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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

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: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -5200000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.9e+97)
   1.0
   (if (<= y -1.4e+59)
     (/ (- x) y)
     (if (<= y -5200000.0)
       1.0
       (if (<= y 3.9e-51) x (if (<= y 1.0) (* y (- -1.0 y)) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.9e+97) {
		tmp = 1.0;
	} else if (y <= -1.4e+59) {
		tmp = -x / y;
	} else if (y <= -5200000.0) {
		tmp = 1.0;
	} else if (y <= 3.9e-51) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = y * (-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 <= (-5.9d+97)) then
        tmp = 1.0d0
    else if (y <= (-1.4d+59)) then
        tmp = -x / y
    else if (y <= (-5200000.0d0)) then
        tmp = 1.0d0
    else if (y <= 3.9d-51) then
        tmp = x
    else if (y <= 1.0d0) then
        tmp = y * ((-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 <= -5.9e+97) {
		tmp = 1.0;
	} else if (y <= -1.4e+59) {
		tmp = -x / y;
	} else if (y <= -5200000.0) {
		tmp = 1.0;
	} else if (y <= 3.9e-51) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = y * (-1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.9e+97:
		tmp = 1.0
	elif y <= -1.4e+59:
		tmp = -x / y
	elif y <= -5200000.0:
		tmp = 1.0
	elif y <= 3.9e-51:
		tmp = x
	elif y <= 1.0:
		tmp = y * (-1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.9e+97)
		tmp = 1.0;
	elseif (y <= -1.4e+59)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= -5200000.0)
		tmp = 1.0;
	elseif (y <= 3.9e-51)
		tmp = x;
	elseif (y <= 1.0)
		tmp = Float64(y * Float64(-1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.9e+97)
		tmp = 1.0;
	elseif (y <= -1.4e+59)
		tmp = -x / y;
	elseif (y <= -5200000.0)
		tmp = 1.0;
	elseif (y <= 3.9e-51)
		tmp = x;
	elseif (y <= 1.0)
		tmp = y * (-1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.9e+97], 1.0, If[LessEqual[y, -1.4e+59], N[((-x) / y), $MachinePrecision], If[LessEqual[y, -5200000.0], 1.0, If[LessEqual[y, 3.9e-51], x, If[LessEqual[y, 1.0], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.90000000000000009e97 or -1.3999999999999999e59 < y < -5.2e6 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.1%

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

   if -5.90000000000000009e97 < y < -1.3999999999999999e59

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.5%

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

   3. Taylor expanded in y around inf 86.5%

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

      1. neg-mul-1 86.5%

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

      2. distribute-neg-frac 86.5%

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

   5. Simplified 86.5%

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

   if -5.2e6 < y < 3.8999999999999997e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.4%

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

   if 3.8999999999999997e-51 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 69.9%

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

      1. metadata-eval 69.9%

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

      2. times-frac 69.9%

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

      3. *-lft-identity 69.9%

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

      4. neg-mul-1 69.9%

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

      5. neg-sub0 69.9%

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

      6. associate--r- 69.9%

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

      7. metadata-eval 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unpow2 67.5%

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

      3. distribute-lft-neg-in 67.5%

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

      4. distribute-rgt-in 67.5%

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

      5. sub-neg 67.5%

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

   7. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -5200000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -6800000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.9e+97)
   1.0
   (if (<= y -1.65e+59)
     (/ (- x) y)
     (if (<= y -6800000000.0)
       1.0
       (if (<= y 1.65e-50)
         (/ x (- 1.0 y))
         (if (<= y 1.0) (* y (- -1.0 y)) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.9e+97) {
		tmp = 1.0;
	} else if (y <= -1.65e+59) {
		tmp = -x / y;
	} else if (y <= -6800000000.0) {
		tmp = 1.0;
	} else if (y <= 1.65e-50) {
		tmp = x / (1.0 - y);
	} else if (y <= 1.0) {
		tmp = y * (-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 <= (-5.9d+97)) then
        tmp = 1.0d0
    else if (y <= (-1.65d+59)) then
        tmp = -x / y
    else if (y <= (-6800000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.65d-50) then
        tmp = x / (1.0d0 - y)
    else if (y <= 1.0d0) then
        tmp = y * ((-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 <= -5.9e+97) {
		tmp = 1.0;
	} else if (y <= -1.65e+59) {
		tmp = -x / y;
	} else if (y <= -6800000000.0) {
		tmp = 1.0;
	} else if (y <= 1.65e-50) {
		tmp = x / (1.0 - y);
	} else if (y <= 1.0) {
		tmp = y * (-1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.9e+97:
		tmp = 1.0
	elif y <= -1.65e+59:
		tmp = -x / y
	elif y <= -6800000000.0:
		tmp = 1.0
	elif y <= 1.65e-50:
		tmp = x / (1.0 - y)
	elif y <= 1.0:
		tmp = y * (-1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.9e+97)
		tmp = 1.0;
	elseif (y <= -1.65e+59)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= -6800000000.0)
		tmp = 1.0;
	elseif (y <= 1.65e-50)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 1.0)
		tmp = Float64(y * Float64(-1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.9e+97)
		tmp = 1.0;
	elseif (y <= -1.65e+59)
		tmp = -x / y;
	elseif (y <= -6800000000.0)
		tmp = 1.0;
	elseif (y <= 1.65e-50)
		tmp = x / (1.0 - y);
	elseif (y <= 1.0)
		tmp = y * (-1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.9e+97], 1.0, If[LessEqual[y, -1.65e+59], N[((-x) / y), $MachinePrecision], If[LessEqual[y, -6800000000.0], 1.0, If[LessEqual[y, 1.65e-50], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.90000000000000009e97 or -1.65e59 < y < -6.8e9 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.1%

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

   if -5.90000000000000009e97 < y < -1.65e59

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.5%

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

   3. Taylor expanded in y around inf 86.5%

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

      1. neg-mul-1 86.5%

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

      2. distribute-neg-frac 86.5%

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

   5. Simplified 86.5%

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

   if -6.8e9 < y < 1.6499999999999999e-50

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.5%

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

   if 1.6499999999999999e-50 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 69.9%

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

      1. metadata-eval 69.9%

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

      2. times-frac 69.9%

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

      3. *-lft-identity 69.9%

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

      4. neg-mul-1 69.9%

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

      5. neg-sub0 69.9%

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

      6. associate--r- 69.9%

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

      7. metadata-eval 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unpow2 67.5%

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

      3. distribute-lft-neg-in 67.5%

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

      4. distribute-rgt-in 67.5%

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

      5. sub-neg 67.5%

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

   7. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -6800000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -42000000 \lor \neg \left(y \leq 2.35 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.8e+97)
   1.0
   (if (<= y -1.65e+59)
     (/ (- x) y)
     (if (or (<= y -42000000.0) (not (<= y 2.35e-50)))
       (/ y (+ y -1.0))
       (/ x (- 1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+97) {
		tmp = 1.0;
	} else if (y <= -1.65e+59) {
		tmp = -x / y;
	} else if ((y <= -42000000.0) || !(y <= 2.35e-50)) {
		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 <= (-5.8d+97)) then
        tmp = 1.0d0
    else if (y <= (-1.65d+59)) then
        tmp = -x / y
    else if ((y <= (-42000000.0d0)) .or. (.not. (y <= 2.35d-50))) 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 <= -5.8e+97) {
		tmp = 1.0;
	} else if (y <= -1.65e+59) {
		tmp = -x / y;
	} else if ((y <= -42000000.0) || !(y <= 2.35e-50)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.8e+97:
		tmp = 1.0
	elif y <= -1.65e+59:
		tmp = -x / y
	elif (y <= -42000000.0) or not (y <= 2.35e-50):
		tmp = y / (y + -1.0)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.8e+97)
		tmp = 1.0;
	elseif (y <= -1.65e+59)
		tmp = Float64(Float64(-x) / y);
	elseif ((y <= -42000000.0) || !(y <= 2.35e-50))
		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 <= -5.8e+97)
		tmp = 1.0;
	elseif (y <= -1.65e+59)
		tmp = -x / y;
	elseif ((y <= -42000000.0) || ~((y <= 2.35e-50)))
		tmp = y / (y + -1.0);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.8e+97], 1.0, If[LessEqual[y, -1.65e+59], N[((-x) / y), $MachinePrecision], If[Or[LessEqual[y, -42000000.0], N[Not[LessEqual[y, 2.35e-50]], $MachinePrecision]], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999974e97

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 78.7%

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

   if -5.79999999999999974e97 < y < -1.65e59

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.5%

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

   3. Taylor expanded in y around inf 86.5%

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

      1. neg-mul-1 86.5%

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

      2. distribute-neg-frac 86.5%

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

   5. Simplified 86.5%

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

   if -1.65e59 < y < -4.2e7 or 2.3500000000000001e-50 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 83.6%

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

      1. metadata-eval 83.6%

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

      2. times-frac 83.6%

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

      3. *-lft-identity 83.6%

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

      4. neg-mul-1 83.6%

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

      5. neg-sub0 83.6%

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

      6. associate--r- 83.6%

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

      7. metadata-eval 83.6%

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

   4. Simplified 83.6%

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

   if -4.2e7 < y < 2.3500000000000001e-50

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.5%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -42000000 \lor \neg \left(y \leq 2.35 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]

Alternative 5: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -46000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 4050000:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 1.0 x) y))))
   (if (<= y -46000000.0)
     t_0
     (if (<= y 9.2e-52)
       (/ x (- 1.0 y))
       (if (<= y 4050000.0) (/ y (+ y -1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double tmp;
	if (y <= -46000000.0) {
		tmp = t_0;
	} else if (y <= 9.2e-52) {
		tmp = x / (1.0 - y);
	} else if (y <= 4050000.0) {
		tmp = y / (y + -1.0);
	} 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 <= (-46000000.0d0)) then
        tmp = t_0
    else if (y <= 9.2d-52) then
        tmp = x / (1.0d0 - y)
    else if (y <= 4050000.0d0) then
        tmp = y / (y + (-1.0d0))
    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 <= -46000000.0) {
		tmp = t_0;
	} else if (y <= 9.2e-52) {
		tmp = x / (1.0 - y);
	} else if (y <= 4050000.0) {
		tmp = y / (y + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((1.0 - x) / y)
	tmp = 0
	if y <= -46000000.0:
		tmp = t_0
	elif y <= 9.2e-52:
		tmp = x / (1.0 - y)
	elif y <= 4050000.0:
		tmp = y / (y + -1.0)
	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 <= -46000000.0)
		tmp = t_0;
	elseif (y <= 9.2e-52)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 4050000.0)
		tmp = Float64(y / Float64(y + -1.0));
	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 <= -46000000.0)
		tmp = t_0;
	elseif (y <= 9.2e-52)
		tmp = x / (1.0 - y);
	elseif (y <= 4050000.0)
		tmp = y / (y + -1.0);
	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, -46000000.0], t$95$0, If[LessEqual[y, 9.2e-52], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4050000.0], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6e7 or 4.05e6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. div-sub 100.0%

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

   4. Simplified 100.0%

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

   if -4.6e7 < y < 9.19999999999999977e-52

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.5%

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

   if 9.19999999999999977e-52 < y < 4.05e6

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 72.4%

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

      1. metadata-eval 72.4%

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

      2. times-frac 72.4%

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

      3. *-lft-identity 72.4%

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

      4. neg-mul-1 72.4%

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

      5. neg-sub0 72.4%

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

      6. associate--r- 72.4%

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

      7. metadata-eval 72.4%

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

   4. Simplified 72.4%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -46000000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 4050000:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -5200000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.2e+97)
   1.0
   (if (<= y -5e+57)
     (/ (- x) y)
     (if (<= y -5200000.0) 1.0 (if (<= y 1.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.2e+97) {
		tmp = 1.0;
	} else if (y <= -5e+57) {
		tmp = -x / y;
	} else if (y <= -5200000.0) {
		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 <= (-6.2d+97)) then
        tmp = 1.0d0
    else if (y <= (-5d+57)) then
        tmp = -x / y
    else if (y <= (-5200000.0d0)) 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 <= -6.2e+97) {
		tmp = 1.0;
	} else if (y <= -5e+57) {
		tmp = -x / y;
	} else if (y <= -5200000.0) {
		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 <= -6.2e+97:
		tmp = 1.0
	elif y <= -5e+57:
		tmp = -x / y
	elif y <= -5200000.0:
		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 <= -6.2e+97)
		tmp = 1.0;
	elseif (y <= -5e+57)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= -5200000.0)
		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 <= -6.2e+97)
		tmp = 1.0;
	elseif (y <= -5e+57)
		tmp = -x / y;
	elseif (y <= -5200000.0)
		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, -6.2e+97], 1.0, If[LessEqual[y, -5e+57], N[((-x) / y), $MachinePrecision], If[LessEqual[y, -5200000.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999962e97 or -4.99999999999999972e57 < y < -5.2e6 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.1%

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

   if -6.19999999999999962e97 < y < -4.99999999999999972e57

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.5%

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

   3. Taylor expanded in y around inf 86.5%

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

      1. neg-mul-1 86.5%

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

      2. distribute-neg-frac 86.5%

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

   5. Simplified 86.5%

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

   if -5.2e6 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+97}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -5200000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 73.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5200000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5200000.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5200000.0) {
		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 <= (-5200000.0d0)) 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 <= -5200000.0) {
		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 <= -5200000.0:
		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 <= -5200000.0)
		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 <= -5200000.0)
		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, -5200000.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e6 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.2%

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

   if -5.2e6 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5200000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 38.3% 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 37.6%

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

3. Final simplification 37.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))