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

Percentage Accurate: 66.2% → 99.9%

Time: 8.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12600 \lor \neg \left(y \leq 9000\right):\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{\frac{1 - x}{y} - \left(1 - x\right)}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -12600.0) (not (<= y 9000.0)))
   (- x (/ (- (+ x -1.0) (/ (- (/ (- 1.0 x) y) (- 1.0 x)) y)) y))
   (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -12600.0) || !(y <= 9000.0)) {
		tmp = x - (((x + -1.0) - ((((1.0 - x) / y) - (1.0 - x)) / y)) / y);
	} else {
		tmp = 1.0 - ((y * (1.0 - x)) / (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 <= (-12600.0d0)) .or. (.not. (y <= 9000.0d0))) then
        tmp = x - (((x + (-1.0d0)) - ((((1.0d0 - x) / y) - (1.0d0 - x)) / y)) / y)
    else
        tmp = 1.0d0 - ((y * (1.0d0 - x)) / (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -12600.0) || !(y <= 9000.0)) {
		tmp = x - (((x + -1.0) - ((((1.0 - x) / y) - (1.0 - x)) / y)) / y);
	} else {
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -12600.0) or not (y <= 9000.0):
		tmp = x - (((x + -1.0) - ((((1.0 - x) / y) - (1.0 - x)) / y)) / y)
	else:
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -12600.0) || !(y <= 9000.0))
		tmp = Float64(x - Float64(Float64(Float64(x + -1.0) - Float64(Float64(Float64(Float64(1.0 - x) / y) - Float64(1.0 - x)) / y)) / y));
	else
		tmp = Float64(1.0 - Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -12600.0) || ~((y <= 9000.0)))
		tmp = x - (((x + -1.0) - ((((1.0 - x) / y) - (1.0 - x)) / y)) / y);
	else
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -12600.0], N[Not[LessEqual[y, 9000.0]], $MachinePrecision]], N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] - N[(N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] - N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -12600 or 9e3 < y

   1. Initial program 35.2%

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

      1. associate-/l* 52.0%

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

      2. remove-double-neg 52.0%

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

      3. remove-double-neg 52.0%

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

      4. +-commutative 52.0%

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

   3. Simplified 52.0%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   if -12600 < y < 9e3

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12600 \lor \neg \left(y \leq 9000\right):\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{\frac{1 - x}{y} - \left(1 - x\right)}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -120000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 2800000000000:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -120000000.0)
   (+ x (/ (- 1.0 x) y))
   (if (<= y 2800000000000.0)
     (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -120000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 2800000000000.0) {
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-120000000.0d0)) then
        tmp = x + ((1.0d0 - x) / y)
    else if (y <= 2800000000000.0d0) then
        tmp = 1.0d0 - ((y * (1.0d0 - x)) / (y + 1.0d0))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -120000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 2800000000000.0) {
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -120000000.0:
		tmp = x + ((1.0 - x) / y)
	elif y <= 2800000000000.0:
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -120000000.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	elseif (y <= 2800000000000.0)
		tmp = Float64(1.0 - Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -120000000.0)
		tmp = x + ((1.0 - x) / y);
	elseif (y <= 2800000000000.0)
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -120000000.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2800000000000.0], N[(1.0 - N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e8

   1. Initial program 37.1%

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

      1. associate-/l* 54.9%

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

      2. remove-double-neg 54.9%

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

      3. remove-double-neg 54.9%

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

      4. +-commutative 54.9%

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

   3. Simplified 54.9%

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

   5. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. neg-sub0 99.9%

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

      6. +-commutative 99.9%

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

      7. sub-neg 99.9%

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

   7. Simplified 99.9%

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

   if -1.2e8 < y < 2.8e12

   1. Initial program 99.8%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Add Preprocessing

   if 2.8e12 < y

   1. Initial program 30.8%

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

      1. associate-/l* 47.5%

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

      2. remove-double-neg 47.5%

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

      3. remove-double-neg 47.5%

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

      4. +-commutative 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. neg-sub0 100.0%

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

      6. +-commutative 100.0%

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

      7. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -120000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 2800000000000:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -180000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 2800000000000:\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -180000000.0)
   (+ x (/ (- 1.0 x) y))
   (if (<= y 2800000000000.0)
     (+ 1.0 (* (+ x -1.0) (/ y (+ y 1.0))))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -180000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 2800000000000.0) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-180000000.0d0)) then
        tmp = x + ((1.0d0 - x) / y)
    else if (y <= 2800000000000.0d0) then
        tmp = 1.0d0 + ((x + (-1.0d0)) * (y / (y + 1.0d0)))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -180000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 2800000000000.0) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -180000000.0:
		tmp = x + ((1.0 - x) / y)
	elif y <= 2800000000000.0:
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -180000000.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	elseif (y <= 2800000000000.0)
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -180000000.0)
		tmp = x + ((1.0 - x) / y);
	elseif (y <= 2800000000000.0)
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -180000000.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2800000000000.0], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e8

   1. Initial program 37.1%

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

      1. associate-/l* 54.9%

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

      2. remove-double-neg 54.9%

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

      3. remove-double-neg 54.9%

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

      4. +-commutative 54.9%

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

   3. Simplified 54.9%

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

   5. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. neg-sub0 99.9%

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

      6. +-commutative 99.9%

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

      7. sub-neg 99.9%

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

   7. Simplified 99.9%

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

   if -1.8e8 < y < 2.8e12

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

      2. remove-double-neg 99.7%

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

      3. remove-double-neg 99.7%

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

      4. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   if 2.8e12 < y

   1. Initial program 30.8%

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

      1. associate-/l* 47.5%

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

      2. remove-double-neg 47.5%

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

      3. remove-double-neg 47.5%

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

      4. +-commutative 47.5%

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

   3. Simplified 47.5%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. neg-sub0 100.0%

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

      6. +-commutative 100.0%

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

      7. sub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -180000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 2800000000000:\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -340000 \lor \neg \left(y \leq 11500\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -340000.0) (not (<= y 11500.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (* x (/ y (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -340000.0) || !(y <= 11500.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (x * (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 <= (-340000.0d0)) .or. (.not. (y <= 11500.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + (x * (y / (y + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -340000.0) || !(y <= 11500.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (x * (y / (y + 1.0)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -340000.0) or not (y <= 11500.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + (x * (y / (y + 1.0)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -340000.0) || !(y <= 11500.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(x * Float64(y / Float64(y + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -340000.0) || ~((y <= 11500.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + (x * (y / (y + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -340000.0], N[Not[LessEqual[y, 11500.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e5 or 11500 < y

   1. Initial program 34.7%

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

      1. associate-/l* 51.6%

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

      2. remove-double-neg 51.6%

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

      3. remove-double-neg 51.6%

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

      4. +-commutative 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in y around -inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-frac-neg 99.5%

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

      3. neg-sub0 99.5%

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

      4. associate-+l- 99.5%

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

      5. neg-sub0 99.5%

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

      6. +-commutative 99.5%

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

      7. sub-neg 99.5%

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

   7. Simplified 99.5%

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

   if -3.4e5 < y < 11500

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. remove-double-neg 99.9%

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

      4. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.3%

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

      1. mul-1-neg 97.3%

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

      2. *-commutative 97.3%

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

      3. associate-*l/ 97.3%

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

      4. distribute-rgt-neg-out 97.3%

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

      5. +-commutative 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -340000 \lor \neg \left(y \leq 11500\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \frac{y}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{elif}\;y \leq 95000:\\ \;\;\;\;1 + \frac{x}{\frac{1}{y} - -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.5e+28)
   (+ x (/ 1.0 y))
   (if (<= y 95000.0) (+ 1.0 (/ x (- (/ 1.0 y) -1.0))) (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.5e+28) {
		tmp = x + (1.0 / y);
	} else if (y <= 95000.0) {
		tmp = 1.0 + (x / ((1.0 / y) - -1.0));
	} else {
		tmp = x + ((1.0 - 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 <= (-6.5d+28)) then
        tmp = x + (1.0d0 / y)
    else if (y <= 95000.0d0) then
        tmp = 1.0d0 + (x / ((1.0d0 / y) - (-1.0d0)))
    else
        tmp = x + ((1.0d0 - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.5e+28) {
		tmp = x + (1.0 / y);
	} else if (y <= 95000.0) {
		tmp = 1.0 + (x / ((1.0 / y) - -1.0));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.5e+28:
		tmp = x + (1.0 / y)
	elif y <= 95000.0:
		tmp = 1.0 + (x / ((1.0 / y) - -1.0))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.5e+28)
		tmp = Float64(x + Float64(1.0 / y));
	elseif (y <= 95000.0)
		tmp = Float64(1.0 + Float64(x / Float64(Float64(1.0 / y) - -1.0)));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.5e+28)
		tmp = x + (1.0 / y);
	elseif (y <= 95000.0)
		tmp = 1.0 + (x / ((1.0 / y) - -1.0));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.5e+28], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 95000.0], N[(1.0 + N[(x / N[(N[(1.0 / y), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000001e28

   1. Initial program 33.7%

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

      1. associate-/l* 52.4%

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

      2. remove-double-neg 52.4%

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

      3. remove-double-neg 52.4%

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

      4. +-commutative 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. neg-sub0 99.9%

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

      6. +-commutative 99.9%

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

      7. sub-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.9%

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

   if -6.5000000000000001e28 < y < 95000

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. remove-double-neg 99.9%

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

      4. +-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 97.4%

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

      1. mul-1-neg 97.4%

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

      2. associate-*l/ 97.4%

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

      3. associate-/r/ 97.3%

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

      4. distribute-frac-neg2 97.3%

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

      5. *-lft-identity 97.3%

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

      6. associate-*l/ 97.3%

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

      7. distribute-rgt-in 97.3%

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

      8. rgt-mult-inverse 97.3%

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

      9. *-lft-identity 97.3%

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

      10. distribute-neg-in 97.3%

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

      11. distribute-neg-frac 97.3%

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

      12. metadata-eval 97.3%

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

      13. metadata-eval 97.3%

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

   9. Simplified 97.3%

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

   if 95000 < y

   1. Initial program 32.6%

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

      1. associate-/l* 48.7%

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

      2. remove-double-neg 48.7%

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

      3. remove-double-neg 48.7%

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

      4. +-commutative 48.7%

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

   3. Simplified 48.7%

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

   5. Taylor expanded in y around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. distribute-frac-neg 99.2%

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

      3. neg-sub0 99.2%

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

      4. associate-+l- 99.2%

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

      5. neg-sub0 99.2%

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

      6. +-commutative 99.2%

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

      7. sub-neg 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{elif}\;y \leq 95000:\\ \;\;\;\;1 + \frac{x}{\frac{1}{y} - -1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + (y * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 36.8%

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

      1. associate-/l* 53.1%

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

      2. remove-double-neg 53.1%

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

      3. remove-double-neg 53.1%

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

      4. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in y around -inf 97.7%

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

      1. mul-1-neg 97.7%

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

      2. distribute-frac-neg 97.7%

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

      3. neg-sub0 97.7%

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

      4. associate-+l- 97.7%

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

      5. neg-sub0 97.7%

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

      6. +-commutative 97.7%

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

      7. sub-neg 97.7%

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

   7. Simplified 97.7%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.6%

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

4. Final simplification 97.7%

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

Alternative 7: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.15))) (+ x (/ (- 1.0 x) y)) (+ 1.0 (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.15)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.15d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.15)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.15):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.15))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.15)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.15]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.1499999999999999 < y

   1. Initial program 36.8%

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

      1. associate-/l* 53.1%

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

      2. remove-double-neg 53.1%

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

      3. remove-double-neg 53.1%

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

      4. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in y around -inf 97.7%

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

      1. mul-1-neg 97.7%

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

      2. distribute-frac-neg 97.7%

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

      3. neg-sub0 97.7%

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

      4. associate-+l- 97.7%

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

      5. neg-sub0 97.7%

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

      6. +-commutative 97.7%

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

      7. sub-neg 97.7%

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

   7. Simplified 97.7%

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

   if -1 < y < 1.1499999999999999

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. associate-*l/ 98.0%

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

      3. associate-/r/ 98.0%

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

      4. distribute-frac-neg2 98.0%

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

      5. *-lft-identity 98.0%

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

      6. associate-*l/ 98.0%

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

      7. distribute-rgt-in 98.0%

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

      8. rgt-mult-inverse 98.0%

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

      9. *-lft-identity 98.0%

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

      10. distribute-neg-in 98.0%

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

      11. distribute-neg-frac 98.0%

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

      12. metadata-eval 98.0%

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

      13. metadata-eval 98.0%

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

   9. Simplified 98.0%

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

   10. Taylor expanded in y around 0 97.1%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + (1.0d0 / y)
    else
        tmp = 1.0d0 + (y * x)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 36.8%

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

      1. associate-/l* 53.1%

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

      2. remove-double-neg 53.1%

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

      3. remove-double-neg 53.1%

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

      4. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in y around -inf 97.7%

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

      1. mul-1-neg 97.7%

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

      2. distribute-frac-neg 97.7%

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

      3. neg-sub0 97.7%

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

      4. associate-+l- 97.7%

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

      5. neg-sub0 97.7%

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

      6. +-commutative 97.7%

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

      7. sub-neg 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x around 0 97.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. associate-*l/ 98.0%

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

      3. associate-/r/ 98.0%

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

      4. distribute-frac-neg2 98.0%

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

      5. *-lft-identity 98.0%

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

      6. associate-*l/ 98.0%

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

      7. distribute-rgt-in 98.0%

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

      8. rgt-mult-inverse 98.0%

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

      9. *-lft-identity 98.0%

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

      10. distribute-neg-in 98.0%

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

      11. distribute-neg-frac 98.0%

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

      12. metadata-eval 98.0%

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

      13. metadata-eval 98.0%

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

   9. Simplified 98.0%

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

   10. Taylor expanded in y around 0 97.1%

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

4. Final simplification 97.0%

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

Alternative 9: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 310000:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 310000.0) (+ 1.0 (* y x)) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 310000.0) {
		tmp = 1.0 + (y * x);
	} else {
		tmp = x;
	}
	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 = x
    else if (y <= 310000.0d0) then
        tmp = 1.0d0 + (y * x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 310000.0) {
		tmp = 1.0 + (y * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 310000.0:
		tmp = 1.0 + (y * x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 310000.0)
		tmp = Float64(1.0 + Float64(y * x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 310000.0)
		tmp = 1.0 + (y * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 310000.0], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3.1e5 < y

   1. Initial program 36.5%

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

      1. associate-/l* 53.0%

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

      2. remove-double-neg 53.0%

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

      3. remove-double-neg 53.0%

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

      4. +-commutative 53.0%

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

   3. Simplified 53.0%

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

   5. Taylor expanded in y around inf 74.9%

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

   if -1 < y < 3.1e5

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. remove-double-neg 99.8%

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

      3. remove-double-neg 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 97.4%

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

      1. mul-1-neg 97.4%

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

      2. associate-*l/ 97.4%

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

      3. associate-/r/ 97.3%

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

      4. distribute-frac-neg2 97.3%

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

      5. *-lft-identity 97.3%

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

      6. associate-*l/ 97.3%

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

      7. distribute-rgt-in 97.3%

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

      8. rgt-mult-inverse 97.3%

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

      9. *-lft-identity 97.3%

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

      10. distribute-neg-in 97.3%

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

      11. distribute-neg-frac 97.3%

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

      12. metadata-eval 97.3%

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

      13. metadata-eval 97.3%

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

   9. Simplified 97.3%

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

   10. Taylor expanded in y around 0 96.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 310000:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.23:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.23) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.23) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	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 = x
    else if (y <= 0.23d0) then
        tmp = 1.0d0 - y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.23) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.23:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.23)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.23)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.23], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.23000000000000001 < y

   1. Initial program 37.3%

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

      1. associate-/l* 53.5%

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

      2. remove-double-neg 53.5%

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

      3. remove-double-neg 53.5%

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

      4. +-commutative 53.5%

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

   3. Simplified 53.5%

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

   5. Taylor expanded in y around inf 73.9%

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

   if -1 < y < 0.23000000000000001

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.2%

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

   6. Taylor expanded in x around 0 75.9%

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

Alternative 11: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 310000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 310000.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 310000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	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 = x
    else if (y <= 310000.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 310000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 310000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 310000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 310000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 310000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3.1e5 < y

   1. Initial program 36.5%

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

      1. associate-/l* 53.0%

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

      2. remove-double-neg 53.0%

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

      3. remove-double-neg 53.0%

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

      4. +-commutative 53.0%

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

   3. Simplified 53.0%

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

   5. Taylor expanded in y around inf 74.9%

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

   if -1 < y < 3.1e5

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. remove-double-neg 99.8%

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

      3. remove-double-neg 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 97.4%

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

      1. mul-1-neg 97.4%

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

      2. associate-*l/ 97.4%

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

      3. associate-/r/ 97.3%

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

      4. distribute-frac-neg2 97.3%

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

      5. *-lft-identity 97.3%

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

      6. associate-*l/ 97.3%

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

      7. distribute-rgt-in 97.3%

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

      8. rgt-mult-inverse 97.3%

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

      9. *-lft-identity 97.3%

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

      10. distribute-neg-in 97.3%

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

      11. distribute-neg-frac 97.3%

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

      12. metadata-eval 97.3%

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

      13. metadata-eval 97.3%

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

   9. Simplified 97.3%

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

   10. Taylor expanded in x around 0 74.4%

       \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 38.2% accurate, 11.0× 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 68.9%

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

   1. associate-/l* 76.9%

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

   2. remove-double-neg 76.9%

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

   3. remove-double-neg 76.9%

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

   4. +-commutative 76.9%

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

3. Simplified 76.9%

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

   1. clear-num 76.9%

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

   2. un-div-inv 76.9%

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

6. Applied egg-rr 76.9%

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

7. Taylor expanded in x around inf 66.5%

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

   1. mul-1-neg 66.5%

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

   2. associate-*l/ 74.5%

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

   3. associate-/r/ 74.5%

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

   4. distribute-frac-neg2 74.5%

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

   5. *-lft-identity 74.5%

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

   6. associate-*l/ 74.5%

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

   7. distribute-rgt-in 74.5%

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

   8. rgt-mult-inverse 74.5%

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

   9. *-lft-identity 74.5%

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

   10. distribute-neg-in 74.5%

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

   11. distribute-neg-frac 74.5%

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

   12. metadata-eval 74.5%

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

   13. metadata-eval 74.5%

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

9. Simplified 74.5%

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

10. Taylor expanded in x around 0 39.8%

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

Developer Target 1: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (/ 1.0 y) (- (/ x y) x))))
   (if (< y -3693.8482788297247)
     t_0
     (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))

C

double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 / y) - ((x / y) - x)
    if (y < (-3693.8482788297247d0)) then
        tmp = t_0
    else if (y < 6799310503.41891d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 / y) - ((x / y) - x)
	tmp = 0
	if y < -3693.8482788297247:
		tmp = t_0
	elif y < 6799310503.41891:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 / y) - Float64(Float64(x / y) - x))
	tmp = 0.0
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 / y) - ((x / y) - x);
	tmp = 0.0;
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -3693.8482788297247], t$95$0, If[Less[y, 6799310503.41891], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024158 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -36938482788297247/10000000000000) (- (/ 1 y) (- (/ x y) x)) (if (< y 679931050341891/100000) (- 1 (/ (* (- 1 x) y) (+ y 1))) (- (/ 1 y) (- (/ x y) x)))))

  (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))