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

Percentage Accurate: 100.0% → 100.0%

Time: 9.7s

Alternatives: 10

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{1 - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 1.0 y)))

C

double code(double x, double y) {
	return (x - y) / (1.0 - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (1.0d0 - y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (1.0 - y);
}

Python

def code(x, y):
	return (x - y) / (1.0 - y)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(1.0 - y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (1.0 - y);
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{1 - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 1.0 y)))

C

double code(double x, double y) {
	return (x - y) / (1.0 - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (1.0d0 - y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (1.0 - y);
}

Python

def code(x, y):
	return (x - y) / (1.0 - y)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(1.0 - y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (1.0 - y);
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{1 - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 1.0 y)))

C

double code(double x, double y) {
	return (x - y) / (1.0 - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (1.0d0 - y)
end function

Java

public static double code(double x, double y) {
	return (x - y) / (1.0 - y);
}

Python

def code(x, y):
	return (x - y) / (1.0 - y)

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(1.0 - y))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (1.0 - y);
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 85.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x + -1}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-23}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ (+ x -1.0) y))))
   (if (<= y -4.2e+15)
     t_0
     (if (<= y -2.8e-105)
       (/ x (- 1.0 y))
       (if (<= y -6.6e-140)
         (- y)
         (if (<= y 3.5e-70)
           x
           (if (<= y 9.2e-23) (- y) (if (<= y 1.0) (+ x (* x y)) t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - ((x + -1.0) / y);
	double tmp;
	if (y <= -4.2e+15) {
		tmp = t_0;
	} else if (y <= -2.8e-105) {
		tmp = x / (1.0 - y);
	} else if (y <= -6.6e-140) {
		tmp = -y;
	} else if (y <= 3.5e-70) {
		tmp = x;
	} else if (y <= 9.2e-23) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x + (x * 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 + (-1.0d0)) / y)
    if (y <= (-4.2d+15)) then
        tmp = t_0
    else if (y <= (-2.8d-105)) then
        tmp = x / (1.0d0 - y)
    else if (y <= (-6.6d-140)) then
        tmp = -y
    else if (y <= 3.5d-70) then
        tmp = x
    else if (y <= 9.2d-23) then
        tmp = -y
    else if (y <= 1.0d0) then
        tmp = x + (x * 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 + -1.0) / y);
	double tmp;
	if (y <= -4.2e+15) {
		tmp = t_0;
	} else if (y <= -2.8e-105) {
		tmp = x / (1.0 - y);
	} else if (y <= -6.6e-140) {
		tmp = -y;
	} else if (y <= 3.5e-70) {
		tmp = x;
	} else if (y <= 9.2e-23) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x + (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - ((x + -1.0) / y)
	tmp = 0
	if y <= -4.2e+15:
		tmp = t_0
	elif y <= -2.8e-105:
		tmp = x / (1.0 - y)
	elif y <= -6.6e-140:
		tmp = -y
	elif y <= 3.5e-70:
		tmp = x
	elif y <= 9.2e-23:
		tmp = -y
	elif y <= 1.0:
		tmp = x + (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(Float64(x + -1.0) / y))
	tmp = 0.0
	if (y <= -4.2e+15)
		tmp = t_0;
	elseif (y <= -2.8e-105)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= -6.6e-140)
		tmp = Float64(-y);
	elseif (y <= 3.5e-70)
		tmp = x;
	elseif (y <= 9.2e-23)
		tmp = Float64(-y);
	elseif (y <= 1.0)
		tmp = Float64(x + Float64(x * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - ((x + -1.0) / y);
	tmp = 0.0;
	if (y <= -4.2e+15)
		tmp = t_0;
	elseif (y <= -2.8e-105)
		tmp = x / (1.0 - y);
	elseif (y <= -6.6e-140)
		tmp = -y;
	elseif (y <= 3.5e-70)
		tmp = x;
	elseif (y <= 9.2e-23)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x + (x * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+15], t$95$0, If[LessEqual[y, -2.8e-105], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.6e-140], (-y), If[LessEqual[y, 3.5e-70], x, If[LessEqual[y, 9.2e-23], (-y), If[LessEqual[y, 1.0], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.2e15 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

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

   5. Simplified 100.0%

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

   if -4.2e15 < y < -2.8e-105

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 67.4%

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

   if -2.8e-105 < y < -6.59999999999999975e-140 or 3.49999999999999974e-70 < y < 9.2000000000000004e-23

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 66.2%

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

      2. pow2 66.2%

         \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   4. Applied egg-rr 66.2%

      \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   5. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{\frac{y \cdot {\left(\sqrt{-1}\right)}^{2}}{1 - y}} \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

      3. rem-square-sqrt 81.5%

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

      4. neg-mul-1 81.5%

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

      5. distribute-neg-frac 81.5%

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

      6. distribute-neg-frac2 81.5%

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

      7. neg-sub0 81.5%

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

      8. associate--r- 81.5%

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

      9. metadata-eval 81.5%

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

      10. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 81.5%

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

      1. neg-mul-1 81.5%

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

   10. Simplified 81.5%

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

   if -6.59999999999999975e-140 < y < 3.49999999999999974e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.7%

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

   if 9.2000000000000004e-23 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

      \[\leadsto \color{blue}{x + y \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1 - \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-23}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x + -1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + x \cdot y\\ \mathbf{if}\;y \leq -0.005:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-103}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-19}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (* x y))))
   (if (<= y -0.005)
     1.0
     (if (<= y -1.7e-103)
       t_0
       (if (<= y -8e-140)
         (- y)
         (if (<= y 1.05e-71)
           x
           (if (<= y 1.06e-19) (- y) (if (<= y 1.0) t_0 1.0))))))))

C

double code(double x, double y) {
	double t_0 = x + (x * y);
	double tmp;
	if (y <= -0.005) {
		tmp = 1.0;
	} else if (y <= -1.7e-103) {
		tmp = t_0;
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 1.05e-71) {
		tmp = x;
	} else if (y <= 1.06e-19) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x + (x * y)
    if (y <= (-0.005d0)) then
        tmp = 1.0d0
    else if (y <= (-1.7d-103)) then
        tmp = t_0
    else if (y <= (-8d-140)) then
        tmp = -y
    else if (y <= 1.05d-71) then
        tmp = x
    else if (y <= 1.06d-19) then
        tmp = -y
    else if (y <= 1.0d0) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + (x * y);
	double tmp;
	if (y <= -0.005) {
		tmp = 1.0;
	} else if (y <= -1.7e-103) {
		tmp = t_0;
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 1.05e-71) {
		tmp = x;
	} else if (y <= 1.06e-19) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + (x * y)
	tmp = 0
	if y <= -0.005:
		tmp = 1.0
	elif y <= -1.7e-103:
		tmp = t_0
	elif y <= -8e-140:
		tmp = -y
	elif y <= 1.05e-71:
		tmp = x
	elif y <= 1.06e-19:
		tmp = -y
	elif y <= 1.0:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(x * y))
	tmp = 0.0
	if (y <= -0.005)
		tmp = 1.0;
	elseif (y <= -1.7e-103)
		tmp = t_0;
	elseif (y <= -8e-140)
		tmp = Float64(-y);
	elseif (y <= 1.05e-71)
		tmp = x;
	elseif (y <= 1.06e-19)
		tmp = Float64(-y);
	elseif (y <= 1.0)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + (x * y);
	tmp = 0.0;
	if (y <= -0.005)
		tmp = 1.0;
	elseif (y <= -1.7e-103)
		tmp = t_0;
	elseif (y <= -8e-140)
		tmp = -y;
	elseif (y <= 1.05e-71)
		tmp = x;
	elseif (y <= 1.06e-19)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.005], 1.0, If[LessEqual[y, -1.7e-103], t$95$0, If[LessEqual[y, -8e-140], (-y), If[LessEqual[y, 1.05e-71], x, If[LessEqual[y, 1.06e-19], (-y), If[LessEqual[y, 1.0], t$95$0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.0050000000000000001 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.8%

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

   if -0.0050000000000000001 < y < -1.70000000000000001e-103 or 1.06e-19 < y < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 67.4%

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

   4. Taylor expanded in y around 0 65.7%

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

      1. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   if -1.70000000000000001e-103 < y < -7.9999999999999999e-140 or 1.0500000000000001e-71 < y < 1.06e-19

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 66.2%

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

      2. pow2 66.2%

         \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   4. Applied egg-rr 66.2%

      \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   5. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{\frac{y \cdot {\left(\sqrt{-1}\right)}^{2}}{1 - y}} \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

      3. rem-square-sqrt 81.5%

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

      4. neg-mul-1 81.5%

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

      5. distribute-neg-frac 81.5%

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

      6. distribute-neg-frac2 81.5%

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

      7. neg-sub0 81.5%

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

      8. associate--r- 81.5%

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

      9. metadata-eval 81.5%

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

      10. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 81.5%

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

      1. neg-mul-1 81.5%

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

   10. Simplified 81.5%

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

   if -7.9999999999999999e-140 < y < 1.0500000000000001e-71

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.005:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-103}:\\ \;\;\;\;x + x \cdot y\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-71}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-19}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-17}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= y -3.1e+43)
     1.0
     (if (<= y -7.2e-106)
       t_0
       (if (<= y -8e-140)
         (- y)
         (if (<= y 1.15e-67)
           x
           (if (<= y 1.8e-17) (- y) (if (<= y 3.5e+17) t_0 1.0))))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -3.1e+43) {
		tmp = 1.0;
	} else if (y <= -7.2e-106) {
		tmp = t_0;
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 1.15e-67) {
		tmp = x;
	} else if (y <= 1.8e-17) {
		tmp = -y;
	} else if (y <= 3.5e+17) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x / (1.0d0 - y)
    if (y <= (-3.1d+43)) then
        tmp = 1.0d0
    else if (y <= (-7.2d-106)) then
        tmp = t_0
    else if (y <= (-8d-140)) then
        tmp = -y
    else if (y <= 1.15d-67) then
        tmp = x
    else if (y <= 1.8d-17) then
        tmp = -y
    else if (y <= 3.5d+17) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -3.1e+43) {
		tmp = 1.0;
	} else if (y <= -7.2e-106) {
		tmp = t_0;
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 1.15e-67) {
		tmp = x;
	} else if (y <= 1.8e-17) {
		tmp = -y;
	} else if (y <= 3.5e+17) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if y <= -3.1e+43:
		tmp = 1.0
	elif y <= -7.2e-106:
		tmp = t_0
	elif y <= -8e-140:
		tmp = -y
	elif y <= 1.15e-67:
		tmp = x
	elif y <= 1.8e-17:
		tmp = -y
	elif y <= 3.5e+17:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(1.0 - y))
	tmp = 0.0
	if (y <= -3.1e+43)
		tmp = 1.0;
	elseif (y <= -7.2e-106)
		tmp = t_0;
	elseif (y <= -8e-140)
		tmp = Float64(-y);
	elseif (y <= 1.15e-67)
		tmp = x;
	elseif (y <= 1.8e-17)
		tmp = Float64(-y);
	elseif (y <= 3.5e+17)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (1.0 - y);
	tmp = 0.0;
	if (y <= -3.1e+43)
		tmp = 1.0;
	elseif (y <= -7.2e-106)
		tmp = t_0;
	elseif (y <= -8e-140)
		tmp = -y;
	elseif (y <= 1.15e-67)
		tmp = x;
	elseif (y <= 1.8e-17)
		tmp = -y;
	elseif (y <= 3.5e+17)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+43], 1.0, If[LessEqual[y, -7.2e-106], t$95$0, If[LessEqual[y, -8e-140], (-y), If[LessEqual[y, 1.15e-67], x, If[LessEqual[y, 1.8e-17], (-y), If[LessEqual[y, 3.5e+17], t$95$0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1000000000000002e43 or 3.5e17 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.3%

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

   if -3.1000000000000002e43 < y < -7.20000000000000025e-106 or 1.79999999999999997e-17 < y < 3.5e17

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 69.4%

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

   if -7.20000000000000025e-106 < y < -7.9999999999999999e-140 or 1.15e-67 < y < 1.79999999999999997e-17

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 66.2%

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

      2. pow2 66.2%

         \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   4. Applied egg-rr 66.2%

      \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   5. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{\frac{y \cdot {\left(\sqrt{-1}\right)}^{2}}{1 - y}} \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

      3. rem-square-sqrt 81.5%

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

      4. neg-mul-1 81.5%

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

      5. distribute-neg-frac 81.5%

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

      6. distribute-neg-frac2 81.5%

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

      7. neg-sub0 81.5%

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

      8. associate--r- 81.5%

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

      9. metadata-eval 81.5%

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

      10. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 81.5%

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

      1. neg-mul-1 81.5%

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

   10. Simplified 81.5%

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

   if -7.9999999999999999e-140 < y < 1.15e-67

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.7%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-17}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-17}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+15)
   1.0
   (if (<= y -5.8e-105)
     x
     (if (<= y -8e-140)
       (- y)
       (if (<= y 1.22e-67)
         x
         (if (<= y 9e-17) (- y) (if (<= y 4.1e+17) (/ x (- y)) 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = 1.0;
	} else if (y <= -5.8e-105) {
		tmp = x;
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 1.22e-67) {
		tmp = x;
	} else if (y <= 9e-17) {
		tmp = -y;
	} else if (y <= 4.1e+17) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.2d+15)) then
        tmp = 1.0d0
    else if (y <= (-5.8d-105)) then
        tmp = x
    else if (y <= (-8d-140)) then
        tmp = -y
    else if (y <= 1.22d-67) then
        tmp = x
    else if (y <= 9d-17) then
        tmp = -y
    else if (y <= 4.1d+17) then
        tmp = x / -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = 1.0;
	} else if (y <= -5.8e-105) {
		tmp = x;
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 1.22e-67) {
		tmp = x;
	} else if (y <= 9e-17) {
		tmp = -y;
	} else if (y <= 4.1e+17) {
		tmp = x / -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+15:
		tmp = 1.0
	elif y <= -5.8e-105:
		tmp = x
	elif y <= -8e-140:
		tmp = -y
	elif y <= 1.22e-67:
		tmp = x
	elif y <= 9e-17:
		tmp = -y
	elif y <= 4.1e+17:
		tmp = x / -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+15)
		tmp = 1.0;
	elseif (y <= -5.8e-105)
		tmp = x;
	elseif (y <= -8e-140)
		tmp = Float64(-y);
	elseif (y <= 1.22e-67)
		tmp = x;
	elseif (y <= 9e-17)
		tmp = Float64(-y);
	elseif (y <= 4.1e+17)
		tmp = Float64(x / Float64(-y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.2e+15)
		tmp = 1.0;
	elseif (y <= -5.8e-105)
		tmp = x;
	elseif (y <= -8e-140)
		tmp = -y;
	elseif (y <= 1.22e-67)
		tmp = x;
	elseif (y <= 9e-17)
		tmp = -y;
	elseif (y <= 4.1e+17)
		tmp = x / -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+15], 1.0, If[LessEqual[y, -5.8e-105], x, If[LessEqual[y, -8e-140], (-y), If[LessEqual[y, 1.22e-67], x, If[LessEqual[y, 9e-17], (-y), If[LessEqual[y, 4.1e+17], N[(x / (-y)), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2e15 or 4.1e17 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 83.1%

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

   if -4.2e15 < y < -5.80000000000000007e-105 or -7.9999999999999999e-140 < y < 1.22e-67

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 81.5%

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

   if -5.80000000000000007e-105 < y < -7.9999999999999999e-140 or 1.22e-67 < y < 8.99999999999999957e-17

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 66.2%

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

      2. pow2 66.2%

         \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   4. Applied egg-rr 66.2%

      \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   5. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{\frac{y \cdot {\left(\sqrt{-1}\right)}^{2}}{1 - y}} \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

      3. rem-square-sqrt 81.5%

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

      4. neg-mul-1 81.5%

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

      5. distribute-neg-frac 81.5%

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

      6. distribute-neg-frac2 81.5%

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

      7. neg-sub0 81.5%

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

      8. associate--r- 81.5%

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

      9. metadata-eval 81.5%

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

      10. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 81.5%

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

      1. neg-mul-1 81.5%

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

   10. Simplified 81.5%

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

   if 8.99999999999999957e-17 < y < 4.1e17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in y around inf 50.2%

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

      1. associate-*r/ 50.2%

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

      2. neg-mul-1 50.2%

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

   6. Simplified 50.2%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-17}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{-18}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+15)
   1.0
   (if (<= y -7.2e-106)
     x
     (if (<= y -8e-140)
       (- y)
       (if (<= y 1.3e-67) x (if (<= y 1e-18) (- y) (if (<= y 1.0) x 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = 1.0;
	} else if (y <= -7.2e-106) {
		tmp = x;
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 1.3e-67) {
		tmp = x;
	} else if (y <= 1e-18) {
		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 <= (-4.2d+15)) then
        tmp = 1.0d0
    else if (y <= (-7.2d-106)) then
        tmp = x
    else if (y <= (-8d-140)) then
        tmp = -y
    else if (y <= 1.3d-67) then
        tmp = x
    else if (y <= 1d-18) 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 <= -4.2e+15) {
		tmp = 1.0;
	} else if (y <= -7.2e-106) {
		tmp = x;
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 1.3e-67) {
		tmp = x;
	} else if (y <= 1e-18) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+15:
		tmp = 1.0
	elif y <= -7.2e-106:
		tmp = x
	elif y <= -8e-140:
		tmp = -y
	elif y <= 1.3e-67:
		tmp = x
	elif y <= 1e-18:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+15)
		tmp = 1.0;
	elseif (y <= -7.2e-106)
		tmp = x;
	elseif (y <= -8e-140)
		tmp = Float64(-y);
	elseif (y <= 1.3e-67)
		tmp = x;
	elseif (y <= 1e-18)
		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 <= -4.2e+15)
		tmp = 1.0;
	elseif (y <= -7.2e-106)
		tmp = x;
	elseif (y <= -8e-140)
		tmp = -y;
	elseif (y <= 1.3e-67)
		tmp = x;
	elseif (y <= 1e-18)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+15], 1.0, If[LessEqual[y, -7.2e-106], x, If[LessEqual[y, -8e-140], (-y), If[LessEqual[y, 1.3e-67], x, If[LessEqual[y, 1e-18], (-y), If[LessEqual[y, 1.0], x, 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e15 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.4%

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

   if -4.2e15 < y < -7.20000000000000025e-106 or -7.9999999999999999e-140 < y < 1.2999999999999999e-67 or 1.0000000000000001e-18 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 81.7%

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

   if -7.20000000000000025e-106 < y < -7.9999999999999999e-140 or 1.2999999999999999e-67 < y < 1.0000000000000001e-18

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 66.2%

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

      2. pow2 66.2%

         \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   4. Applied egg-rr 66.2%

      \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   5. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{\frac{y \cdot {\left(\sqrt{-1}\right)}^{2}}{1 - y}} \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

      3. rem-square-sqrt 81.5%

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

      4. neg-mul-1 81.5%

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

      5. distribute-neg-frac 81.5%

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

      6. distribute-neg-frac2 81.5%

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

      7. neg-sub0 81.5%

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

      8. associate--r- 81.5%

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

      9. metadata-eval 81.5%

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

      10. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in y around 0 81.5%

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

      1. neg-mul-1 81.5%

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

   10. Simplified 81.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{-18}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.58 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.58e+44)
   1.0
   (if (<= y -2.5e-99)
     (/ x (- 1.0 y))
     (if (<= y -8e-140) (- y) (if (<= y 3.4e-68) x (/ y (+ y -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.58e+44) {
		tmp = 1.0;
	} else if (y <= -2.5e-99) {
		tmp = x / (1.0 - y);
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 3.4e-68) {
		tmp = x;
	} else {
		tmp = y / (y + -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 <= (-1.58d+44)) then
        tmp = 1.0d0
    else if (y <= (-2.5d-99)) then
        tmp = x / (1.0d0 - y)
    else if (y <= (-8d-140)) then
        tmp = -y
    else if (y <= 3.4d-68) then
        tmp = x
    else
        tmp = y / (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.58e+44) {
		tmp = 1.0;
	} else if (y <= -2.5e-99) {
		tmp = x / (1.0 - y);
	} else if (y <= -8e-140) {
		tmp = -y;
	} else if (y <= 3.4e-68) {
		tmp = x;
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.58e+44:
		tmp = 1.0
	elif y <= -2.5e-99:
		tmp = x / (1.0 - y)
	elif y <= -8e-140:
		tmp = -y
	elif y <= 3.4e-68:
		tmp = x
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.58e+44)
		tmp = 1.0;
	elseif (y <= -2.5e-99)
		tmp = Float64(x / Float64(1.0 - y));
	elseif (y <= -8e-140)
		tmp = Float64(-y);
	elseif (y <= 3.4e-68)
		tmp = x;
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.58e+44)
		tmp = 1.0;
	elseif (y <= -2.5e-99)
		tmp = x / (1.0 - y);
	elseif (y <= -8e-140)
		tmp = -y;
	elseif (y <= 3.4e-68)
		tmp = x;
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.58e+44], 1.0, If[LessEqual[y, -2.5e-99], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-140], (-y), If[LessEqual[y, 3.4e-68], x, N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.57999999999999993e44

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.8%

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

   if -1.57999999999999993e44 < y < -2.49999999999999985e-99

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 67.5%

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

   if -2.49999999999999985e-99 < y < -7.9999999999999999e-140

   1. Initial program 100.0%

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

      1. add-sqr-sqrt 99.4%

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

      2. pow2 99.4%

         \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   4. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{{\left(\sqrt{\frac{x - y}{1 - y}}\right)}^{2}} \]

   5. Taylor expanded in x around 0 0.0%

      \[\leadsto \color{blue}{\frac{y \cdot {\left(\sqrt{-1}\right)}^{2}}{1 - y}} \]
   6. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

      3. rem-square-sqrt 86.3%

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

      4. neg-mul-1 86.3%

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

      5. distribute-neg-frac 86.3%

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

      6. distribute-neg-frac2 86.3%

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

      7. neg-sub0 86.3%

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

      8. associate--r- 86.3%

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

      9. metadata-eval 86.3%

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

      10. +-commutative 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in y around 0 86.3%

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

      1. neg-mul-1 86.3%

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

   10. Simplified 86.3%

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

   if -7.9999999999999999e-140 < y < 3.40000000000000018e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.7%

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

   if 3.40000000000000018e-68 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.1%

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

      1. neg-mul-1 76.1%

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

      2. distribute-neg-frac2 76.1%

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

      3. neg-sub0 76.1%

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

      4. associate--r- 76.1%

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

      5. metadata-eval 76.1%

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

   5. Simplified 76.1%

      \[\leadsto \color{blue}{\frac{y}{-1 + y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.58 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-140}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.4% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0)))
   (- 1.0 (/ (+ x -1.0) y))
   (+ x (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = 1.0 - ((x + -1.0) / y);
	} else {
		tmp = x + (y * (x + -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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 - ((x + (-1.0d0)) / y)
    else
        tmp = x + (y * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.0%

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

      1. +-commutative 99.0%

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

      2. mul-1-neg 99.0%

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

      3. unsub-neg 99.0%

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

      4. div-sub 99.0%

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

   5. Simplified 99.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

      1. mul-1-neg 98.6%

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

      2. *-commutative 98.6%

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

      3. distribute-lft-neg-in 98.6%

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

      4. cancel-sign-sub 98.6%

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

      5. +-commutative 98.6%

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

      6. metadata-eval 98.6%

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

      7. distribute-lft-in 98.6%

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

      8. metadata-eval 98.6%

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

      9. sub-neg 98.6%

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

      10. mul-1-neg 98.6%

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

      11. remove-double-neg 98.6%

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

      12. sub-neg 98.6%

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

      13. metadata-eval 98.6%

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

      14. +-commutative 98.6%

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

      15. distribute-neg-in 98.6%

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

      16. metadata-eval 98.6%

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

      17. mul-1-neg 98.6%

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

      18. *-commutative 98.6%

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

      19. mul-1-neg 98.6%

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

      20. unsub-neg 98.6%

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

   5. Simplified 98.6%

      \[\leadsto \color{blue}{x - y \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

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

Alternative 9: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+15) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.2d+15)) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+15:
		tmp = 1.0
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+15)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.2e+15)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+15], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e15 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.4%

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

   if -4.2e15 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 40.2%

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

4. Final simplification 40.2%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024044 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))