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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -1}\\ t_1 := \frac{-x}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -126000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-22}:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+28} \lor \neg \left(y \leq 2.35 \cdot 10^{+55}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -1.0))) (t_1 (/ (- x) y)))
   (if (<= y -4.2e+116)
     1.0
     (if (<= y -126000000000.0)
       t_1
       (if (<= y -1.85e-9)
         t_0
         (if (<= y 9.5e-22)
           (- x y)
           (if (or (<= y 8e+28) (not (<= y 2.35e+55))) t_0 t_1)))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -1.0);
	double t_1 = -x / y;
	double tmp;
	if (y <= -4.2e+116) {
		tmp = 1.0;
	} else if (y <= -126000000000.0) {
		tmp = t_1;
	} else if (y <= -1.85e-9) {
		tmp = t_0;
	} else if (y <= 9.5e-22) {
		tmp = x - y;
	} else if ((y <= 8e+28) || !(y <= 2.35e+55)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = y / (y + (-1.0d0))
    t_1 = -x / y
    if (y <= (-4.2d+116)) then
        tmp = 1.0d0
    else if (y <= (-126000000000.0d0)) then
        tmp = t_1
    else if (y <= (-1.85d-9)) then
        tmp = t_0
    else if (y <= 9.5d-22) then
        tmp = x - y
    else if ((y <= 8d+28) .or. (.not. (y <= 2.35d+55))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -1.0);
	double t_1 = -x / y;
	double tmp;
	if (y <= -4.2e+116) {
		tmp = 1.0;
	} else if (y <= -126000000000.0) {
		tmp = t_1;
	} else if (y <= -1.85e-9) {
		tmp = t_0;
	} else if (y <= 9.5e-22) {
		tmp = x - y;
	} else if ((y <= 8e+28) || !(y <= 2.35e+55)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -1.0)
	t_1 = -x / y
	tmp = 0
	if y <= -4.2e+116:
		tmp = 1.0
	elif y <= -126000000000.0:
		tmp = t_1
	elif y <= -1.85e-9:
		tmp = t_0
	elif y <= 9.5e-22:
		tmp = x - y
	elif (y <= 8e+28) or not (y <= 2.35e+55):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -1.0))
	t_1 = Float64(Float64(-x) / y)
	tmp = 0.0
	if (y <= -4.2e+116)
		tmp = 1.0;
	elseif (y <= -126000000000.0)
		tmp = t_1;
	elseif (y <= -1.85e-9)
		tmp = t_0;
	elseif (y <= 9.5e-22)
		tmp = Float64(x - y);
	elseif ((y <= 8e+28) || !(y <= 2.35e+55))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -1.0);
	t_1 = -x / y;
	tmp = 0.0;
	if (y <= -4.2e+116)
		tmp = 1.0;
	elseif (y <= -126000000000.0)
		tmp = t_1;
	elseif (y <= -1.85e-9)
		tmp = t_0;
	elseif (y <= 9.5e-22)
		tmp = x - y;
	elseif ((y <= 8e+28) || ~((y <= 2.35e+55)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-x) / y), $MachinePrecision]}, If[LessEqual[y, -4.2e+116], 1.0, If[LessEqual[y, -126000000000.0], t$95$1, If[LessEqual[y, -1.85e-9], t$95$0, If[LessEqual[y, 9.5e-22], N[(x - y), $MachinePrecision], If[Or[LessEqual[y, 8e+28], N[Not[LessEqual[y, 2.35e+55]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2000000000000002e116

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 92.9%

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

   if -4.2000000000000002e116 < y < -1.26e11 or 7.99999999999999967e28 < y < 2.35e55

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 61.7%

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

      1. sub-neg 61.7%

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

      2. metadata-eval 61.7%

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

      3. neg-mul-1 61.7%

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

      4. distribute-neg-frac 61.7%

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

      5. +-commutative 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in y around inf 61.3%

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

      1. neg-mul-1 61.3%

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

      2. distribute-neg-frac 61.3%

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

   9. Simplified 61.3%

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

   if -1.26e11 < y < -1.85e-9 or 9.4999999999999994e-22 < y < 7.99999999999999967e28 or 2.35e55 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 81.8%

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

   if -1.85e-9 < y < 9.4999999999999994e-22

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 99.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -126000000000:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-22}:\\ \;\;\;\;x - y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+28} \lor \neg \left(y \leq 2.35 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y}\\ \end{array} \]

Alternative 3: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -430000000:\\ \;\;\;\;\frac{-x}{y + -1}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-10} \lor \neg \left(y \leq 9.5 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.6e+116)
   1.0
   (if (<= y -430000000.0)
     (/ (- x) (+ y -1.0))
     (if (or (<= y -2.9e-10) (not (<= y 9.5e-22))) (/ y (+ y -1.0)) (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.6e+116) {
		tmp = 1.0;
	} else if (y <= -430000000.0) {
		tmp = -x / (y + -1.0);
	} else if ((y <= -2.9e-10) || !(y <= 9.5e-22)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x - 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 <= (-3.6d+116)) then
        tmp = 1.0d0
    else if (y <= (-430000000.0d0)) then
        tmp = -x / (y + (-1.0d0))
    else if ((y <= (-2.9d-10)) .or. (.not. (y <= 9.5d-22))) then
        tmp = y / (y + (-1.0d0))
    else
        tmp = x - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.6e+116) {
		tmp = 1.0;
	} else if (y <= -430000000.0) {
		tmp = -x / (y + -1.0);
	} else if ((y <= -2.9e-10) || !(y <= 9.5e-22)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.6e+116:
		tmp = 1.0
	elif y <= -430000000.0:
		tmp = -x / (y + -1.0)
	elif (y <= -2.9e-10) or not (y <= 9.5e-22):
		tmp = y / (y + -1.0)
	else:
		tmp = x - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.6e+116)
		tmp = 1.0;
	elseif (y <= -430000000.0)
		tmp = Float64(Float64(-x) / Float64(y + -1.0));
	elseif ((y <= -2.9e-10) || !(y <= 9.5e-22))
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = Float64(x - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.6e+116)
		tmp = 1.0;
	elseif (y <= -430000000.0)
		tmp = -x / (y + -1.0);
	elseif ((y <= -2.9e-10) || ~((y <= 9.5e-22)))
		tmp = y / (y + -1.0);
	else
		tmp = x - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.6e+116], 1.0, If[LessEqual[y, -430000000.0], N[((-x) / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.9e-10], N[Not[LessEqual[y, 9.5e-22]], $MachinePrecision]], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x - y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.59999999999999971e116

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 92.9%

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

   if -3.59999999999999971e116 < y < -4.3e8

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 57.0%

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

      1. sub-neg 57.0%

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

      2. metadata-eval 57.0%

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

      3. neg-mul-1 57.0%

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

      4. distribute-neg-frac 57.0%

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

      5. +-commutative 57.0%

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

   6. Simplified 57.0%

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

   if -4.3e8 < y < -2.89999999999999981e-10 or 9.4999999999999994e-22 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 75.7%

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

   if -2.89999999999999981e-10 < y < 9.4999999999999994e-22

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 99.8%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -430000000:\\ \;\;\;\;\frac{-x}{y + -1}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-10} \lor \neg \left(y \leq 9.5 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \]

Alternative 4: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2150000000000:\\ \;\;\;\;\frac{-x}{y + -1}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{1}{y + -1}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-22}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+116)
   1.0
   (if (<= y -2150000000000.0)
     (/ (- x) (+ y -1.0))
     (if (<= y -1.85e-9)
       (* y (/ 1.0 (+ y -1.0)))
       (if (<= y 9.5e-22) (- x y) (/ y (+ y -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+116) {
		tmp = 1.0;
	} else if (y <= -2150000000000.0) {
		tmp = -x / (y + -1.0);
	} else if (y <= -1.85e-9) {
		tmp = y * (1.0 / (y + -1.0));
	} else if (y <= 9.5e-22) {
		tmp = x - y;
	} 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 <= (-5d+116)) then
        tmp = 1.0d0
    else if (y <= (-2150000000000.0d0)) then
        tmp = -x / (y + (-1.0d0))
    else if (y <= (-1.85d-9)) then
        tmp = y * (1.0d0 / (y + (-1.0d0)))
    else if (y <= 9.5d-22) then
        tmp = x - y
    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 <= -5e+116) {
		tmp = 1.0;
	} else if (y <= -2150000000000.0) {
		tmp = -x / (y + -1.0);
	} else if (y <= -1.85e-9) {
		tmp = y * (1.0 / (y + -1.0));
	} else if (y <= 9.5e-22) {
		tmp = x - y;
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+116:
		tmp = 1.0
	elif y <= -2150000000000.0:
		tmp = -x / (y + -1.0)
	elif y <= -1.85e-9:
		tmp = y * (1.0 / (y + -1.0))
	elif y <= 9.5e-22:
		tmp = x - y
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+116)
		tmp = 1.0;
	elseif (y <= -2150000000000.0)
		tmp = Float64(Float64(-x) / Float64(y + -1.0));
	elseif (y <= -1.85e-9)
		tmp = Float64(y * Float64(1.0 / Float64(y + -1.0)));
	elseif (y <= 9.5e-22)
		tmp = Float64(x - y);
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+116)
		tmp = 1.0;
	elseif (y <= -2150000000000.0)
		tmp = -x / (y + -1.0);
	elseif (y <= -1.85e-9)
		tmp = y * (1.0 / (y + -1.0));
	elseif (y <= 9.5e-22)
		tmp = x - y;
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+116], 1.0, If[LessEqual[y, -2150000000000.0], N[((-x) / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-9], N[(y * N[(1.0 / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-22], N[(x - y), $MachinePrecision], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.00000000000000025e116

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 92.9%

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

   if -5.00000000000000025e116 < y < -2.15e12

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 57.0%

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

      1. sub-neg 57.0%

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

      2. metadata-eval 57.0%

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

      3. neg-mul-1 57.0%

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

      4. distribute-neg-frac 57.0%

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

      5. +-commutative 57.0%

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

   6. Simplified 57.0%

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

   if -2.15e12 < y < -1.85e-9

   1. Initial program 99.2%

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

      1. sub-neg 99.2%

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

      2. +-commutative 99.2%

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

      3. neg-sub0 99.2%

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

      4. associate-+l- 99.2%

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

      5. sub0-neg 99.2%

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

      6. neg-mul-1 99.2%

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

      7. sub-neg 99.2%

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

      8. +-commutative 99.2%

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

      9. neg-sub0 99.2%

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

      10. associate-+l- 99.2%

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

      11. sub0-neg 99.2%

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

      12. neg-mul-1 99.2%

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

      13. times-frac 99.2%

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

      14. metadata-eval 99.2%

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

      15. *-lft-identity 99.2%

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

      16. sub-neg 99.2%

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

      17. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 99.2%

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

      1. clear-num 98.8%

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

      2. associate-/r/ 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

   6. Applied egg-rr 99.6%

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

   if -1.85e-9 < y < 9.4999999999999994e-22

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 99.8%

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

   if 9.4999999999999994e-22 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 74.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2150000000000:\\ \;\;\;\;\frac{-x}{y + -1}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \frac{1}{y + -1}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-22}:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]

Alternative 5: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.2) (not (<= y 1.0))) (+ 1.0 (/ (- 1.0 x) y)) (- x y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.2) || !(y <= 1.0)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x - 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 <= (-1.2d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) / y)
    else
        tmp = x - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.2) || !(y <= 1.0)) {
		tmp = 1.0 + ((1.0 - x) / y);
	} else {
		tmp = x - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.2) or not (y <= 1.0):
		tmp = 1.0 + ((1.0 - x) / y)
	else:
		tmp = x - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.2) || !(y <= 1.0))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.2) || ~((y <= 1.0)))
		tmp = 1.0 + ((1.0 - x) / y);
	else
		tmp = x - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.2], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999996 or 1 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. associate-+r+ 98.7%

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

      3. mul-1-neg 98.7%

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

      4. unsub-neg 98.7%

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

      5. div-sub 98.7%

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

      6. unsub-neg 98.7%

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

      7. mul-1-neg 98.7%

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

      8. +-commutative 98.7%

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

      9. metadata-eval 98.7%

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

      10. distribute-lft-in 98.7%

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

      11. metadata-eval 98.7%

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

      12. sub-neg 98.7%

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

      13. associate-*r/ 98.7%

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

      14. +-commutative 98.7%

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

      15. associate-*r/ 98.7%

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

      16. sub-neg 98.7%

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

      17. metadata-eval 98.7%

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

      18. distribute-lft-in 98.7%

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

      19. metadata-eval 98.7%

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

      20. +-commutative 98.7%

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

      21. mul-1-neg 98.7%

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

      22. unsub-neg 98.7%

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

   6. Simplified 98.7%

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

   if -1.19999999999999996 < y < 1

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 97.7%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y\\ \end{array} \]

Alternative 6: 98.5% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0)))
   (+ 1.0 (/ (- 1.0 x) 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 + ((1.0 - x) / 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 + ((1.0d0 - x) / 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 + ((1.0 - x) / 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 + ((1.0 - x) / 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(1.0 - x) / 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 + ((1.0 - x) / 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[(1.0 - x), $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 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. associate-+r+ 98.7%

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

      3. mul-1-neg 98.7%

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

      4. unsub-neg 98.7%

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

      5. div-sub 98.7%

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

      6. unsub-neg 98.7%

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

      7. mul-1-neg 98.7%

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

      8. +-commutative 98.7%

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

      9. metadata-eval 98.7%

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

      10. distribute-lft-in 98.7%

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

      11. metadata-eval 98.7%

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

      12. sub-neg 98.7%

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

      13. associate-*r/ 98.7%

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

      14. +-commutative 98.7%

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

      15. associate-*r/ 98.7%

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

      16. sub-neg 98.7%

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

      17. metadata-eval 98.7%

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

      18. distribute-lft-in 98.7%

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

      19. metadata-eval 98.7%

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

      20. +-commutative 98.7%

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

      21. mul-1-neg 98.7%

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

      22. unsub-neg 98.7%

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

   6. Simplified 98.7%

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

   if -1 < y < 1

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

      4. mul-1-neg 97.9%

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

      5. unsub-neg 97.9%

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

   6. Simplified 97.9%

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

4. Final simplification 98.3%

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

Alternative 7: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1250:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.6e+116)
   1.0
   (if (<= y -1250.0) (/ (- x) y) (if (<= y 1.0) (- x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.6e+116) {
		tmp = 1.0;
	} else if (y <= -1250.0) {
		tmp = -x / y;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.6d+116)) then
        tmp = 1.0d0
    else if (y <= (-1250.0d0)) then
        tmp = -x / y
    else if (y <= 1.0d0) then
        tmp = x - y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.6e+116) {
		tmp = 1.0;
	} else if (y <= -1250.0) {
		tmp = -x / y;
	} else if (y <= 1.0) {
		tmp = x - y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.6e+116:
		tmp = 1.0
	elif y <= -1250.0:
		tmp = -x / y
	elif y <= 1.0:
		tmp = x - y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.6e+116)
		tmp = 1.0;
	elseif (y <= -1250.0)
		tmp = Float64(Float64(-x) / y);
	elseif (y <= 1.0)
		tmp = Float64(x - y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.6e+116)
		tmp = 1.0;
	elseif (y <= -1250.0)
		tmp = -x / y;
	elseif (y <= 1.0)
		tmp = x - y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.6e+116], 1.0, If[LessEqual[y, -1250.0], N[((-x) / y), $MachinePrecision], If[LessEqual[y, 1.0], N[(x - y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.59999999999999971e116 or 1 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 79.3%

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

   if -3.59999999999999971e116 < y < -1250

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 57.0%

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

      1. sub-neg 57.0%

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

      2. metadata-eval 57.0%

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

      3. neg-mul-1 57.0%

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

      4. distribute-neg-frac 57.0%

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

      5. +-commutative 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in y around inf 56.5%

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

      1. neg-mul-1 56.5%

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

      2. distribute-neg-frac 56.5%

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

   9. Simplified 56.5%

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

   if -1250 < y < 1

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 97.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1250:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+117}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.00182:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.4e+117)
   1.0
   (if (<= y -0.00182) (/ (- x) y) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.4e+117) {
		tmp = 1.0;
	} else if (y <= -0.00182) {
		tmp = -x / 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 <= (-4.4d+117)) then
        tmp = 1.0d0
    else if (y <= (-0.00182d0)) then
        tmp = -x / 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 <= -4.4e+117) {
		tmp = 1.0;
	} else if (y <= -0.00182) {
		tmp = -x / y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.4e+117:
		tmp = 1.0
	elif y <= -0.00182:
		tmp = -x / y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.4e+117)
		tmp = 1.0;
	elseif (y <= -0.00182)
		tmp = Float64(Float64(-x) / 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 <= -4.4e+117)
		tmp = 1.0;
	elseif (y <= -0.00182)
		tmp = -x / y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.4e+117], 1.0, If[LessEqual[y, -0.00182], N[((-x) / y), $MachinePrecision], If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.40000000000000028e117 or 1 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 79.3%

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

   if -4.40000000000000028e117 < y < -0.00182

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. +-commutative 99.8%

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

      3. neg-sub0 99.8%

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

      4. associate-+l- 99.8%

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

      5. sub0-neg 99.8%

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

      6. neg-mul-1 99.8%

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

      7. sub-neg 99.8%

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

      8. +-commutative 99.8%

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

      9. neg-sub0 99.8%

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

      10. associate-+l- 99.8%

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

      11. sub0-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. times-frac 99.8%

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

      14. metadata-eval 99.8%

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

      15. *-lft-identity 99.8%

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

      16. sub-neg 99.8%

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

      17. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 52.9%

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

      1. sub-neg 52.9%

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

      2. metadata-eval 52.9%

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

      3. neg-mul-1 52.9%

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

      4. distribute-neg-frac 52.9%

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

      5. +-commutative 52.9%

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

   6. Simplified 52.9%

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

   7. Taylor expanded in y around inf 52.4%

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

      1. neg-mul-1 52.4%

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

      2. distribute-neg-frac 52.4%

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

   9. Simplified 52.4%

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

   if -0.00182 < y < 1

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.6%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+117}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.00182:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 74.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.85e-9) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.85e-9) {
		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 <= (-1.85d-9)) 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 <= -1.85e-9) {
		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 <= -1.85e-9:
		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 <= -1.85e-9)
		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 <= -1.85e-9)
		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, -1.85e-9], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e-9 or 1 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. sub0-neg 99.9%

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

      6. neg-mul-1 99.9%

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

      7. sub-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. neg-sub0 99.9%

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

      10. associate-+l- 99.9%

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

      11. sub0-neg 99.9%

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

      12. neg-mul-1 99.9%

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

      13. times-frac 99.9%

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

      14. metadata-eval 99.9%

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

      15. *-lft-identity 99.9%

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

      16. sub-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 68.2%

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

   if -1.85e-9 < y < 1

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. neg-sub0 100.0%

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

      10. associate-+l- 100.0%

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

      11. sub0-neg 100.0%

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

      12. neg-mul-1 100.0%

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

      13. times-frac 100.0%

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

      14. metadata-eval 100.0%

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

      15. *-lft-identity 100.0%

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

      16. sub-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 81.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 39.4% 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 99.9%

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

   1. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. neg-sub0 99.9%

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

   4. associate-+l- 99.9%

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

   5. sub0-neg 99.9%

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

   6. neg-mul-1 99.9%

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

   7. sub-neg 99.9%

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

   8. +-commutative 99.9%

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

   9. neg-sub0 99.9%

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

   10. associate-+l- 99.9%

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

   11. sub0-neg 99.9%

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

   12. neg-mul-1 99.9%

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

   13. times-frac 99.9%

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

   14. metadata-eval 99.9%

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

   15. *-lft-identity 99.9%

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

   16. sub-neg 99.9%

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

   17. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around inf 40.9%

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

5. Final simplification 40.9%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023222 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))