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

Percentage Accurate: 100.0% → 100.0%

Time: 7.5s

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: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0115:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.0115)
   (/ y (+ y -1.0))
   (if (<= y 7.1e-9)
     (+ x (* y (+ x -1.0)))
     (if (<= y 6.4e+42) (/ x (- 1.0 y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.0115) {
		tmp = y / (y + -1.0);
	} else if (y <= 7.1e-9) {
		tmp = x + (y * (x + -1.0));
	} else if (y <= 6.4e+42) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.0115d0)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 7.1d-9) then
        tmp = x + (y * (x + (-1.0d0)))
    else if (y <= 6.4d+42) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.0115) {
		tmp = y / (y + -1.0);
	} else if (y <= 7.1e-9) {
		tmp = x + (y * (x + -1.0));
	} else if (y <= 6.4e+42) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.0115:
		tmp = y / (y + -1.0)
	elif y <= 7.1e-9:
		tmp = x + (y * (x + -1.0))
	elif y <= 6.4e+42:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.0115)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 7.1e-9)
		tmp = Float64(x + Float64(y * Float64(x + -1.0)));
	elseif (y <= 6.4e+42)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.0115)
		tmp = y / (y + -1.0);
	elseif (y <= 7.1e-9)
		tmp = x + (y * (x + -1.0));
	elseif (y <= 6.4e+42)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.0115], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.1e-9], N[(x + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+42], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.0115

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.9%

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

      1. neg-mul-1 73.9%

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

      2. distribute-neg-frac2 73.9%

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

      3. neg-sub0 73.9%

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

      4. associate--r- 73.9%

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

      5. metadata-eval 73.9%

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

   5. Simplified 73.9%

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

   if -0.0115 < y < 7.09999999999999988e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. sub-neg 99.2%

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

   5. Simplified 99.2%

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

   if 7.09999999999999988e-9 < y < 6.40000000000000004e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.8%

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

   if 6.40000000000000004e42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0115:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00045:\\ \;\;\;\;\frac{1}{\frac{y + -1}{y}}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.00045)
   (/ 1.0 (/ (+ y -1.0) y))
   (if (<= y 7.1e-9)
     (+ x (* y (+ x -1.0)))
     (if (<= y 1.9e+43) (/ x (- 1.0 y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.00045) {
		tmp = 1.0 / ((y + -1.0) / y);
	} else if (y <= 7.1e-9) {
		tmp = x + (y * (x + -1.0));
	} else if (y <= 1.9e+43) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.00045d0)) then
        tmp = 1.0d0 / ((y + (-1.0d0)) / y)
    else if (y <= 7.1d-9) then
        tmp = x + (y * (x + (-1.0d0)))
    else if (y <= 1.9d+43) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.00045) {
		tmp = 1.0 / ((y + -1.0) / y);
	} else if (y <= 7.1e-9) {
		tmp = x + (y * (x + -1.0));
	} else if (y <= 1.9e+43) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.00045:
		tmp = 1.0 / ((y + -1.0) / y)
	elif y <= 7.1e-9:
		tmp = x + (y * (x + -1.0))
	elif y <= 1.9e+43:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.00045)
		tmp = Float64(1.0 / Float64(Float64(y + -1.0) / y));
	elseif (y <= 7.1e-9)
		tmp = Float64(x + Float64(y * Float64(x + -1.0)));
	elseif (y <= 1.9e+43)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.00045)
		tmp = 1.0 / ((y + -1.0) / y);
	elseif (y <= 7.1e-9)
		tmp = x + (y * (x + -1.0));
	elseif (y <= 1.9e+43)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.00045], N[(1.0 / N[(N[(y + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.1e-9], N[(x + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+43], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4999999999999999e-4

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.6%

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

   4. Applied egg-rr 99.6%

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

      1. associate-*l/ 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. neg-mul-1 73.9%

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

      3. neg-sub0 73.9%

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

      4. associate--r- 73.9%

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

      5. metadata-eval 73.9%

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

   9. Simplified 73.9%

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

   if -4.4999999999999999e-4 < y < 7.09999999999999988e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. sub-neg 99.2%

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

   5. Simplified 99.2%

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

   if 7.09999999999999988e-9 < y < 1.90000000000000004e43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.8%

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

   if 1.90000000000000004e43 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00045:\\ \;\;\;\;\frac{1}{\frac{y + -1}{y}}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.31:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.31) 1.0 (if (<= y 1.0) (+ x (* x y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.31) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x + (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 <= (-0.31d0)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x + (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 <= -0.31) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x + (x * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.31:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x + (x * y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.31)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(x + Float64(x * y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.31)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x + (x * y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.31], 1.0, If[LessEqual[y, 1.0], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -0.309999999999999998 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -0.309999999999999998 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.6%

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

   4. Taylor expanded in y around 0 76.2%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.31:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.8e+19) 1.0 (if (<= y 4e+42) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.8e+19) {
		tmp = 1.0;
	} else if (y <= 4e+42) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-8.8d+19)) then
        tmp = 1.0d0
    else if (y <= 4d+42) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8.8e+19) {
		tmp = 1.0;
	} else if (y <= 4e+42) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.8e+19:
		tmp = 1.0
	elif y <= 4e+42:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.8e+19)
		tmp = 1.0;
	elseif (y <= 4e+42)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.8e+19)
		tmp = 1.0;
	elseif (y <= 4e+42)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.8e+19], 1.0, If[LessEqual[y, 4e+42], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8e19 or 4.00000000000000018e42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.3%

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

   if -8.8e19 < y < 4.00000000000000018e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.8e-53) (/ y (+ y -1.0)) (if (<= y 4.2e+43) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.8e-53) {
		tmp = y / (y + -1.0);
	} else if (y <= 4.2e+43) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.8d-53)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 4.2d+43) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.8e-53) {
		tmp = y / (y + -1.0);
	} else if (y <= 4.2e+43) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.8e-53:
		tmp = y / (y + -1.0)
	elif y <= 4.2e+43:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.8e-53)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 4.2e+43)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.8e-53)
		tmp = y / (y + -1.0);
	elseif (y <= 4.2e+43)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.8e-53], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+43], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999998e-53

   1. Initial program 99.9%

      \[\frac{x - y}{1 - y} \]
   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%

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

   if -3.7999999999999998e-53 < y < 4.20000000000000003e43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.1%

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

   if 4.20000000000000003e43 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -0.2) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.2) {
		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 <= (-0.2d0)) 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 <= -0.2) {
		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 <= -0.2:
		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 <= -0.2)
		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 <= -0.2)
		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, -0.2], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -0.20000000000000001 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.3%

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

   if -0.20000000000000001 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.9%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.6% 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 38.5%

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

4. Final simplification 38.5%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))