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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

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. Final simplification 100.0%

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

Alternative 2: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-27}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.95e-7)
   1.0
   (if (<= y -9.8e-27)
     (- y)
     (if (<= y 1.0) x (if (<= y 7.8e+127) (/ (- x) y) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.95e-7) {
		tmp = 1.0;
	} else if (y <= -9.8e-27) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 7.8e+127) {
		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 <= (-3.95d-7)) then
        tmp = 1.0d0
    else if (y <= (-9.8d-27)) then
        tmp = -y
    else if (y <= 1.0d0) then
        tmp = x
    else if (y <= 7.8d+127) 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 <= -3.95e-7) {
		tmp = 1.0;
	} else if (y <= -9.8e-27) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 7.8e+127) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.95e-7:
		tmp = 1.0
	elif y <= -9.8e-27:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	elif y <= 7.8e+127:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.95e-7)
		tmp = 1.0;
	elseif (y <= -9.8e-27)
		tmp = Float64(-y);
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 7.8e+127)
		tmp = Float64(Float64(-x) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.95e-7)
		tmp = 1.0;
	elseif (y <= -9.8e-27)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 7.8e+127)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.95e-7], 1.0, If[LessEqual[y, -9.8e-27], (-y), If[LessEqual[y, 1.0], x, If[LessEqual[y, 7.8e+127], N[((-x) / y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.94999999999999977e-7 or 7.79999999999999962e127 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.4%

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

   if -3.94999999999999977e-7 < y < -9.79999999999999952e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.0%

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

      1. metadata-eval 91.0%

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

      2. times-frac 91.0%

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

      3. *-lft-identity 91.0%

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

      4. neg-mul-1 91.0%

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

      5. neg-sub0 91.0%

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

      6. associate--r- 91.0%

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

      7. metadata-eval 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in y around 0 84.4%

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

      1. neg-mul-1 84.4%

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

   7. Simplified 84.4%

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

   if -9.79999999999999952e-27 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.4%

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

   if 1 < y < 7.79999999999999962e127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 61.4%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. associate-*r/ 60.4%

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

      2. neg-mul-1 60.4%

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

   5. Simplified 60.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-27}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.95e-7)
   1.0
   (if (<= y -4.8e-24)
     (* y (- -1.0 y))
     (if (<= y 1.0) x (if (<= y 7.8e+127) (/ (- x) y) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.95e-7) {
		tmp = 1.0;
	} else if (y <= -4.8e-24) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 7.8e+127) {
		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 <= (-3.95d-7)) then
        tmp = 1.0d0
    else if (y <= (-4.8d-24)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 1.0d0) then
        tmp = x
    else if (y <= 7.8d+127) 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 <= -3.95e-7) {
		tmp = 1.0;
	} else if (y <= -4.8e-24) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} else if (y <= 7.8e+127) {
		tmp = -x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.95e-7:
		tmp = 1.0
	elif y <= -4.8e-24:
		tmp = y * (-1.0 - y)
	elif y <= 1.0:
		tmp = x
	elif y <= 7.8e+127:
		tmp = -x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.95e-7)
		tmp = 1.0;
	elseif (y <= -4.8e-24)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 7.8e+127)
		tmp = Float64(Float64(-x) / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.95e-7)
		tmp = 1.0;
	elseif (y <= -4.8e-24)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.0)
		tmp = x;
	elseif (y <= 7.8e+127)
		tmp = -x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.95e-7], 1.0, If[LessEqual[y, -4.8e-24], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], x, If[LessEqual[y, 7.8e+127], N[((-x) / y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.94999999999999977e-7 or 7.79999999999999962e127 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.4%

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

   if -3.94999999999999977e-7 < y < -4.7999999999999996e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.0%

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

      1. metadata-eval 91.0%

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

      2. times-frac 91.0%

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

      3. *-lft-identity 91.0%

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

      4. neg-mul-1 91.0%

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

      5. neg-sub0 91.0%

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

      6. associate--r- 91.0%

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

      7. metadata-eval 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in y around 0 91.0%

      \[\leadsto \color{blue}{-1 \cdot y + -1 \cdot {y}^{2}} \]
   6. Step-by-step derivation

      1. mul-1-neg 91.0%

         \[\leadsto -1 \cdot y + \color{blue}{\left(-{y}^{2}\right)} \]

      2. unpow2 91.0%

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

      3. distribute-lft-neg-in 91.0%

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

      4. distribute-rgt-in 91.0%

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

      5. sub-neg 91.0%

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

   7. Simplified 91.0%

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

   if -4.7999999999999996e-24 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.4%

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

   if 1 < y < 7.79999999999999962e127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 61.4%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. associate-*r/ 60.4%

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

      2. neg-mul-1 60.4%

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

   5. Simplified 60.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7000000000.0) 1.0 (if (<= y 7.8e+127) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7000000000.0) {
		tmp = 1.0;
	} else if (y <= 7.8e+127) {
		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 <= (-7000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 7.8d+127) 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 <= -7000000000.0) {
		tmp = 1.0;
	} else if (y <= 7.8e+127) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7000000000.0:
		tmp = 1.0
	elif y <= 7.8e+127:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7000000000.0)
		tmp = 1.0;
	elseif (y <= 7.8e+127)
		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 <= -7000000000.0)
		tmp = 1.0;
	elseif (y <= 7.8e+127)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7000000000.0], 1.0, If[LessEqual[y, 7.8e+127], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -7e9 or 7.79999999999999962e127 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.8%

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

   if -7e9 < y < 7.79999999999999962e127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 72.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.6e-25)
   (/ y (+ y -1.0))
   (if (<= y 7.8e+127) (/ x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.6e-25) {
		tmp = y / (y + -1.0);
	} else if (y <= 7.8e+127) {
		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 <= (-4.6d-25)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 7.8d+127) 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 <= -4.6e-25) {
		tmp = y / (y + -1.0);
	} else if (y <= 7.8e+127) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.6e-25:
		tmp = y / (y + -1.0)
	elif y <= 7.8e+127:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.6e-25)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 7.8e+127)
		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 <= -4.6e-25)
		tmp = y / (y + -1.0);
	elseif (y <= 7.8e+127)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.6e-25], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+127], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5999999999999998e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.9%

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

      1. metadata-eval 78.9%

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

      2. times-frac 78.9%

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

      3. *-lft-identity 78.9%

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

      4. neg-mul-1 78.9%

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

      5. neg-sub0 78.9%

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

      6. associate--r- 78.9%

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

      7. metadata-eval 78.9%

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

   4. Simplified 78.9%

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

   if -4.5999999999999998e-25 < y < 7.79999999999999962e127

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.6%

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

   if 7.79999999999999962e127 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-24}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.95e-7) 1.0 (if (<= y -2.55e-24) (- y) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.95e-7) {
		tmp = 1.0;
	} else if (y <= -2.55e-24) {
		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 <= (-3.95d-7)) then
        tmp = 1.0d0
    else if (y <= (-2.55d-24)) 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 <= -3.95e-7) {
		tmp = 1.0;
	} else if (y <= -2.55e-24) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.95e-7:
		tmp = 1.0
	elif y <= -2.55e-24:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.95e-7)
		tmp = 1.0;
	elseif (y <= -2.55e-24)
		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 <= -3.95e-7)
		tmp = 1.0;
	elseif (y <= -2.55e-24)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.95e-7], 1.0, If[LessEqual[y, -2.55e-24], (-y), If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.94999999999999977e-7 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 69.3%

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

   if -3.94999999999999977e-7 < y < -2.55000000000000013e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.0%

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

      1. metadata-eval 91.0%

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

      2. times-frac 91.0%

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

      3. *-lft-identity 91.0%

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

      4. neg-mul-1 91.0%

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

      5. neg-sub0 91.0%

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

      6. associate--r- 91.0%

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

      7. metadata-eval 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in y around 0 84.4%

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

      1. neg-mul-1 84.4%

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

   7. Simplified 84.4%

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

   if -2.55000000000000013e-24 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-24}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 73.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -29:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -29.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -29.0) {
		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 <= (-29.0d0)) 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 <= -29.0) {
		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 <= -29.0:
		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 <= -29.0)
		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 <= -29.0)
		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, -29.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -29 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 70.3%

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

   if -29 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -29:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

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. Taylor expanded in y around inf 38.4%

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

3. Final simplification 38.4%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))