Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 7.5s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 73.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+65}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y -2.5e-36)
     (- y)
     (if (<= y 1.0)
       x
       (if (<= y 1.42e+65) 1.0 (if (<= y 6.5e+103) (/ (- x) y) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -2.5e-36) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 1.42e+65) {
		tmp = 1.0;
	} else if (y <= 6.5e+103) {
		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 <= (-2.5d-36)) then
        tmp = -y
    else if (y <= 1.0d0) then
        tmp = x
    else if (y <= 1.42d+65) then
        tmp = 1.0d0
    else if (y <= 6.5d+103) 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 <= -2.5e-36) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 1.42e+65) {
		tmp = 1.0;
	} else if (y <= 6.5e+103) {
		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 <= -2.5e-36:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	elif y <= 1.42e+65:
		tmp = 1.0
	elif y <= 6.5e+103:
		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 <= -2.5e-36)
		tmp = Float64(-y);
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 1.42e+65)
		tmp = 1.0;
	elseif (y <= 6.5e+103)
		tmp = Float64(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 <= -2.5e-36)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 1.42e+65)
		tmp = 1.0;
	elseif (y <= 6.5e+103)
		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, -2.5e-36], (-y), If[LessEqual[y, 1.0], x, If[LessEqual[y, 1.42e+65], 1.0, If[LessEqual[y, 6.5e+103], N[((-x) / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1 or 1 < y < 1.42000000000000012e65 or 6.50000000000000001e103 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.1%

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

   if -1 < y < -2.50000000000000002e-36

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 89.8%

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

      1. neg-mul-1 89.8%

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

      2. distribute-neg-frac2 89.8%

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

      3. neg-sub0 89.8%

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

      4. associate--r- 89.8%

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

      5. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in y around 0 78.9%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. mul-1-neg 78.9%

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

   8. Simplified 78.9%

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

   if -2.50000000000000002e-36 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.9%

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

   if 1.42000000000000012e65 < y < 6.50000000000000001e103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.1%

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

   4. Taylor expanded in y around inf 84.1%

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

      1. neg-mul-1 84.1%

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

      2. distribute-neg-frac 84.1%

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

   6. Simplified 84.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+65}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -31000.0)
   1.0
   (if (<= y -3.8e-33)
     (* y (- -1.0 y))
     (if (<= y 1.0)
       x
       (if (<= y 5.2e+64) 1.0 (if (<= y 2.8e+104) (/ (- x) y) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -31000.0) {
		tmp = 1.0;
	} else if (y <= -3.8e-33) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 5.2e+64) {
		tmp = 1.0;
	} else if (y <= 2.8e+104) {
		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 <= (-31000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-3.8d-33)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 1.0d0) then
        tmp = x
    else if (y <= 5.2d+64) then
        tmp = 1.0d0
    else if (y <= 2.8d+104) 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 <= -31000.0) {
		tmp = 1.0;
	} else if (y <= -3.8e-33) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 5.2e+64) {
		tmp = 1.0;
	} else if (y <= 2.8e+104) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -31000.0:
		tmp = 1.0
	elif y <= -3.8e-33:
		tmp = y * (-1.0 - y)
	elif y <= 1.0:
		tmp = x
	elif y <= 5.2e+64:
		tmp = 1.0
	elif y <= 2.8e+104:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -31000.0)
		tmp = 1.0;
	elseif (y <= -3.8e-33)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 5.2e+64)
		tmp = 1.0;
	elseif (y <= 2.8e+104)
		tmp = Float64(Float64(-x) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -31000.0)
		tmp = 1.0;
	elseif (y <= -3.8e-33)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 5.2e+64)
		tmp = 1.0;
	elseif (y <= 2.8e+104)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -31000.0], 1.0, If[LessEqual[y, -3.8e-33], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], x, If[LessEqual[y, 5.2e+64], 1.0, If[LessEqual[y, 2.8e+104], N[((-x) / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -31000 or 1 < y < 5.19999999999999994e64 or 2.8e104 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.7%

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

   if -31000 < y < -3.79999999999999994e-33

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 81.7%

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

      1. neg-mul-1 81.7%

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

      2. distribute-neg-frac2 81.7%

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

      3. neg-sub0 81.7%

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

      4. associate--r- 81.7%

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

      5. metadata-eval 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in y around 0 82.1%

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

      1. sub-neg 82.1%

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

      2. mul-1-neg 82.1%

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

      3. metadata-eval 82.1%

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

      4. +-commutative 82.1%

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

      5. unsub-neg 82.1%

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

   8. Simplified 82.1%

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

   if -3.79999999999999994e-33 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.9%

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

   if 5.19999999999999994e64 < y < 2.8e104

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.1%

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

   4. Taylor expanded in y around inf 84.1%

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

      1. neg-mul-1 84.1%

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

      2. distribute-neg-frac 84.1%

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

   6. Simplified 84.1%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 960000000000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+103}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -31000.0)
   1.0
   (if (<= y -3.8e-35)
     (* y (- -1.0 y))
     (if (<= y 960000000000.0)
       (/ x (- 1.0 y))
       (if (<= y 6.4e+64) 1.0 (if (<= y 1.25e+103) (/ (- x) y) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -31000.0) {
		tmp = 1.0;
	} else if (y <= -3.8e-35) {
		tmp = y * (-1.0 - y);
	} else if (y <= 960000000000.0) {
		tmp = x / (1.0 - y);
	} else if (y <= 6.4e+64) {
		tmp = 1.0;
	} else if (y <= 1.25e+103) {
		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 <= (-31000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-3.8d-35)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 960000000000.0d0) then
        tmp = x / (1.0d0 - y)
    else if (y <= 6.4d+64) then
        tmp = 1.0d0
    else if (y <= 1.25d+103) 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 <= -31000.0) {
		tmp = 1.0;
	} else if (y <= -3.8e-35) {
		tmp = y * (-1.0 - y);
	} else if (y <= 960000000000.0) {
		tmp = x / (1.0 - y);
	} else if (y <= 6.4e+64) {
		tmp = 1.0;
	} else if (y <= 1.25e+103) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -31000.0:
		tmp = 1.0
	elif y <= -3.8e-35:
		tmp = y * (-1.0 - y)
	elif y <= 960000000000.0:
		tmp = x / (1.0 - y)
	elif y <= 6.4e+64:
		tmp = 1.0
	elif y <= 1.25e+103:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -31000.0)
		tmp = 1.0;
	elseif (y <= -3.8e-35)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 960000000000.0)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 6.4e+64)
		tmp = 1.0;
	elseif (y <= 1.25e+103)
		tmp = Float64(Float64(-x) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -31000.0)
		tmp = 1.0;
	elseif (y <= -3.8e-35)
		tmp = y * (-1.0 - y);
	elseif (y <= 960000000000.0)
		tmp = x / (1.0 - y);
	elseif (y <= 6.4e+64)
		tmp = 1.0;
	elseif (y <= 1.25e+103)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -31000.0], 1.0, If[LessEqual[y, -3.8e-35], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 960000000000.0], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+64], 1.0, If[LessEqual[y, 1.25e+103], N[((-x) / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -31000 or 9.6e11 < y < 6.40000000000000037e64 or 1.25e103 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.3%

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

   if -31000 < y < -3.8000000000000001e-35

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 81.7%

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

      1. neg-mul-1 81.7%

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

      2. distribute-neg-frac2 81.7%

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

      3. neg-sub0 81.7%

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

      4. associate--r- 81.7%

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

      5. metadata-eval 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in y around 0 82.1%

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

      1. sub-neg 82.1%

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

      2. mul-1-neg 82.1%

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

      3. metadata-eval 82.1%

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

      4. +-commutative 82.1%

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

      5. unsub-neg 82.1%

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

   8. Simplified 82.1%

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

   if -3.8000000000000001e-35 < y < 9.6e11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.7%

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

   if 6.40000000000000037e64 < y < 1.25e103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.1%

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

   4. Taylor expanded in y around inf 84.1%

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

      1. neg-mul-1 84.1%

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

      2. distribute-neg-frac 84.1%

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

   6. Simplified 84.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 960000000000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+103}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -0.98:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 31.5:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 1.0 x) y))))
   (if (<= y -0.98)
     t_0
     (if (<= y -1.6e-39)
       (* y (- -1.0 y))
       (if (<= y 31.5) (/ x (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double tmp;
	if (y <= -0.98) {
		tmp = t_0;
	} else if (y <= -1.6e-39) {
		tmp = y * (-1.0 - y);
	} else if (y <= 31.5) {
		tmp = x / (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 + ((1.0d0 - x) / y)
    if (y <= (-0.98d0)) then
        tmp = t_0
    else if (y <= (-1.6d-39)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 31.5d0) then
        tmp = x / (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 + ((1.0 - x) / y);
	double tmp;
	if (y <= -0.98) {
		tmp = t_0;
	} else if (y <= -1.6e-39) {
		tmp = y * (-1.0 - y);
	} else if (y <= 31.5) {
		tmp = x / (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((1.0 - x) / y)
	tmp = 0
	if y <= -0.98:
		tmp = t_0
	elif y <= -1.6e-39:
		tmp = y * (-1.0 - y)
	elif y <= 31.5:
		tmp = x / (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(1.0 - x) / y))
	tmp = 0.0
	if (y <= -0.98)
		tmp = t_0;
	elseif (y <= -1.6e-39)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 31.5)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((1.0 - x) / y);
	tmp = 0.0;
	if (y <= -0.98)
		tmp = t_0;
	elseif (y <= -1.6e-39)
		tmp = y * (-1.0 - y);
	elseif (y <= 31.5)
		tmp = x / (1.0 - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.98], t$95$0, If[LessEqual[y, -1.6e-39], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 31.5], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.97999999999999998 or 31.5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. sub-neg 98.7%

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

      4. div-sub 98.7%

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

   5. Simplified 98.7%

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

   if -0.97999999999999998 < y < -1.5999999999999999e-39

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 89.8%

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

      1. neg-mul-1 89.8%

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

      2. distribute-neg-frac2 89.8%

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

      3. neg-sub0 89.8%

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

      4. associate--r- 89.8%

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

      5. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in y around 0 89.9%

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

      1. sub-neg 89.9%

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

      2. mul-1-neg 89.9%

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

      3. metadata-eval 89.9%

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

      4. +-commutative 89.9%

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

      5. unsub-neg 89.9%

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

   8. Simplified 89.9%

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

   if -1.5999999999999999e-39 < y < 31.5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.2%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.98:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 31.5:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-35}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y -1.5e-35) (- y) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -1.5e-35) {
		tmp = -y;
	} else if (y <= 1.0) {
		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 <= (-1.5d-35)) then
        tmp = -y
    else if (y <= 1.0d0) 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 <= -1.5e-35) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= -1.5e-35:
		tmp = -y
	elif y <= 1.0:
		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 <= -1.5e-35)
		tmp = Float64(-y);
	elseif (y <= 1.0)
		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 <= -1.5e-35)
		tmp = -y;
	elseif (y <= 1.0)
		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, -1.5e-35], (-y), If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.5%

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

   if -1 < y < -1.49999999999999994e-35

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 89.8%

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

      1. neg-mul-1 89.8%

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

      2. distribute-neg-frac2 89.8%

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

      3. neg-sub0 89.8%

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

      4. associate--r- 89.8%

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

      5. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in y around 0 78.9%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   7. Step-by-step derivation

      1. mul-1-neg 78.9%

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

   8. Simplified 78.9%

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

   if -1.49999999999999994e-35 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-35}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+67} \lor \neg \left(x \leq 7.8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.2e+67) (not (<= x 7.8e-63)))
   (/ x (- 1.0 y))
   (/ y (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.2e+67) || !(x <= 7.8e-63)) {
		tmp = x / (1.0 - y);
	} 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 <= (-3.2d+67)) .or. (.not. (x <= 7.8d-63))) then
        tmp = x / (1.0d0 - y)
    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 <= -3.2e+67) || !(x <= 7.8e-63)) {
		tmp = x / (1.0 - y);
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.2e+67) or not (x <= 7.8e-63):
		tmp = x / (1.0 - y)
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.2e+67) || !(x <= 7.8e-63))
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.2e+67) || ~((x <= 7.8e-63)))
		tmp = x / (1.0 - y);
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.2e+67], N[Not[LessEqual[x, 7.8e-63]], $MachinePrecision]], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999983e67 or 7.80000000000000044e-63 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.7%

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

   if -3.19999999999999983e67 < x < 7.80000000000000044e-63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. neg-mul-1 80.0%

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

      2. distribute-neg-frac2 80.0%

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

      3. neg-sub0 80.0%

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

      4. associate--r- 80.0%

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

      5. metadata-eval 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+67} \lor \neg \left(x \leq 7.8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -5e-14) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e-14) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		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 <= (-5d-14)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) 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 <= -5e-14) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e-14:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e-14)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e-14)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e-14], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000002e-14 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 70.1%

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

   if -5.0000000000000002e-14 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 100.0%

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

3. Taylor expanded in y around inf 37.3%

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

4. Final simplification 37.3%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))