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. Add Preprocessing

Alternative 2: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -260000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 950:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -260000000000.0)
     t_0
     (if (<= y 1.2e-56)
       (/ x (- 1.0 y))
       (if (<= y 950.0) (/ y (+ y -1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -260000000000.0) {
		tmp = t_0;
	} else if (y <= 1.2e-56) {
		tmp = x / (1.0 - y);
	} else if (y <= 950.0) {
		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 - (x / y)
    if (y <= (-260000000000.0d0)) then
        tmp = t_0
    else if (y <= 1.2d-56) then
        tmp = x / (1.0d0 - y)
    else if (y <= 950.0d0) 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 - (x / y);
	double tmp;
	if (y <= -260000000000.0) {
		tmp = t_0;
	} else if (y <= 1.2e-56) {
		tmp = x / (1.0 - y);
	} else if (y <= 950.0) {
		tmp = y / (y + -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -260000000000.0:
		tmp = t_0
	elif y <= 1.2e-56:
		tmp = x / (1.0 - y)
	elif y <= 950.0:
		tmp = y / (y + -1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -260000000000.0)
		tmp = t_0;
	elseif (y <= 1.2e-56)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= 950.0)
		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 - (x / y);
	tmp = 0.0;
	if (y <= -260000000000.0)
		tmp = t_0;
	elseif (y <= 1.2e-56)
		tmp = x / (1.0 - y);
	elseif (y <= 950.0)
		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[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -260000000000.0], t$95$0, If[LessEqual[y, 1.2e-56], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 950.0], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e11 or 950 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. *-commutative 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

      4. sub-neg 87.2%

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

      5. associate-/r* 75.3%

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

      6. distribute-neg-frac 75.3%

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

      7. metadata-eval 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in x around inf 87.2%

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

      1. neg-mul-1 87.2%

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

      2. neg-sub0 87.2%

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

      3. associate-+l- 87.2%

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

      4. sub-neg 87.2%

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

      5. *-rgt-identity 87.2%

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

      6. times-frac 75.2%

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

      7. neg-mul-1 75.2%

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

      8. distribute-rgt-in 75.2%

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

      9. neg-sub0 75.2%

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

      10. associate-*l/ 75.3%

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

      11. *-lft-identity 75.3%

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

      12. distribute-neg-frac2 75.3%

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

      13. +-commutative 75.3%

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

      14. neg-sub0 75.3%

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

      15. associate--r- 75.3%

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

      16. metadata-eval 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in y around inf 74.9%

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

   10. Taylor expanded in x around 0 99.5%

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

       1. mul-1-neg 99.5%

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

       2. unsub-neg 99.5%

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

   12. Simplified 99.5%

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

   if -2.6e11 < y < 1.2e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.6%

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

   if 1.2e-56 < y < 950

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 66.3%

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

      1. neg-mul-1 66.3%

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

      2. distribute-neg-frac2 66.3%

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

      3. neg-sub0 66.3%

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

      4. associate--r- 66.3%

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

      5. metadata-eval 66.3%

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

   5. Simplified 66.3%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -260000000000:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 950:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -0.18:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -0.18)
     t_0
     (if (<= y 6e-57) (* x (+ y 1.0)) (if (<= y 1.0) (- y) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -0.18) {
		tmp = t_0;
	} else if (y <= 6e-57) {
		tmp = x * (y + 1.0);
	} else if (y <= 1.0) {
		tmp = -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 - (x / y)
    if (y <= (-0.18d0)) then
        tmp = t_0
    else if (y <= 6d-57) then
        tmp = x * (y + 1.0d0)
    else if (y <= 1.0d0) then
        tmp = -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 - (x / y);
	double tmp;
	if (y <= -0.18) {
		tmp = t_0;
	} else if (y <= 6e-57) {
		tmp = x * (y + 1.0);
	} else if (y <= 1.0) {
		tmp = -y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -0.18:
		tmp = t_0
	elif y <= 6e-57:
		tmp = x * (y + 1.0)
	elif y <= 1.0:
		tmp = -y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -0.18)
		tmp = t_0;
	elseif (y <= 6e-57)
		tmp = Float64(x * Float64(y + 1.0));
	elseif (y <= 1.0)
		tmp = Float64(-y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -0.18)
		tmp = t_0;
	elseif (y <= 6e-57)
		tmp = x * (y + 1.0);
	elseif (y <= 1.0)
		tmp = -y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.18], t$95$0, If[LessEqual[y, 6e-57], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], (-y), t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.17999999999999999 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. *-commutative 87.3%

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

      3. distribute-rgt-neg-in 87.3%

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

      4. sub-neg 87.3%

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

      5. associate-/r* 75.5%

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

      6. distribute-neg-frac 75.5%

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

      7. metadata-eval 75.5%

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

   5. Simplified 75.5%

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

   6. Taylor expanded in x around inf 87.3%

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

      1. neg-mul-1 87.3%

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

      2. neg-sub0 87.3%

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

      3. associate-+l- 87.3%

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

      4. sub-neg 87.3%

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

      5. *-rgt-identity 87.3%

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

      6. times-frac 75.4%

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

      7. neg-mul-1 75.4%

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

      8. distribute-rgt-in 75.4%

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

      9. neg-sub0 75.4%

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

      10. associate-*l/ 75.5%

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

      11. *-lft-identity 75.5%

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

      12. distribute-neg-frac2 75.5%

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

      13. +-commutative 75.5%

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

      14. neg-sub0 75.5%

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

      15. associate--r- 75.5%

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

      16. metadata-eval 75.5%

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

   8. Simplified 75.5%

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

   9. Taylor expanded in y around inf 74.9%

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

   10. Taylor expanded in x around 0 99.3%

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

       1. mul-1-neg 99.3%

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

       2. unsub-neg 99.3%

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

   12. Simplified 99.3%

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

   if -0.17999999999999999 < y < 6.00000000000000001e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.4%

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

   4. Taylor expanded in y around 0 80.1%

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

      1. *-commutative 80.1%

         \[\leadsto x + \color{blue}{y \cdot x} \]

      2. distribute-rgt1-in 80.1%

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

   6. Applied egg-rr 80.1%

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

   if 6.00000000000000001e-57 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 66.3%

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

      1. neg-mul-1 66.3%

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

      2. distribute-neg-frac2 66.3%

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

      3. neg-sub0 66.3%

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

      4. associate--r- 66.3%

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

      5. metadata-eval 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in y around 0 57.4%

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

      1. neg-mul-1 57.4%

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

   8. Simplified 57.4%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.18:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.8:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+15}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.8)
   1.0
   (if (<= y 7.2e-57) (* x (+ y 1.0)) (if (<= y 5.8e+15) (- y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.8) {
		tmp = 1.0;
	} else if (y <= 7.2e-57) {
		tmp = x * (y + 1.0);
	} else if (y <= 5.8e+15) {
		tmp = -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 <= (-0.8d0)) then
        tmp = 1.0d0
    else if (y <= 7.2d-57) then
        tmp = x * (y + 1.0d0)
    else if (y <= 5.8d+15) then
        tmp = -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.8) {
		tmp = 1.0;
	} else if (y <= 7.2e-57) {
		tmp = x * (y + 1.0);
	} else if (y <= 5.8e+15) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.8:
		tmp = 1.0
	elif y <= 7.2e-57:
		tmp = x * (y + 1.0)
	elif y <= 5.8e+15:
		tmp = -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.8)
		tmp = 1.0;
	elseif (y <= 7.2e-57)
		tmp = Float64(x * Float64(y + 1.0));
	elseif (y <= 5.8e+15)
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.8)
		tmp = 1.0;
	elseif (y <= 7.2e-57)
		tmp = x * (y + 1.0);
	elseif (y <= 5.8e+15)
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.8], 1.0, If[LessEqual[y, 7.2e-57], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+15], (-y), 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.80000000000000004 or 5.8e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 80.7%

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

   if -0.80000000000000004 < y < 7.2000000000000005e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.4%

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

   4. Taylor expanded in y around 0 80.1%

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

      1. *-commutative 80.1%

         \[\leadsto x + \color{blue}{y \cdot x} \]

      2. distribute-rgt1-in 80.1%

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

   6. Applied egg-rr 80.1%

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

   if 7.2000000000000005e-57 < y < 5.8e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 56.5%

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

      1. neg-mul-1 56.5%

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

      2. distribute-neg-frac2 56.5%

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

      3. neg-sub0 56.5%

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

      4. associate--r- 56.5%

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

      5. metadata-eval 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in y around 0 49.8%

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

      1. neg-mul-1 49.8%

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

   8. Simplified 49.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.8:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+15}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -260000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+15}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -260000000000.0)
   1.0
   (if (<= y 1.9e-56) x (if (<= y 5.8e+15) (- y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -260000000000.0) {
		tmp = 1.0;
	} else if (y <= 1.9e-56) {
		tmp = x;
	} else if (y <= 5.8e+15) {
		tmp = -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 <= (-260000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.9d-56) then
        tmp = x
    else if (y <= 5.8d+15) then
        tmp = -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -260000000000.0) {
		tmp = 1.0;
	} else if (y <= 1.9e-56) {
		tmp = x;
	} else if (y <= 5.8e+15) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -260000000000.0:
		tmp = 1.0
	elif y <= 1.9e-56:
		tmp = x
	elif y <= 5.8e+15:
		tmp = -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -260000000000.0)
		tmp = 1.0;
	elseif (y <= 1.9e-56)
		tmp = x;
	elseif (y <= 5.8e+15)
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -260000000000.0)
		tmp = 1.0;
	elseif (y <= 1.9e-56)
		tmp = x;
	elseif (y <= 5.8e+15)
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -260000000000.0], 1.0, If[LessEqual[y, 1.9e-56], x, If[LessEqual[y, 5.8e+15], (-y), 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e11 or 5.8e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.3%

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

   if -2.6e11 < y < 1.9000000000000001e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.2%

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

   if 1.9000000000000001e-56 < y < 5.8e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 56.5%

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

      1. neg-mul-1 56.5%

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

      2. distribute-neg-frac2 56.5%

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

      3. neg-sub0 56.5%

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

      4. associate--r- 56.5%

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

      5. metadata-eval 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in y around 0 49.8%

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

      1. neg-mul-1 49.8%

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

   8. Simplified 49.8%

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

Alternative 6: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -260000000000 \lor \neg \left(y \leq 5.8 \cdot 10^{+15}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -260000000000.0) (not (<= y 5.8e+15)))
   (- 1.0 (/ x y))
   (/ x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -260000000000.0) || !(y <= 5.8e+15)) {
		tmp = 1.0 - (x / y);
	} 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 <= (-260000000000.0d0)) .or. (.not. (y <= 5.8d+15))) then
        tmp = 1.0d0 - (x / y)
    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 <= -260000000000.0) || !(y <= 5.8e+15)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -260000000000.0) or not (y <= 5.8e+15):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -260000000000.0) || !(y <= 5.8e+15))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -260000000000.0) || ~((y <= 5.8e+15)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -260000000000.0], N[Not[LessEqual[y, 5.8e+15]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e11 or 5.8e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around -inf 86.9%

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

      1. mul-1-neg 86.9%

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

      2. *-commutative 86.9%

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

      3. distribute-rgt-neg-in 86.9%

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

      4. sub-neg 86.9%

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

      5. associate-/r* 74.7%

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

      6. distribute-neg-frac 74.7%

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

      7. metadata-eval 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in x around inf 86.9%

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

      1. neg-mul-1 86.9%

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

      2. neg-sub0 86.9%

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

      3. associate-+l- 86.9%

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

      4. sub-neg 86.9%

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

      5. *-rgt-identity 86.9%

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

      6. times-frac 74.7%

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

      7. neg-mul-1 74.7%

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

      8. distribute-rgt-in 74.7%

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

      9. neg-sub0 74.7%

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

      10. associate-*l/ 74.8%

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

      11. *-lft-identity 74.8%

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

      12. distribute-neg-frac2 74.8%

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

      13. +-commutative 74.8%

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

      14. neg-sub0 74.8%

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

      15. associate--r- 74.8%

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

      16. metadata-eval 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in y around inf 74.6%

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

   10. Taylor expanded in x around 0 99.8%

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

       1. mul-1-neg 99.8%

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

       2. unsub-neg 99.8%

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

   12. Simplified 99.8%

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

   if -2.6e11 < y < 5.8e15

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.6%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -260000000000 \lor \neg \left(y \leq 5.8 \cdot 10^{+15}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -260000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -260000000000.0) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -260000000000.0) {
		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 <= (-260000000000.0d0)) 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 <= -260000000000.0) {
		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 <= -260000000000.0:
		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 <= -260000000000.0)
		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 <= -260000000000.0)
		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, -260000000000.0], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e11 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.5%

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

   if -2.6e11 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.5%

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

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. Add Preprocessing

3. Taylor expanded in y around inf 42.4%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))