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

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 7

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: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+51}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= y -2.7e+36)
     1.0
     (if (<= y -1.12e-10)
       t_0
       (if (<= y -1.45e-29) (* y (- -1.0 y)) (if (<= y 1.1e+51) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -2.7e+36) {
		tmp = 1.0;
	} else if (y <= -1.12e-10) {
		tmp = t_0;
	} else if (y <= -1.45e-29) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.1e+51) {
		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 <= (-2.7d+36)) then
        tmp = 1.0d0
    else if (y <= (-1.12d-10)) then
        tmp = t_0
    else if (y <= (-1.45d-29)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 1.1d+51) 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 <= -2.7e+36) {
		tmp = 1.0;
	} else if (y <= -1.12e-10) {
		tmp = t_0;
	} else if (y <= -1.45e-29) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.1e+51) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if y <= -2.7e+36:
		tmp = 1.0
	elif y <= -1.12e-10:
		tmp = t_0
	elif y <= -1.45e-29:
		tmp = y * (-1.0 - y)
	elif y <= 1.1e+51:
		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 <= -2.7e+36)
		tmp = 1.0;
	elseif (y <= -1.12e-10)
		tmp = t_0;
	elseif (y <= -1.45e-29)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 1.1e+51)
		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 <= -2.7e+36)
		tmp = 1.0;
	elseif (y <= -1.12e-10)
		tmp = t_0;
	elseif (y <= -1.45e-29)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.1e+51)
		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, -2.7e+36], 1.0, If[LessEqual[y, -1.12e-10], t$95$0, If[LessEqual[y, -1.45e-29], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+51], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7000000000000001e36 or 1.09999999999999996e51 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.7%

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

   if -2.7000000000000001e36 < y < -1.12e-10 or -1.45000000000000012e-29 < y < 1.09999999999999996e51

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.8%

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

   if -1.12e-10 < y < -1.45000000000000012e-29

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.7%

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

      1. neg-mul-1 85.7%

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

      2. distribute-neg-frac2 85.7%

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

      3. neg-sub0 85.7%

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

      4. associate--r- 85.7%

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

      5. metadata-eval 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in y around 0 85.9%

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

      1. sub-neg 85.9%

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

      2. neg-mul-1 85.9%

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

      3. metadata-eval 85.9%

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

      4. +-commutative 85.9%

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

      5. sub-neg 85.9%

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

   8. Simplified 85.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.2:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.55e+35)
   1.0
   (if (<= y -0.2)
     (/ (- x) y)
     (if (<= y -3.1e-35) (* y (- -1.0 y)) (if (<= y 1.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.55e+35) {
		tmp = 1.0;
	} else if (y <= -0.2) {
		tmp = -x / y;
	} else if (y <= -3.1e-35) {
		tmp = y * (-1.0 - 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 <= (-1.55d+35)) then
        tmp = 1.0d0
    else if (y <= (-0.2d0)) then
        tmp = -x / y
    else if (y <= (-3.1d-35)) then
        tmp = y * ((-1.0d0) - 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 <= -1.55e+35) {
		tmp = 1.0;
	} else if (y <= -0.2) {
		tmp = -x / y;
	} else if (y <= -3.1e-35) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.55e+35:
		tmp = 1.0
	elif y <= -0.2:
		tmp = -x / y
	elif y <= -3.1e-35:
		tmp = y * (-1.0 - y)
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.55e+35)
		tmp = 1.0;
	elseif (y <= -0.2)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= -3.1e-35)
		tmp = Float64(y * Float64(-1.0 - 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 <= -1.55e+35)
		tmp = 1.0;
	elseif (y <= -0.2)
		tmp = -x / y;
	elseif (y <= -3.1e-35)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.55e+35], 1.0, If[LessEqual[y, -0.2], N[((-x) / y), $MachinePrecision], If[LessEqual[y, -3.1e-35], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], x, 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.54999999999999993e35 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.4%

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

   if -1.54999999999999993e35 < y < -0.20000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.2%

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

   4. Taylor expanded in y around inf 60.0%

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

      1. associate-*r/ 60.0%

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

      2. neg-mul-1 60.0%

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

   6. Simplified 60.0%

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

   if -0.20000000000000001 < y < -3.10000000000000012e-35

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 70.8%

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

      1. neg-mul-1 70.8%

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

      2. distribute-neg-frac2 70.8%

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

      3. neg-sub0 70.8%

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

      4. associate--r- 70.8%

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

      5. metadata-eval 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in y around 0 67.3%

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

      1. sub-neg 67.3%

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

      2. neg-mul-1 67.3%

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

      3. metadata-eval 67.3%

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

      4. +-commutative 67.3%

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

      5. sub-neg 67.3%

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

   8. Simplified 67.3%

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

   if -3.10000000000000012e-35 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.2:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-35}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.75e+37) 1.0 (if (<= y -1.0) (/ (- x) y) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.75e+37) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = -x / 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 <= (-1.75d+37)) then
        tmp = 1.0d0
    else if (y <= (-1.0d0)) then
        tmp = -x / 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 <= -1.75e+37) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = -x / y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.75e+37:
		tmp = 1.0
	elif y <= -1.0:
		tmp = -x / y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.75e+37)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = Float64(Float64(-x) / 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 <= -1.75e+37)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = -x / y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.75e+37], 1.0, If[LessEqual[y, -1.0], N[((-x) / y), $MachinePrecision], If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.75e37 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.4%

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

   if -1.75e37 < y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.5%

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

   4. Taylor expanded in y around inf 65.4%

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

      1. associate-*r/ 65.4%

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

      2. neg-mul-1 65.4%

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

   6. Simplified 65.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+33} \lor \neg \left(x \leq 1.5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3e+33) (not (<= x 1.5e+39))) (/ x (- 1.0 y)) (/ y (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3e+33) || !(x <= 1.5e+39)) {
		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 <= (-3d+33)) .or. (.not. (x <= 1.5d+39))) 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 <= -3e+33) || !(x <= 1.5e+39)) {
		tmp = x / (1.0 - y);
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3e+33) or not (x <= 1.5e+39):
		tmp = x / (1.0 - y)
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3e+33) || !(x <= 1.5e+39))
		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 <= -3e+33) || ~((x <= 1.5e+39)))
		tmp = x / (1.0 - y);
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3e+33], N[Not[LessEqual[x, 1.5e+39]], $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 < -2.99999999999999984e33 or 1.5e39 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.5%

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

   if -2.99999999999999984e33 < x < 1.5e39

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.1%

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

      1. neg-mul-1 77.1%

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

      2. distribute-neg-frac2 77.1%

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

      3. neg-sub0 77.1%

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

      4. associate--r- 77.1%

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

      5. metadata-eval 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+33} \lor \neg \left(x \leq 1.5 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Derivation

1. Split input into 2 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 76.1%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.6%

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

4. Final simplification 75.8%

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

Alternative 7: 39.6% 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 39.4%

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

4. Final simplification 39.4%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024054 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))