double y) {
	return (y / (y + 1.0)) + (x / (y + 1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y / (y + 1.0d0)) + (x / (y + 1.0d0))
end function

Java

public static double code(double x, double y) {
	return (y / (y + 1.0)) + (x / (y + 1.0));
}

Python

def code(x, y):
	return (y / (y + 1.0)) + (x / (y + 1.0))

Julia

function code(x, y)
	return Float64(Float64(y / Float64(y + 1.0)) + Float64(x / Float64(y + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = (y / (y + 1.0)) + (x / (y + 1.0));
end

Wolfram

code[x_, y_] := N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 100.0%

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

   1. +-commutative 100.0%

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

   2. +-commutative 100.0%

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

   3. +-commutative 100.0%

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

5. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{y}{y + 1} + \frac{x}{y + 1}} \]
6. Add Preprocessing

Alternative 2: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ t_1 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -70000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 27000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))) (t_1 (/ x (+ y 1.0))))
   (if (<= y -70000000.0)
     t_0
     (if (<= y -8.5e-43)
       t_1
       (if (<= y -1.6e-110) (/ y (+ y 1.0)) (if (<= y 27000000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -70000000.0) {
		tmp = t_0;
	} else if (y <= -8.5e-43) {
		tmp = t_1;
	} else if (y <= -1.6e-110) {
		tmp = y / (y + 1.0);
	} else if (y <= 27000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    t_1 = x / (y + 1.0d0)
    if (y <= (-70000000.0d0)) then
        tmp = t_0
    else if (y <= (-8.5d-43)) then
        tmp = t_1
    else if (y <= (-1.6d-110)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 27000000.0d0) then
        tmp = t_1
    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 t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -70000000.0) {
		tmp = t_0;
	} else if (y <= -8.5e-43) {
		tmp = t_1;
	} else if (y <= -1.6e-110) {
		tmp = y / (y + 1.0);
	} else if (y <= 27000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	t_1 = x / (y + 1.0)
	tmp = 0
	if y <= -70000000.0:
		tmp = t_0
	elif y <= -8.5e-43:
		tmp = t_1
	elif y <= -1.6e-110:
		tmp = y / (y + 1.0)
	elif y <= 27000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	t_1 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -70000000.0)
		tmp = t_0;
	elseif (y <= -8.5e-43)
		tmp = t_1;
	elseif (y <= -1.6e-110)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 27000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	t_1 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -70000000.0)
		tmp = t_0;
	elseif (y <= -8.5e-43)
		tmp = t_1;
	elseif (y <= -1.6e-110)
		tmp = y / (y + 1.0);
	elseif (y <= 27000000.0)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -70000000.0], t$95$0, If[LessEqual[y, -8.5e-43], t$95$1, If[LessEqual[y, -1.6e-110], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 27000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e7 or 2.7e7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.6%

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

   7. Taylor expanded in y around inf 99.0%

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

   if -7e7 < y < -8.50000000000000056e-43 or -1.60000000000000014e-110 < y < 2.7e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.7%

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

      1. +-commutative 76.7%

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

   5. Simplified 76.7%

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

   if -8.50000000000000056e-43 < y < -1.60000000000000014e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

Alternative 3: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ t_1 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -1100000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-110}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 30000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))) (t_1 (/ x (+ y 1.0))))
   (if (<= y -1100000.0)
     t_0
     (if (<= y -5.5e-43)
       t_1
       (if (<= y -1.6e-110) y (if (<= y 30000000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -1100000.0) {
		tmp = t_0;
	} else if (y <= -5.5e-43) {
		tmp = t_1;
	} else if (y <= -1.6e-110) {
		tmp = y;
	} else if (y <= 30000000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    t_1 = x / (y + 1.0d0)
    if (y <= (-1100000.0d0)) then
        tmp = t_0
    else if (y <= (-5.5d-43)) then
        tmp = t_1
    else if (y <= (-1.6d-110)) then
        tmp = y
    else if (y <= 30000000.0d0) then
        tmp = t_1
    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 t_1 = x / (y + 1.0);
	double tmp;
	if (y <= -1100000.0) {
		tmp = t_0;
	} else if (y <= -5.5e-43) {
		tmp = t_1;
	} else if (y <= -1.6e-110) {
		tmp = y;
	} else if (y <= 30000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	t_1 = x / (y + 1.0)
	tmp = 0
	if y <= -1100000.0:
		tmp = t_0
	elif y <= -5.5e-43:
		tmp = t_1
	elif y <= -1.6e-110:
		tmp = y
	elif y <= 30000000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	t_1 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -1100000.0)
		tmp = t_0;
	elseif (y <= -5.5e-43)
		tmp = t_1;
	elseif (y <= -1.6e-110)
		tmp = y;
	elseif (y <= 30000000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	t_1 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -1100000.0)
		tmp = t_0;
	elseif (y <= -5.5e-43)
		tmp = t_1;
	elseif (y <= -1.6e-110)
		tmp = y;
	elseif (y <= 30000000.0)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1100000.0], t$95$0, If[LessEqual[y, -5.5e-43], t$95$1, If[LessEqual[y, -1.6e-110], y, If[LessEqual[y, 30000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e6 or 3e7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.6%

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

   7. Taylor expanded in y around inf 99.0%

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

   if -1.1e6 < y < -5.50000000000000013e-43 or -1.60000000000000014e-110 < y < 3e7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.7%

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

      1. +-commutative 76.7%

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

   5. Simplified 76.7%

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

   if -5.50000000000000013e-43 < y < -1.60000000000000014e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in y around 0 74.6%

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

Alternative 4: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ t_1 := x - y \cdot x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-110}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.08:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))) (t_1 (- x (* y x))))
   (if (<= y -1.0)
     t_0
     (if (<= y -2.4e-42)
       t_1
       (if (<= y -1.6e-110) y (if (<= y 0.08) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double t_1 = x - (y * x);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -2.4e-42) {
		tmp = t_1;
	} else if (y <= -1.6e-110) {
		tmp = y;
	} else if (y <= 0.08) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    t_1 = x - (y * x)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-2.4d-42)) then
        tmp = t_1
    else if (y <= (-1.6d-110)) then
        tmp = y
    else if (y <= 0.08d0) then
        tmp = t_1
    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 t_1 = x - (y * x);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -2.4e-42) {
		tmp = t_1;
	} else if (y <= -1.6e-110) {
		tmp = y;
	} else if (y <= 0.08) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	t_1 = x - (y * x)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= -2.4e-42:
		tmp = t_1
	elif y <= -1.6e-110:
		tmp = y
	elif y <= 0.08:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	t_1 = Float64(x - Float64(y * x))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -2.4e-42)
		tmp = t_1;
	elseif (y <= -1.6e-110)
		tmp = y;
	elseif (y <= 0.08)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	t_1 = x - (y * x);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -2.4e-42)
		tmp = t_1;
	elseif (y <= -1.6e-110)
		tmp = y;
	elseif (y <= 0.08)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -2.4e-42], t$95$1, If[LessEqual[y, -1.6e-110], y, If[LessEqual[y, 0.08], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.0800000000000000017 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.1%

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

   7. Taylor expanded in y around inf 97.3%

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

   if -1 < y < -2.40000000000000003e-42 or -1.60000000000000014e-110 < y < 0.0800000000000000017

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.7%

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

      1. +-commutative 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in y around 0 76.4%

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

      1. associate-*r* 76.4%

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

      2. neg-mul-1 76.4%

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

   8. Simplified 76.4%

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

      1. distribute-lft-neg-out 76.4%

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

      2. unsub-neg 76.4%

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

      3. *-commutative 76.4%

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

   10. Applied egg-rr 76.4%

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

   if -2.40000000000000003e-42 < y < -1.60000000000000014e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in y around 0 74.6%

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

Alternative 5: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-110}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.0135:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -1.0)
     t_0
     (if (<= y -1.3e-41) x (if (<= y -1.6e-110) y (if (<= y 0.0135) x 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 <= -1.3e-41) {
		tmp = x;
	} else if (y <= -1.6e-110) {
		tmp = y;
	} else if (y <= 0.0135) {
		tmp = x;
	} 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 <= (-1.3d-41)) then
        tmp = x
    else if (y <= (-1.6d-110)) then
        tmp = y
    else if (y <= 0.0135d0) then
        tmp = x
    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 <= -1.3e-41) {
		tmp = x;
	} else if (y <= -1.6e-110) {
		tmp = y;
	} else if (y <= 0.0135) {
		tmp = x;
	} 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 <= -1.3e-41:
		tmp = x
	elif y <= -1.6e-110:
		tmp = y
	elif y <= 0.0135:
		tmp = x
	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 <= -1.3e-41)
		tmp = x;
	elseif (y <= -1.6e-110)
		tmp = y;
	elseif (y <= 0.0135)
		tmp = x;
	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 <= -1.3e-41)
		tmp = x;
	elseif (y <= -1.6e-110)
		tmp = y;
	elseif (y <= 0.0135)
		tmp = x;
	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, -1.3e-41], x, If[LessEqual[y, -1.6e-110], y, If[LessEqual[y, 0.0135], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.0134999999999999998 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.1%

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

   7. Taylor expanded in y around inf 97.3%

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

   if -1 < y < -1.3e-41 or -1.60000000000000014e-110 < y < 0.0134999999999999998

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.4%

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

   if -1.3e-41 < y < -1.60000000000000014e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in y around 0 74.6%

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

Alternative 6: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-110}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 27000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y -3.5e-43)
     x
     (if (<= y -1.6e-110) y (if (<= y 27000000.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -3.5e-43) {
		tmp = x;
	} else if (y <= -1.6e-110) {
		tmp = y;
	} else if (y <= 27000000.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= (-3.5d-43)) then
        tmp = x
    else if (y <= (-1.6d-110)) then
        tmp = y
    else if (y <= 27000000.0d0) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -3.5e-43) {
		tmp = x;
	} else if (y <= -1.6e-110) {
		tmp = y;
	} else if (y <= 27000000.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= -3.5e-43:
		tmp = x
	elif y <= -1.6e-110:
		tmp = y
	elif y <= 27000000.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= -3.5e-43)
		tmp = x;
	elseif (y <= -1.6e-110)
		tmp = y;
	elseif (y <= 27000000.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= -3.5e-43)
		tmp = x;
	elseif (y <= -1.6e-110)
		tmp = y;
	elseif (y <= 27000000.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, -3.5e-43], x, If[LessEqual[y, -1.6e-110], y, If[LessEqual[y, 27000000.0], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 2.7e7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.1%

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

   if -1 < y < -3.49999999999999997e-43 or -1.60000000000000014e-110 < y < 2.7e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.8%

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

   if -3.49999999999999997e-43 < y < -1.60000000000000014e-110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in y around 0 74.6%

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

Alternative 7: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-5} \lor \neg \left(y \leq 3.15 \cdot 10^{-6}\right):\\ \;\;\;\;1 + \frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.9e-5) (not (<= y 3.15e-6)))
   (+ 1.0 (/ x (+ y 1.0)))
   (+ x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.9e-5) || !(y <= 3.15e-6)) {
		tmp = 1.0 + (x / (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 <= (-1.9d-5)) .or. (.not. (y <= 3.15d-6))) then
        tmp = 1.0d0 + (x / (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 <= -1.9e-5) || !(y <= 3.15e-6)) {
		tmp = 1.0 + (x / (y + 1.0));
	} else {
		tmp = x + (y * (1.0 - x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.9e-5) or not (y <= 3.15e-6):
		tmp = 1.0 + (x / (y + 1.0))
	else:
		tmp = x + (y * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.9e-5) || !(y <= 3.15e-6))
		tmp = Float64(1.0 + Float64(x / 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 <= -1.9e-5) || ~((y <= 3.15e-6)))
		tmp = 1.0 + (x / (y + 1.0));
	else
		tmp = x + (y * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.9e-5], N[Not[LessEqual[y, 3.15e-6]], $MachinePrecision]], N[(1.0 + N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e-5 or 3.14999999999999991e-6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.1%

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

   if -1.9000000000000001e-5 < y < 3.14999999999999991e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-5} \lor \neg \left(y \leq 3.15 \cdot 10^{-6}\right):\\ \;\;\;\;1 + \frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -500000 \lor \neg \left(x \leq 3.4 \cdot 10^{-69}\right):\\ \;\;\;\;1 + \frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -500000.0) (not (<= x 3.4e-69)))
   (+ 1.0 (/ x (+ y 1.0)))
   (/ y (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -500000.0) || !(x <= 3.4e-69)) {
		tmp = 1.0 + (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 <= (-500000.0d0)) .or. (.not. (x <= 3.4d-69))) then
        tmp = 1.0d0 + (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 <= -500000.0) || !(x <= 3.4e-69)) {
		tmp = 1.0 + (x / (y + 1.0));
	} else {
		tmp = y / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -500000.0) or not (x <= 3.4e-69):
		tmp = 1.0 + (x / (y + 1.0))
	else:
		tmp = y / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -500000.0) || !(x <= 3.4e-69))
		tmp = Float64(1.0 + 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 <= -500000.0) || ~((x <= 3.4e-69)))
		tmp = 1.0 + (x / (y + 1.0));
	else
		tmp = y / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -500000.0], N[Not[LessEqual[x, 3.4e-69]], $MachinePrecision]], N[(1.0 + N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5e5 or 3.40000000000000008e-69 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 95.0%

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

   if -5e5 < x < 3.40000000000000008e-69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.0%

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

      1. +-commutative 85.0%

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

   5. Simplified 85.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -500000 \lor \neg \left(x \leq 3.4 \cdot 10^{-69}\right):\\ \;\;\;\;1 + \frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 27000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 27000000.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 27000000.0) {
		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 <= 27000000.0d0) 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 <= 27000000.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 27000000.0:
		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 <= 27000000.0)
		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 <= 27000000.0)
		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, 27000000.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.7e7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.1%

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

   if -1 < y < 2.7e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.6%

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

Alternative 10: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y + x}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ y x) (+ y 1.0)))

C

double code(double x, double y) {
	return (y + x) / (y + 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + x) / (y + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (y + x) / (y + 1.0);
}

Python

def code(x, y):
	return (y + x) / (y + 1.0)

Julia

function code(x, y)
	return Float64(Float64(y + x) / Float64(y + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (y + x) / (y + 1.0);
end

Wolfram

code[x_, y_] := N[(N[(y + x), $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%

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

Alternative 11: 38.8% 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 40.3%

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))