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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.2e+71)
   1.0
   (if (<= y -1.0)
     (/ x (- y))
     (if (<= y -6.2e-69)
       (* y (- -1.0 y))
       (if (<= y 4.9e+30) (/ x (- 1.0 y)) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.2e+71) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / -y;
	} else if (y <= -6.2e-69) {
		tmp = y * (-1.0 - y);
	} else if (y <= 4.9e+30) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.2d+71)) then
        tmp = 1.0d0
    else if (y <= (-1.0d0)) then
        tmp = x / -y
    else if (y <= (-6.2d-69)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 4.9d+30) then
        tmp = x / (1.0d0 - y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.2e+71) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / -y;
	} else if (y <= -6.2e-69) {
		tmp = y * (-1.0 - y);
	} else if (y <= 4.9e+30) {
		tmp = x / (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.2e+71:
		tmp = 1.0
	elif y <= -1.0:
		tmp = x / -y
	elif y <= -6.2e-69:
		tmp = y * (-1.0 - y)
	elif y <= 4.9e+30:
		tmp = x / (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.2e+71)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = Float64(x / Float64(-y));
	elseif (y <= -6.2e-69)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 4.9e+30)
		tmp = Float64(x / Float64(1.0 - y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.2e+71)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = x / -y;
	elseif (y <= -6.2e-69)
		tmp = y * (-1.0 - y);
	elseif (y <= 4.9e+30)
		tmp = x / (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.2e+71], 1.0, If[LessEqual[y, -1.0], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, -6.2e-69], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+30], N[(x / N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1999999999999999e71 or 4.89999999999999984e30 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 86.4%

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

   if -1.1999999999999999e71 < y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.9%

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

   4. Taylor expanded in y around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. neg-mul-1 62.9%

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

   6. Simplified 62.9%

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

   if -1 < y < -6.1999999999999999e-69

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. distribute-neg-frac2 86.3%

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

      3. neg-sub0 86.3%

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

      4. associate--r- 86.3%

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

      5. metadata-eval 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 86.5%

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

      1. sub-neg 86.5%

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

      2. neg-mul-1 86.5%

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

      3. distribute-neg-in 86.5%

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

      4. +-commutative 86.5%

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

      5. distribute-neg-in 86.5%

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

      6. metadata-eval 86.5%

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

      7. sub-neg 86.5%

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

   8. Simplified 86.5%

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

   if -6.1999999999999999e-69 < y < 4.89999999999999984e30

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.6%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{1 - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+67}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.34:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.26e+67)
   1.0
   (if (<= y -0.34)
     (/ x (- y))
     (if (<= y -1.8e-73) (* y (- -1.0 y)) (if (<= y 1.0) (+ x (* x y)) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.26e+67) {
		tmp = 1.0;
	} else if (y <= -0.34) {
		tmp = x / -y;
	} else if (y <= -1.8e-73) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x + (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 <= (-1.26d+67)) then
        tmp = 1.0d0
    else if (y <= (-0.34d0)) then
        tmp = x / -y
    else if (y <= (-1.8d-73)) then
        tmp = y * ((-1.0d0) - y)
    else if (y <= 1.0d0) then
        tmp = x + (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 <= -1.26e+67) {
		tmp = 1.0;
	} else if (y <= -0.34) {
		tmp = x / -y;
	} else if (y <= -1.8e-73) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x + (x * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.26e+67:
		tmp = 1.0
	elif y <= -0.34:
		tmp = x / -y
	elif y <= -1.8e-73:
		tmp = y * (-1.0 - y)
	elif y <= 1.0:
		tmp = x + (x * y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.26e+67)
		tmp = 1.0;
	elseif (y <= -0.34)
		tmp = Float64(x / Float64(-y));
	elseif (y <= -1.8e-73)
		tmp = Float64(y * Float64(-1.0 - y));
	elseif (y <= 1.0)
		tmp = Float64(x + Float64(x * y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.26e+67)
		tmp = 1.0;
	elseif (y <= -0.34)
		tmp = x / -y;
	elseif (y <= -1.8e-73)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.0)
		tmp = x + (x * y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.26e+67], 1.0, If[LessEqual[y, -0.34], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, -1.8e-73], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.26e67 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.1%

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

   if -1.26e67 < y < -0.340000000000000024

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.9%

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

   4. Taylor expanded in y around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. neg-mul-1 62.9%

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

   6. Simplified 62.9%

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

   if -0.340000000000000024 < y < -1.8e-73

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. distribute-neg-frac2 86.3%

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

      3. neg-sub0 86.3%

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

      4. associate--r- 86.3%

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

      5. metadata-eval 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 86.5%

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

      1. sub-neg 86.5%

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

      2. neg-mul-1 86.5%

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

      3. distribute-neg-in 86.5%

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

      4. +-commutative 86.5%

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

      5. distribute-neg-in 86.5%

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

      6. metadata-eval 86.5%

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

      7. sub-neg 86.5%

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

   8. Simplified 86.5%

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

   if -1.8e-73 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.3%

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

   4. Taylor expanded in y around 0 76.3%

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

      1. *-commutative 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+67}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.34:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.6e+66)
   1.0
   (if (<= y -3.1)
     (/ x (- y))
     (if (<= y 6.8e-10) (+ x (* y (+ x -1.0))) (/ y (+ y -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.6e+66) {
		tmp = 1.0;
	} else if (y <= -3.1) {
		tmp = x / -y;
	} else if (y <= 6.8e-10) {
		tmp = x + (y * (x + -1.0));
	} 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 <= (-7.6d+66)) then
        tmp = 1.0d0
    else if (y <= (-3.1d0)) then
        tmp = x / -y
    else if (y <= 6.8d-10) then
        tmp = x + (y * (x + (-1.0d0)))
    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 <= -7.6e+66) {
		tmp = 1.0;
	} else if (y <= -3.1) {
		tmp = x / -y;
	} else if (y <= 6.8e-10) {
		tmp = x + (y * (x + -1.0));
	} else {
		tmp = y / (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.6e+66:
		tmp = 1.0
	elif y <= -3.1:
		tmp = x / -y
	elif y <= 6.8e-10:
		tmp = x + (y * (x + -1.0))
	else:
		tmp = y / (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.6e+66)
		tmp = 1.0;
	elseif (y <= -3.1)
		tmp = Float64(x / Float64(-y));
	elseif (y <= 6.8e-10)
		tmp = Float64(x + Float64(y * Float64(x + -1.0)));
	else
		tmp = Float64(y / Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.6e+66)
		tmp = 1.0;
	elseif (y <= -3.1)
		tmp = x / -y;
	elseif (y <= 6.8e-10)
		tmp = x + (y * (x + -1.0));
	else
		tmp = y / (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.6e+66], 1.0, If[LessEqual[y, -3.1], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, 6.8e-10], N[(x + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.6000000000000004e66

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 91.3%

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

   if -7.6000000000000004e66 < y < -3.10000000000000009

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.9%

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

   4. Taylor expanded in y around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. neg-mul-1 62.9%

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

   6. Simplified 62.9%

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

   if -3.10000000000000009 < y < 6.8000000000000003e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. unsub-neg 99.6%

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

      3. mul-1-neg 99.6%

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

      4. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   if 6.8000000000000003e-10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. neg-mul-1 79.6%

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

      2. distribute-neg-frac2 79.6%

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

      3. neg-sub0 79.6%

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

      4. associate--r- 79.6%

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

      5. metadata-eval 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.6e+66)
   1.0
   (if (<= y -1.0)
     (/ x (- y))
     (if (<= y -1.5e-69) (* y (- -1.0 y)) (if (<= y 1.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.6e+66) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / -y;
	} else if (y <= -1.5e-69) {
		tmp = y * (-1.0 - 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 <= (-7.6d+66)) then
        tmp = 1.0d0
    else if (y <= (-1.0d0)) then
        tmp = x / -y
    else if (y <= (-1.5d-69)) then
        tmp = y * ((-1.0d0) - 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 <= -7.6e+66) {
		tmp = 1.0;
	} else if (y <= -1.0) {
		tmp = x / -y;
	} else if (y <= -1.5e-69) {
		tmp = y * (-1.0 - y);
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.6e+66:
		tmp = 1.0
	elif y <= -1.0:
		tmp = x / -y
	elif y <= -1.5e-69:
		tmp = y * (-1.0 - y)
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.6e+66)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = Float64(x / Float64(-y));
	elseif (y <= -1.5e-69)
		tmp = Float64(y * Float64(-1.0 - 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 <= -7.6e+66)
		tmp = 1.0;
	elseif (y <= -1.0)
		tmp = x / -y;
	elseif (y <= -1.5e-69)
		tmp = y * (-1.0 - y);
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.6e+66], 1.0, If[LessEqual[y, -1.0], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, -1.5e-69], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], x, 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.6000000000000004e66 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.1%

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

   if -7.6000000000000004e66 < y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.9%

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

   4. Taylor expanded in y around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. neg-mul-1 62.9%

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

   6. Simplified 62.9%

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

   if -1 < y < -1.49999999999999995e-69

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. distribute-neg-frac2 86.3%

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

      3. neg-sub0 86.3%

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

      4. associate--r- 86.3%

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

      5. metadata-eval 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 86.5%

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

      1. sub-neg 86.5%

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

      2. neg-mul-1 86.5%

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

      3. distribute-neg-in 86.5%

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

      4. +-commutative 86.5%

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

      5. distribute-neg-in 86.5%

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

      6. metadata-eval 86.5%

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

      7. sub-neg 86.5%

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

   8. Simplified 86.5%

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

   if -1.49999999999999995e-69 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.0%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+66}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.122:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.85e+70)
   1.0
   (if (<= y -0.122)
     (/ x (- y))
     (if (<= y -7.8e-69) (- y) (if (<= y 1.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.85e+70) {
		tmp = 1.0;
	} else if (y <= -0.122) {
		tmp = x / -y;
	} else if (y <= -7.8e-69) {
		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 <= (-1.85d+70)) then
        tmp = 1.0d0
    else if (y <= (-0.122d0)) then
        tmp = x / -y
    else if (y <= (-7.8d-69)) 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 <= -1.85e+70) {
		tmp = 1.0;
	} else if (y <= -0.122) {
		tmp = x / -y;
	} else if (y <= -7.8e-69) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.85e+70:
		tmp = 1.0
	elif y <= -0.122:
		tmp = x / -y
	elif y <= -7.8e-69:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.85e+70)
		tmp = 1.0;
	elseif (y <= -0.122)
		tmp = Float64(x / Float64(-y));
	elseif (y <= -7.8e-69)
		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 <= -1.85e+70)
		tmp = 1.0;
	elseif (y <= -0.122)
		tmp = x / -y;
	elseif (y <= -7.8e-69)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.85e+70], 1.0, If[LessEqual[y, -0.122], N[(x / (-y)), $MachinePrecision], If[LessEqual[y, -7.8e-69], (-y), If[LessEqual[y, 1.0], x, 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.84999999999999994e70 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.1%

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

   if -1.84999999999999994e70 < y < -0.122

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.9%

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

   4. Taylor expanded in y around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. neg-mul-1 62.9%

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

   6. Simplified 62.9%

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

   if -0.122 < y < -7.79999999999999961e-69

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. distribute-neg-frac2 86.3%

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

      3. neg-sub0 86.3%

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

      4. associate--r- 86.3%

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

      5. metadata-eval 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 83.4%

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

      1. neg-mul-1 83.4%

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

   8. Simplified 83.4%

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

   if -7.79999999999999961e-69 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.122:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y -1.12e-69) (- y) (if (<= y 1.0) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -1.12e-69) {
		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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= (-1.12d-69)) 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 <= -1.0) {
		tmp = 1.0;
	} else if (y <= -1.12e-69) {
		tmp = -y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= -1.12e-69:
		tmp = -y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= -1.12e-69)
		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 <= -1.0)
		tmp = 1.0;
	elseif (y <= -1.12e-69)
		tmp = -y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, -1.12e-69], (-y), If[LessEqual[y, 1.0], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.3%

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

   if -1 < y < -1.12e-69

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. distribute-neg-frac2 86.3%

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

      3. neg-sub0 86.3%

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

      4. associate--r- 86.3%

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

      5. metadata-eval 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 83.4%

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

      1. neg-mul-1 83.4%

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

   8. Simplified 83.4%

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

   if -1.12e-69 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.0%

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

Alternative 8: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-74} \lor \neg \left(y \leq 4.1 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5e-74) (not (<= y 4.1e-10))) (/ y (+ y -1.0)) (+ x (* x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e-74) || !(y <= 4.1e-10)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x + (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 <= (-4.5d-74)) .or. (.not. (y <= 4.1d-10))) then
        tmp = y / (y + (-1.0d0))
    else
        tmp = x + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e-74) || !(y <= 4.1e-10)) {
		tmp = y / (y + -1.0);
	} else {
		tmp = x + (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5e-74) or not (y <= 4.1e-10):
		tmp = y / (y + -1.0)
	else:
		tmp = x + (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5e-74) || !(y <= 4.1e-10))
		tmp = Float64(y / Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.5e-74) || ~((y <= 4.1e-10)))
		tmp = y / (y + -1.0);
	else
		tmp = x + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5e-74], N[Not[LessEqual[y, 4.1e-10]], $MachinePrecision]], N[(y / N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e-74 or 4.0999999999999998e-10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.5%

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

      1. neg-mul-1 78.5%

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

      2. distribute-neg-frac2 78.5%

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

      3. neg-sub0 78.5%

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

      4. associate--r- 78.5%

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

      5. metadata-eval 78.5%

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

   5. Simplified 78.5%

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

   if -4.4999999999999999e-74 < y < 4.0999999999999998e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.9%

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

   4. Taylor expanded in y around 0 77.0%

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

      1. *-commutative 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-74} \lor \neg \left(y \leq 4.1 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{y}{y + -1}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.4e-13) 1.0 (if (<= y 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.4e-13) {
		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 <= (-3.4d-13)) 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 <= -3.4e-13) {
		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 <= -3.4e-13:
		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 <= -3.4e-13)
		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 <= -3.4e-13)
		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, -3.4e-13], 1.0, If[LessEqual[y, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000015e-13 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 76.2%

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

   if -3.40000000000000015e-13 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 70.9%

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

Alternative 10: 39.1% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 39.9%

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

Reproduce

herbie shell --seed 2024157 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (/ (- x y) (- 1.0 y)))