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

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 8

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: 71.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{y}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+158}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -0.21:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-7}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+69}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x) y)))
   (if (<= y -4.4e+158)
     1.0
     (if (<= y -3e+106)
       t_0
       (if (<= y -0.21)
         1.0
         (if (<= y 1.52e-30)
           x
           (if (<= y 6.8e-7)
             (- y)
             (if (<= y 1.0) x (if (<= y 2.9e+69) t_0 1.0)))))))))

C

double code(double x, double y) {
	double t_0 = -x / y;
	double tmp;
	if (y <= -4.4e+158) {
		tmp = 1.0;
	} else if (y <= -3e+106) {
		tmp = t_0;
	} else if (y <= -0.21) {
		tmp = 1.0;
	} else if (y <= 1.52e-30) {
		tmp = x;
	} else if (y <= 6.8e-7) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 2.9e+69) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -x / y
    if (y <= (-4.4d+158)) then
        tmp = 1.0d0
    else if (y <= (-3d+106)) then
        tmp = t_0
    else if (y <= (-0.21d0)) then
        tmp = 1.0d0
    else if (y <= 1.52d-30) then
        tmp = x
    else if (y <= 6.8d-7) then
        tmp = -y
    else if (y <= 1.0d0) then
        tmp = x
    else if (y <= 2.9d+69) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -x / y;
	double tmp;
	if (y <= -4.4e+158) {
		tmp = 1.0;
	} else if (y <= -3e+106) {
		tmp = t_0;
	} else if (y <= -0.21) {
		tmp = 1.0;
	} else if (y <= 1.52e-30) {
		tmp = x;
	} else if (y <= 6.8e-7) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 2.9e+69) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -x / y
	tmp = 0
	if y <= -4.4e+158:
		tmp = 1.0
	elif y <= -3e+106:
		tmp = t_0
	elif y <= -0.21:
		tmp = 1.0
	elif y <= 1.52e-30:
		tmp = x
	elif y <= 6.8e-7:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	elif y <= 2.9e+69:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-x) / y)
	tmp = 0.0
	if (y <= -4.4e+158)
		tmp = 1.0;
	elseif (y <= -3e+106)
		tmp = t_0;
	elseif (y <= -0.21)
		tmp = 1.0;
	elseif (y <= 1.52e-30)
		tmp = x;
	elseif (y <= 6.8e-7)
		tmp = Float64(-y);
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 2.9e+69)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -x / y;
	tmp = 0.0;
	if (y <= -4.4e+158)
		tmp = 1.0;
	elseif (y <= -3e+106)
		tmp = t_0;
	elseif (y <= -0.21)
		tmp = 1.0;
	elseif (y <= 1.52e-30)
		tmp = x;
	elseif (y <= 6.8e-7)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 2.9e+69)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[((-x) / y), $MachinePrecision]}, If[LessEqual[y, -4.4e+158], 1.0, If[LessEqual[y, -3e+106], t$95$0, If[LessEqual[y, -0.21], 1.0, If[LessEqual[y, 1.52e-30], x, If[LessEqual[y, 6.8e-7], (-y), If[LessEqual[y, 1.0], x, If[LessEqual[y, 2.9e+69], t$95$0, 1.0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4000000000000002e158 or -3.0000000000000001e106 < y < -0.209999999999999992 or 2.8999999999999998e69 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 76.4%

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

   if -4.4000000000000002e158 < y < -3.0000000000000001e106 or 1 < y < 2.8999999999999998e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 69.3%

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

   4. Taylor expanded in y around inf 64.6%

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

      1. associate-*r/ 64.6%

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

      2. neg-mul-1 64.6%

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

   6. Simplified 64.6%

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

   if -0.209999999999999992 < y < 1.52e-30 or 6.79999999999999948e-7 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.0%

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

   if 1.52e-30 < y < 6.79999999999999948e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. metadata-eval 100.0%

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

      2. times-frac 100.0%

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

      3. *-lft-identity 100.0%

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

      4. neg-mul-1 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate--r- 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.2%

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

      1. neg-mul-1 89.2%

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

   8. Simplified 89.2%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+158}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+106}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -0.21:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-7}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+69}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+158}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+107}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+57}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+69}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= y -4.5e+158)
     1.0
     (if (<= y -1.3e+107)
       (/ (- x) y)
       (if (<= y -7.5e+57)
         1.0
         (if (<= y 3.7e-30)
           t_0
           (if (<= y 3.9e-7) (- y) (if (<= y 2.8e+69) t_0 1.0))))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -4.5e+158) {
		tmp = 1.0;
	} else if (y <= -1.3e+107) {
		tmp = -x / y;
	} else if (y <= -7.5e+57) {
		tmp = 1.0;
	} else if (y <= 3.7e-30) {
		tmp = t_0;
	} else if (y <= 3.9e-7) {
		tmp = -y;
	} else if (y <= 2.8e+69) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - y)
    if (y <= (-4.5d+158)) then
        tmp = 1.0d0
    else if (y <= (-1.3d+107)) then
        tmp = -x / y
    else if (y <= (-7.5d+57)) then
        tmp = 1.0d0
    else if (y <= 3.7d-30) then
        tmp = t_0
    else if (y <= 3.9d-7) then
        tmp = -y
    else if (y <= 2.8d+69) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -4.5e+158) {
		tmp = 1.0;
	} else if (y <= -1.3e+107) {
		tmp = -x / y;
	} else if (y <= -7.5e+57) {
		tmp = 1.0;
	} else if (y <= 3.7e-30) {
		tmp = t_0;
	} else if (y <= 3.9e-7) {
		tmp = -y;
	} else if (y <= 2.8e+69) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if y <= -4.5e+158:
		tmp = 1.0
	elif y <= -1.3e+107:
		tmp = -x / y
	elif y <= -7.5e+57:
		tmp = 1.0
	elif y <= 3.7e-30:
		tmp = t_0
	elif y <= 3.9e-7:
		tmp = -y
	elif y <= 2.8e+69:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (y <= -4.5e+158)
		tmp = 1.0;
	elseif (y <= -1.3e+107)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= -7.5e+57)
		tmp = 1.0;
	elseif (y <= 3.7e-30)
		tmp = t_0;
	elseif (y <= 3.9e-7)
		tmp = Float64(-y);
	elseif (y <= 2.8e+69)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (1.0 - y);
	tmp = 0.0;
	if (y <= -4.5e+158)
		tmp = 1.0;
	elseif (y <= -1.3e+107)
		tmp = -x / y;
	elseif (y <= -7.5e+57)
		tmp = 1.0;
	elseif (y <= 3.7e-30)
		tmp = t_0;
	elseif (y <= 3.9e-7)
		tmp = -y;
	elseif (y <= 2.8e+69)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+158], 1.0, If[LessEqual[y, -1.3e+107], N[((-x) / y), $MachinePrecision], If[LessEqual[y, -7.5e+57], 1.0, If[LessEqual[y, 3.7e-30], t$95$0, If[LessEqual[y, 3.9e-7], (-y), If[LessEqual[y, 2.8e+69], t$95$0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.50000000000000046e158 or -1.3000000000000001e107 < y < -7.5000000000000006e57 or 2.79999999999999982e69 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.5%

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

   if -4.50000000000000046e158 < y < -1.3000000000000001e107

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.3%

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

   4. Taylor expanded in y around inf 76.3%

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

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

   6. Simplified 76.3%

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

   if -7.5000000000000006e57 < y < 3.7000000000000003e-30 or 3.90000000000000025e-7 < y < 2.79999999999999982e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 67.0%

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

   if 3.7000000000000003e-30 < y < 3.90000000000000025e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. metadata-eval 100.0%

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

      2. times-frac 100.0%

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

      3. *-lft-identity 100.0%

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

      4. neg-mul-1 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate--r- 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.2%

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

      1. neg-mul-1 89.2%

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

   8. Simplified 89.2%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+158}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+107}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+57}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ t_1 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -36000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 1.0 x) y))) (t_1 (/ x (- 1.0 y))))
   (if (<= y -36000000000.0)
     t_0
     (if (<= y 1.3e-30)
       t_1
       (if (<= y 3.9e-7) (/ y (+ y -1.0)) (if (<= y 2.3e+14) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (y <= -36000000000.0) {
		tmp = t_0;
	} else if (y <= 1.3e-30) {
		tmp = t_1;
	} else if (y <= 3.9e-7) {
		tmp = y / (y + -1.0);
	} else if (y <= 2.3e+14) {
		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 + ((1.0d0 - x) / y)
    t_1 = x / (1.0d0 - y)
    if (y <= (-36000000000.0d0)) then
        tmp = t_0
    else if (y <= 1.3d-30) then
        tmp = t_1
    else if (y <= 3.9d-7) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 2.3d+14) 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 + ((1.0 - x) / y);
	double t_1 = x / (1.0 - y);
	double tmp;
	if (y <= -36000000000.0) {
		tmp = t_0;
	} else if (y <= 1.3e-30) {
		tmp = t_1;
	} else if (y <= 3.9e-7) {
		tmp = y / (y + -1.0);
	} else if (y <= 2.3e+14) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((1.0 - x) / y)
	t_1 = x / (1.0 - y)
	tmp = 0
	if y <= -36000000000.0:
		tmp = t_0
	elif y <= 1.3e-30:
		tmp = t_1
	elif y <= 3.9e-7:
		tmp = y / (y + -1.0)
	elif y <= 2.3e+14:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(1.0 - x) / y))
	t_1 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (y <= -36000000000.0)
		tmp = t_0;
	elseif (y <= 1.3e-30)
		tmp = t_1;
	elseif (y <= 3.9e-7)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 2.3e+14)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((1.0 - x) / y);
	t_1 = x / (1.0 - y);
	tmp = 0.0;
	if (y <= -36000000000.0)
		tmp = t_0;
	elseif (y <= 1.3e-30)
		tmp = t_1;
	elseif (y <= 3.9e-7)
		tmp = y / (y + -1.0);
	elseif (y <= 2.3e+14)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -36000000000.0], t$95$0, If[LessEqual[y, 1.3e-30], t$95$1, If[LessEqual[y, 3.9e-7], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+14], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e10 or 2.3e14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. div-sub 100.0%

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

   5. Simplified 100.0%

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

   if -3.6e10 < y < 1.29999999999999993e-30 or 3.90000000000000025e-7 < y < 2.3e14

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 68.7%

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

   if 1.29999999999999993e-30 < y < 3.90000000000000025e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. metadata-eval 100.0%

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

      2. times-frac 100.0%

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

      3. *-lft-identity 100.0%

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

      4. neg-mul-1 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate--r- 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -36000000000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.5)
   1.0
   (if (<= y 5.5e-30) x (if (<= y 8e-7) (- y) (if (<= y 1.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.5) {
		tmp = 1.0;
	} else if (y <= 5.5e-30) {
		tmp = x;
	} else if (y <= 8e-7) {
		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 <= (-3.5d0)) then
        tmp = 1.0d0
    else if (y <= 5.5d-30) then
        tmp = x
    else if (y <= 8d-7) 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 <= -3.5) {
		tmp = 1.0;
	} else if (y <= 5.5e-30) {
		tmp = x;
	} else if (y <= 8e-7) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.5:
		tmp = 1.0
	elif y <= 5.5e-30:
		tmp = x
	elif y <= 8e-7:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.5)
		tmp = 1.0;
	elseif (y <= 5.5e-30)
		tmp = x;
	elseif (y <= 8e-7)
		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 <= -3.5)
		tmp = 1.0;
	elseif (y <= 5.5e-30)
		tmp = x;
	elseif (y <= 8e-7)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.5], 1.0, If[LessEqual[y, 5.5e-30], x, If[LessEqual[y, 8e-7], (-y), If[LessEqual[y, 1.0], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 66.9%

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

   if -3.5 < y < 5.49999999999999976e-30 or 7.9999999999999996e-7 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.0%

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

   if 5.49999999999999976e-30 < y < 7.9999999999999996e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. metadata-eval 100.0%

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

      2. times-frac 100.0%

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

      3. *-lft-identity 100.0%

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

      4. neg-mul-1 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate--r- 100.0%

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

      7. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 89.2%

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

      1. neg-mul-1 89.2%

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

   8. Simplified 89.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-37} \lor \neg \left(x \leq 6 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7e-37) (not (<= x 6e+35))) (/ x (- 1.0 y)) (/ y (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7e-37) || !(x <= 6e+35)) {
		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 <= (-7d-37)) .or. (.not. (x <= 6d+35))) 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 <= -7e-37) || !(x <= 6e+35)) {
		tmp = x / (1.0 - y);
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7e-37) or not (x <= 6e+35):
		tmp = x / (1.0 - y)
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7e-37) || !(x <= 6e+35))
		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 <= -7e-37) || ~((x <= 6e+35)))
		tmp = x / (1.0 - y);
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7e-37], N[Not[LessEqual[x, 6e+35]], $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 < -7.0000000000000003e-37 or 5.99999999999999981e35 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.0%

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

   if -7.0000000000000003e-37 < x < 5.99999999999999981e35

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.8%

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

      1. metadata-eval 80.8%

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

      2. times-frac 80.8%

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

      3. *-lft-identity 80.8%

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

      4. neg-mul-1 80.8%

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

      5. neg-sub0 80.8%

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

      6. associate--r- 80.8%

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

      7. metadata-eval 80.8%

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

   5. Simplified 80.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-37} \lor \neg \left(x \leq 6 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -3.5) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.5) {
		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 <= (-3.5d0)) 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 <= -3.5) {
		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 <= -3.5:
		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 <= -3.5)
		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 <= -3.5)
		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, -3.5], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 66.9%

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

   if -3.5 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 64.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.2% 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 36.3%

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

4. Final simplification 36.3%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))