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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 86.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -900000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-92}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 28000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 1.0 x) y))))
   (if (<= y -900000000000.0)
     t_0
     (if (<= y -3.7e-30)
       (/ y (+ y -1.0))
       (if (<= y 5.5e-101)
         x
         (if (<= y 2.3e-92) (- y) (if (<= y 28000.0) (/ x (- 1.0 y)) t_0)))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((1.0 - x) / y);
	double tmp;
	if (y <= -900000000000.0) {
		tmp = t_0;
	} else if (y <= -3.7e-30) {
		tmp = y / (y + -1.0);
	} else if (y <= 5.5e-101) {
		tmp = x;
	} else if (y <= 2.3e-92) {
		tmp = -y;
	} else if (y <= 28000.0) {
		tmp = x / (1.0 - 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 + ((1.0d0 - x) / y)
    if (y <= (-900000000000.0d0)) then
        tmp = t_0
    else if (y <= (-3.7d-30)) then
        tmp = y / (y + (-1.0d0))
    else if (y <= 5.5d-101) then
        tmp = x
    else if (y <= 2.3d-92) then
        tmp = -y
    else if (y <= 28000.0d0) then
        tmp = x / (1.0d0 - 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 + ((1.0 - x) / y);
	double tmp;
	if (y <= -900000000000.0) {
		tmp = t_0;
	} else if (y <= -3.7e-30) {
		tmp = y / (y + -1.0);
	} else if (y <= 5.5e-101) {
		tmp = x;
	} else if (y <= 2.3e-92) {
		tmp = -y;
	} else if (y <= 28000.0) {
		tmp = x / (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((1.0 - x) / y)
	tmp = 0
	if y <= -900000000000.0:
		tmp = t_0
	elif y <= -3.7e-30:
		tmp = y / (y + -1.0)
	elif y <= 5.5e-101:
		tmp = x
	elif y <= 2.3e-92:
		tmp = -y
	elif y <= 28000.0:
		tmp = x / (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(1.0 - x) / y))
	tmp = 0.0
	if (y <= -900000000000.0)
		tmp = t_0;
	elseif (y <= -3.7e-30)
		tmp = Float64(y / Float64(y + -1.0));
	elseif (y <= 5.5e-101)
		tmp = x;
	elseif (y <= 2.3e-92)
		tmp = Float64(-y);
	elseif (y <= 28000.0)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((1.0 - x) / y);
	tmp = 0.0;
	if (y <= -900000000000.0)
		tmp = t_0;
	elseif (y <= -3.7e-30)
		tmp = y / (y + -1.0);
	elseif (y <= 5.5e-101)
		tmp = x;
	elseif (y <= 2.3e-92)
		tmp = -y;
	elseif (y <= 28000.0)
		tmp = x / (1.0 - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -900000000000.0], t$95$0, If[LessEqual[y, -3.7e-30], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-101], x, If[LessEqual[y, 2.3e-92], (-y), If[LessEqual[y, 28000.0], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9e11 or 28000 < 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 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+r+ 99.7%

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

      3. mul-1-neg 99.7%

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

      4. unsub-neg 99.7%

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

      5. div-sub 99.7%

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

      6. unsub-neg 99.7%

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

      7. mul-1-neg 99.7%

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

      8. +-commutative 99.7%

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

      9. metadata-eval 99.7%

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

      10. distribute-lft-in 99.7%

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

      11. metadata-eval 99.7%

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

      12. sub-neg 99.7%

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

      13. associate-*r/ 99.7%

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

      14. +-commutative 99.7%

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

      15. associate-*r/ 99.7%

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

      16. sub-neg 99.7%

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

      17. metadata-eval 99.7%

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

      18. distribute-lft-in 99.7%

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

      19. metadata-eval 99.7%

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

      20. +-commutative 99.7%

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

      21. mul-1-neg 99.7%

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

      22. unsub-neg 99.7%

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

   6. Simplified 99.7%

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

   if -9e11 < y < -3.7000000000000003e-30

   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 0 92.3%

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

   if -3.7000000000000003e-30 < y < 5.49999999999999973e-101

   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 87.5%

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

   if 5.49999999999999973e-101 < y < 2.30000000000000016e-92

   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 x around 0 86.9%

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

   5. Taylor expanded in y around 0 86.9%

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

      1. mul-1-neg 86.9%

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

   7. Simplified 86.9%

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

   if 2.30000000000000016e-92 < y < 28000

   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 58.0%

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

      1. sub-neg 58.0%

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

      2. metadata-eval 58.0%

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

      3. neg-mul-1 58.0%

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

      4. distribute-neg-frac 58.0%

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

      5. +-commutative 58.0%

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

   6. Simplified 58.0%

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

      1. frac-2neg 58.0%

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

      2. div-inv 58.0%

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

      3. remove-double-neg 58.0%

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

      4. +-commutative 58.0%

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

   8. Applied egg-rr 58.0%

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

      1. associate-*r/ 58.0%

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

      2. *-rgt-identity 58.0%

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

      3. neg-sub0 58.0%

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

      4. +-commutative 58.0%

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

      5. associate--r+ 58.0%

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

      6. metadata-eval 58.0%

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

   10. Simplified 58.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900000000000:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-92}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 28000:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{1 - x}{y}\\ \end{array} \]

Alternative 3: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 - y}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-92}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+16}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 1.0 y))))
   (if (<= y -2e+38)
     1.0
     (if (<= y 5.5e-101)
       t_0
       (if (<= y 2.3e-92) (- y) (if (<= y 3.6e+16) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (1.0 - y);
	double tmp;
	if (y <= -2e+38) {
		tmp = 1.0;
	} else if (y <= 5.5e-101) {
		tmp = t_0;
	} else if (y <= 2.3e-92) {
		tmp = -y;
	} else if (y <= 3.6e+16) {
		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 <= (-2d+38)) then
        tmp = 1.0d0
    else if (y <= 5.5d-101) then
        tmp = t_0
    else if (y <= 2.3d-92) then
        tmp = -y
    else if (y <= 3.6d+16) 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 <= -2e+38) {
		tmp = 1.0;
	} else if (y <= 5.5e-101) {
		tmp = t_0;
	} else if (y <= 2.3e-92) {
		tmp = -y;
	} else if (y <= 3.6e+16) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (1.0 - y)
	tmp = 0
	if y <= -2e+38:
		tmp = 1.0
	elif y <= 5.5e-101:
		tmp = t_0
	elif y <= 2.3e-92:
		tmp = -y
	elif y <= 3.6e+16:
		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 <= -2e+38)
		tmp = 1.0;
	elseif (y <= 5.5e-101)
		tmp = t_0;
	elseif (y <= 2.3e-92)
		tmp = Float64(-y);
	elseif (y <= 3.6e+16)
		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 <= -2e+38)
		tmp = 1.0;
	elseif (y <= 5.5e-101)
		tmp = t_0;
	elseif (y <= 2.3e-92)
		tmp = -y;
	elseif (y <= 3.6e+16)
		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, -2e+38], 1.0, If[LessEqual[y, 5.5e-101], t$95$0, If[LessEqual[y, 2.3e-92], (-y), If[LessEqual[y, 3.6e+16], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999995e38 or 3.6e16 < 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 77.6%

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

   if -1.99999999999999995e38 < y < 5.49999999999999973e-101 or 2.30000000000000016e-92 < y < 3.6e16

   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 x around inf 74.8%

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

      1. sub-neg 74.8%

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

      2. metadata-eval 74.8%

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

      3. neg-mul-1 74.8%

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

      4. distribute-neg-frac 74.8%

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

      5. +-commutative 74.8%

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

   6. Simplified 74.8%

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

      1. frac-2neg 74.8%

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

      2. div-inv 74.8%

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

      3. remove-double-neg 74.8%

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

      4. +-commutative 74.8%

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

   8. Applied egg-rr 74.8%

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

      1. associate-*r/ 74.8%

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

      2. *-rgt-identity 74.8%

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

      3. neg-sub0 74.8%

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

      4. +-commutative 74.8%

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

      5. associate--r+ 74.8%

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

      6. metadata-eval 74.8%

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

   10. Simplified 74.8%

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

   if 5.49999999999999973e-101 < y < 2.30000000000000016e-92

   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 x around 0 86.9%

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

   5. Taylor expanded in y around 0 86.9%

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

      1. mul-1-neg 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+38}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-92}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.75:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-92}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.75)
   1.0
   (if (<= y -2.2e-29)
     (* y (- -1.0 y))
     (if (<= y 5.5e-101) x (if (<= y 2.3e-92) (- y) (if (<= y 1.0) x 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.75) {
		tmp = 1.0;
	} else if (y <= -2.2e-29) {
		tmp = y * (-1.0 - y);
	} else if (y <= 5.5e-101) {
		tmp = x;
	} else if (y <= 2.3e-92) {
		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 <= (-0.75d0)) then
        tmp = 1.0d0
    else if (y <= (-2.2d-29)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 5.5d-101) then
        tmp = x
    else if (y <= 2.3d-92) 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 <= -0.75) {
		tmp = 1.0;
	} else if (y <= -2.2e-29) {
		tmp = y * (-1.0 - y);
	} else if (y <= 5.5e-101) {
		tmp = x;
	} else if (y <= 2.3e-92) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.75:
		tmp = 1.0
	elif y <= -2.2e-29:
		tmp = y * (-1.0 - y)
	elif y <= 5.5e-101:
		tmp = x
	elif y <= 2.3e-92:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.75)
		tmp = 1.0;
	elseif (y <= -2.2e-29)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 5.5e-101)
		tmp = x;
	elseif (y <= 2.3e-92)
		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 <= -0.75)
		tmp = 1.0;
	elseif (y <= -2.2e-29)
		tmp = y * (-1.0 - y);
	elseif (y <= 5.5e-101)
		tmp = x;
	elseif (y <= 2.3e-92)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.75], 1.0, If[LessEqual[y, -2.2e-29], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-101], x, If[LessEqual[y, 2.3e-92], (-y), If[LessEqual[y, 1.0], x, 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.75 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 73.3%

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

   if -0.75 < y < -2.1999999999999999e-29

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. neg-sub0 99.6%

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

      4. associate-+l- 99.6%

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

      5. sub0-neg 99.6%

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

      6. neg-mul-1 99.6%

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

      7. sub-neg 99.6%

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

      8. +-commutative 99.6%

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

      9. neg-sub0 99.6%

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

      10. associate-+l- 99.6%

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

      11. sub0-neg 99.6%

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

      12. neg-mul-1 99.6%

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

      13. times-frac 99.6%

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

      14. metadata-eval 99.6%

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

      15. *-lft-identity 99.6%

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

      16. sub-neg 99.6%

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

      17. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 87.5%

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

   5. Taylor expanded in y around 0 76.3%

      \[\leadsto \color{blue}{-1 \cdot {y}^{2} + \left(-1 \cdot {y}^{3} + -1 \cdot y\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 76.3%

         \[\leadsto \color{blue}{\left(-1 \cdot {y}^{2} + -1 \cdot {y}^{3}\right) + -1 \cdot y} \]

      2. mul-1-neg 76.3%

         \[\leadsto \left(-1 \cdot {y}^{2} + -1 \cdot {y}^{3}\right) + \color{blue}{\left(-y\right)} \]

      3. unsub-neg 76.3%

         \[\leadsto \color{blue}{\left(-1 \cdot {y}^{2} + -1 \cdot {y}^{3}\right) - y} \]

      4. unpow2 76.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(y \cdot y\right)} + -1 \cdot {y}^{3}\right) - y \]

      5. associate-*r* 76.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot y} + -1 \cdot {y}^{3}\right) - y \]

      6. *-commutative 76.3%

         \[\leadsto \left(\color{blue}{\left(y \cdot -1\right)} \cdot y + -1 \cdot {y}^{3}\right) - y \]

      7. associate-*r* 76.3%

         \[\leadsto \left(\color{blue}{y \cdot \left(-1 \cdot y\right)} + -1 \cdot {y}^{3}\right) - y \]

      8. mul-1-neg 76.3%

         \[\leadsto \left(y \cdot \left(-1 \cdot y\right) + \color{blue}{\left(-{y}^{3}\right)}\right) - y \]

      9. cube-mult 76.3%

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

      10. distribute-rgt-neg-out 76.3%

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

      11. distribute-lft-out 76.3%

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

      12. mul-1-neg 76.3%

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

      13. distribute-neg-in 76.3%

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

      14. +-commutative 76.3%

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

      15. fma-def 76.3%

          \[\leadsto y \cdot \left(-\color{blue}{\mathsf{fma}\left(y, y, y\right)}\right) - y \]

   7. Simplified 76.3%

      \[\leadsto \color{blue}{y \cdot \left(-\mathsf{fma}\left(y, y, y\right)\right) - y} \]

   8. Taylor expanded in y around 0 72.7%

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

      1. neg-mul-1 72.7%

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

      2. +-commutative 72.7%

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

      3. unpow2 72.7%

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

      4. neg-mul-1 72.7%

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

      5. sub-neg 72.7%

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

      6. neg-mul-1 72.7%

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

      7. distribute-rgt-out-- 72.7%

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

   10. Simplified 72.7%

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

   if -2.1999999999999999e-29 < y < 5.49999999999999973e-101 or 2.30000000000000016e-92 < 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 80.7%

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

   if 5.49999999999999973e-101 < y < 2.30000000000000016e-92

   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 x around 0 86.9%

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

   5. Taylor expanded in y around 0 86.9%

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

      1. mul-1-neg 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.75:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-92}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-86}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.95e-25)
   1.0
   (if (<= y 5.5e-101) x (if (<= y 1.15e-86) (- y) (if (<= y 1.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.95e-25) {
		tmp = 1.0;
	} else if (y <= 5.5e-101) {
		tmp = x;
	} else if (y <= 1.15e-86) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.95d-25)) then
        tmp = 1.0d0
    else if (y <= 5.5d-101) then
        tmp = x
    else if (y <= 1.15d-86) then
        tmp = -y
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.95e-25) {
		tmp = 1.0;
	} else if (y <= 5.5e-101) {
		tmp = x;
	} else if (y <= 1.15e-86) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.95e-25:
		tmp = 1.0
	elif y <= 5.5e-101:
		tmp = x
	elif y <= 1.15e-86:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.95e-25)
		tmp = 1.0;
	elseif (y <= 5.5e-101)
		tmp = x;
	elseif (y <= 1.15e-86)
		tmp = Float64(-y);
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.95e-25)
		tmp = 1.0;
	elseif (y <= 5.5e-101)
		tmp = x;
	elseif (y <= 1.15e-86)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.95e-25], 1.0, If[LessEqual[y, 5.5e-101], x, If[LessEqual[y, 1.15e-86], (-y), If[LessEqual[y, 1.0], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9499999999999998e-25 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 71.0%

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

   if -3.9499999999999998e-25 < y < 5.49999999999999973e-101 or 1.14999999999999998e-86 < 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 79.6%

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

   if 5.49999999999999973e-101 < y < 1.14999999999999998e-86

   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 x around 0 86.9%

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

   5. Taylor expanded in y around 0 86.9%

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

      1. mul-1-neg 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-86}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-51} \lor \neg \left(x \leq 1.55 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3e-51) (not (<= x 1.55e-25)))
   (/ x (- 1.0 y))
   (/ y (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3e-51) || !(x <= 1.55e-25)) {
		tmp = x / (1.0 - 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 ((x <= (-3d-51)) .or. (.not. (x <= 1.55d-25))) then
        tmp = x / (1.0d0 - 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 ((x <= -3e-51) || !(x <= 1.55e-25)) {
		tmp = x / (1.0 - y);
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3e-51) or not (x <= 1.55e-25):
		tmp = x / (1.0 - y)
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3e-51) || !(x <= 1.55e-25))
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3e-51) || ~((x <= 1.55e-25)))
		tmp = x / (1.0 - y);
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3e-51], N[Not[LessEqual[x, 1.55e-25]], $MachinePrecision]], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000002e-51 or 1.54999999999999997e-25 < x

   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 x around inf 75.1%

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

      1. sub-neg 75.1%

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

      2. metadata-eval 75.1%

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

      3. neg-mul-1 75.1%

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

      4. distribute-neg-frac 75.1%

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

      5. +-commutative 75.1%

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

   6. Simplified 75.1%

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

      1. frac-2neg 75.1%

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

      2. div-inv 75.1%

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

      3. remove-double-neg 75.1%

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

      4. +-commutative 75.1%

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

   8. Applied egg-rr 75.1%

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

      1. associate-*r/ 75.1%

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

      2. *-rgt-identity 75.1%

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

      3. neg-sub0 75.1%

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

      4. +-commutative 75.1%

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

      5. associate--r+ 75.1%

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

      6. metadata-eval 75.1%

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

   10. Simplified 75.1%

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

   if -3.00000000000000002e-51 < x < 1.54999999999999997e-25

   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 x around 0 84.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-51} \lor \neg \left(x \leq 1.55 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]

Alternative 7: 74.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.95e-25) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.95e-25) {
		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 <= (-3.95d-25)) 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 <= -3.95e-25) {
		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 <= -3.95e-25:
		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 <= -3.95e-25)
		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 <= -3.95e-25)
		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, -3.95e-25], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9499999999999998e-25 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 71.0%

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

   if -3.9499999999999998e-25 < 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 76.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.95 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 38.8% 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. 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 38.2%

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

5. Final simplification 38.2%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023255 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))