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

Percentage Accurate: 100.0% → 100.0%

Time: 7.3s

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: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -14500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 7:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 1.0 x) y))))
   (if (<= y -14500000000.0)
     t_0
     (if (<= y -8.4e-36)
       (/ y (+ y -1.0))
       (if (<= y 7.0) (/ 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 <= -14500000000.0) {
		tmp = t_0;
	} else if (y <= -8.4e-36) {
		tmp = y / (y + -1.0);
	} else if (y <= 7.0) {
		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 <= (-14500000000.0d0)) then
        tmp = t_0
    else if (y <= (-8.4d-36)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 7.0d0) 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 <= -14500000000.0) {
		tmp = t_0;
	} else if (y <= -8.4e-36) {
		tmp = y / (y + -1.0);
	} else if (y <= 7.0) {
		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 <= -14500000000.0:
		tmp = t_0
	elif y <= -8.4e-36:
		tmp = y / (y + -1.0)
	elif y <= 7.0:
		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 <= -14500000000.0)
		tmp = t_0;
	elseif (y <= -8.4e-36)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 7.0)
		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 <= -14500000000.0)
		tmp = t_0;
	elseif (y <= -8.4e-36)
		tmp = y / (y + -1.0);
	elseif (y <= 7.0)
		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, -14500000000.0], t$95$0, If[LessEqual[y, -8.4e-36], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.0], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e10 or 7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.8%

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

      1. +-commutative 98.8%

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

      2. mul-1-neg 98.8%

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

      3. sub-neg 98.8%

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

      4. div-sub 98.8%

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

   5. Simplified 98.8%

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

   if -1.45e10 < y < -8.39999999999999964e-36

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 78.9%

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

      1. neg-mul-1 78.9%

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

      2. distribute-neg-frac2 78.9%

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

      3. neg-sub0 78.9%

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

      4. associate--r- 78.9%

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

      5. metadata-eval 78.9%

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

   5. Simplified 78.9%

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

   if -8.39999999999999964e-36 < y < 7

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.5%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14500000000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 7:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.00019:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.5e-7)
   1.0
   (if (<= y 0.00019) x (if (<= y 1.8e+119) (/ x (- y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.5e-7) {
		tmp = 1.0;
	} else if (y <= 0.00019) {
		tmp = x;
	} else if (y <= 1.8e+119) {
		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 <= (-4.5d-7)) then
        tmp = 1.0d0
    else if (y <= 0.00019d0) then
        tmp = x
    else if (y <= 1.8d+119) 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 <= -4.5e-7) {
		tmp = 1.0;
	} else if (y <= 0.00019) {
		tmp = x;
	} else if (y <= 1.8e+119) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.5e-7:
		tmp = 1.0
	elif y <= 0.00019:
		tmp = x
	elif y <= 1.8e+119:
		tmp = x / -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.5e-7)
		tmp = 1.0;
	elseif (y <= 0.00019)
		tmp = x;
	elseif (y <= 1.8e+119)
		tmp = Float64(x / Float64(-y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.5e-7)
		tmp = 1.0;
	elseif (y <= 0.00019)
		tmp = x;
	elseif (y <= 1.8e+119)
		tmp = x / -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.5e-7], 1.0, If[LessEqual[y, 0.00019], x, If[LessEqual[y, 1.8e+119], N[(x / (-y)), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999998e-7 or 1.80000000000000001e119 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 83.9%

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

   if -4.4999999999999998e-7 < y < 1.9000000000000001e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.2%

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

   if 1.9000000000000001e-4 < y < 1.80000000000000001e119

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 64.6%

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

   4. Taylor expanded in y around inf 64.1%

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

      1. mul-1-neg 64.1%

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

      2. distribute-neg-frac2 64.1%

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

   6. Simplified 64.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.00019:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-36} \lor \neg \left(y \leq 1.8 \cdot 10^{+119}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.4e-36) (not (<= y 1.8e+119)))
   (/ y (+ y -1.0))
   (/ x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.4e-36) || !(y <= 1.8e+119)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-8.4d-36)) .or. (.not. (y <= 1.8d+119))) then
        tmp = y / (y + (-1.0d0))
    else
        tmp = x / (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8.4e-36) || !(y <= 1.8e+119)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.4e-36) or not (y <= 1.8e+119):
		tmp = y / (y + -1.0)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.4e-36) || !(y <= 1.8e+119))
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = Float64(x / Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8.4e-36) || ~((y <= 1.8e+119)))
		tmp = y / (y + -1.0);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.4e-36], N[Not[LessEqual[y, 1.8e+119]], $MachinePrecision]], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.39999999999999964e-36 or 1.80000000000000001e119 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.9%

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

      1. neg-mul-1 84.9%

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

      2. distribute-neg-frac2 84.9%

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

      3. neg-sub0 84.9%

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

      4. associate--r- 84.9%

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

      5. metadata-eval 84.9%

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

   5. Simplified 84.9%

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

   if -8.39999999999999964e-36 < y < 1.80000000000000001e119

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.3%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-36} \lor \neg \left(y \leq 1.8 \cdot 10^{+119}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.5e+53) 1.0 (if (<= y 1.8e+119) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.5e+53) {
		tmp = 1.0;
	} else if (y <= 1.8e+119) {
		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 <= (-8.5d+53)) then
        tmp = 1.0d0
    else if (y <= 1.8d+119) 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 <= -8.5e+53) {
		tmp = 1.0;
	} else if (y <= 1.8e+119) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.5e+53:
		tmp = 1.0
	elif y <= 1.8e+119:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.5e+53)
		tmp = 1.0;
	elseif (y <= 1.8e+119)
		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 <= -8.5e+53)
		tmp = 1.0;
	elseif (y <= 1.8e+119)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.5e+53], 1.0, If[LessEqual[y, 1.8e+119], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000002e53 or 1.80000000000000001e119 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.4%

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

   if -8.5000000000000002e53 < y < 1.80000000000000001e119

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.5e-7) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.5e-7) {
		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 <= (-4.5d-7)) 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 <= -4.5e-7) {
		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 <= -4.5e-7:
		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 <= -4.5e-7)
		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 <= -4.5e-7)
		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, -4.5e-7], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999998e-7 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.8%

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

   if -4.4999999999999998e-7 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.6%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.0% 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 39.3%

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

4. Final simplification 39.3%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024075 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))