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

Percentage Accurate: 66.0% → 99.9%

Time: 10.2s

Alternatives: 14

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: 66.0% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x + -1\right) - \frac{x + -1}{y}}{y}\\ \mathbf{if}\;y \leq -12000:\\ \;\;\;\;x + \frac{\left(t\_0 - -1\right) - x}{y}\\ \mathbf{elif}\;y \leq 340000:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- (+ x -1.0) (/ (+ x -1.0) y)) y)))
   (if (<= y -12000.0)
     (+ x (/ (- (- t_0 -1.0) x) y))
     (if (<= y 340000.0) (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0))) (- x t_0)))))

C

double code(double x, double y) {
	double t_0 = ((x + -1.0) - ((x + -1.0) / y)) / y;
	double tmp;
	if (y <= -12000.0) {
		tmp = x + (((t_0 - -1.0) - x) / y);
	} else if (y <= 340000.0) {
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	} else {
		tmp = x - 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 = ((x + (-1.0d0)) - ((x + (-1.0d0)) / y)) / y
    if (y <= (-12000.0d0)) then
        tmp = x + (((t_0 - (-1.0d0)) - x) / y)
    else if (y <= 340000.0d0) then
        tmp = 1.0d0 - ((y * (1.0d0 - x)) / (y + 1.0d0))
    else
        tmp = x - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((x + -1.0) - ((x + -1.0) / y)) / y;
	double tmp;
	if (y <= -12000.0) {
		tmp = x + (((t_0 - -1.0) - x) / y);
	} else if (y <= 340000.0) {
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	} else {
		tmp = x - t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((x + -1.0) - ((x + -1.0) / y)) / y
	tmp = 0
	if y <= -12000.0:
		tmp = x + (((t_0 - -1.0) - x) / y)
	elif y <= 340000.0:
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0))
	else:
		tmp = x - t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(x + -1.0) - Float64(Float64(x + -1.0) / y)) / y)
	tmp = 0.0
	if (y <= -12000.0)
		tmp = Float64(x + Float64(Float64(Float64(t_0 - -1.0) - x) / y));
	elseif (y <= 340000.0)
		tmp = Float64(1.0 - Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0)));
	else
		tmp = Float64(x - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((x + -1.0) - ((x + -1.0) / y)) / y;
	tmp = 0.0;
	if (y <= -12000.0)
		tmp = x + (((t_0 - -1.0) - x) / y);
	elseif (y <= 340000.0)
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	else
		tmp = x - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(x + -1.0), $MachinePrecision] - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -12000.0], N[(x + N[(N[(N[(t$95$0 - -1.0), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 340000.0], N[(1.0 - N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -12000

   1. Initial program 36.8%

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

      1. associate-/l* 57.9%

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

      2. +-commutative 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

   if -12000 < y < 3.4e5

   1. Initial program 99.9%

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

   if 3.4e5 < y

   1. Initial program 32.0%

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

      1. associate-/l* 56.7%

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

      2. +-commutative 56.7%

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

   3. Simplified 56.7%

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

   5. Taylor expanded in y around inf 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12000:\\ \;\;\;\;x + \frac{\left(\frac{\left(x + -1\right) - \frac{x + -1}{y}}{y} - -1\right) - x}{y}\\ \mathbf{elif}\;y \leq 340000:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{x + -1}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -200000 \lor \neg \left(y \leq 320000\right):\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{x + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -200000.0) (not (<= y 320000.0)))
   (- x (/ (- (+ x -1.0) (/ (+ x -1.0) y)) y))
   (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -200000.0) || !(y <= 320000.0)) {
		tmp = x - (((x + -1.0) - ((x + -1.0) / 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 <= (-200000.0d0)) .or. (.not. (y <= 320000.0d0))) then
        tmp = x - (((x + (-1.0d0)) - ((x + (-1.0d0)) / 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 <= -200000.0) || !(y <= 320000.0)) {
		tmp = x - (((x + -1.0) - ((x + -1.0) / y)) / y);
	} else {
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -200000.0) or not (y <= 320000.0):
		tmp = x - (((x + -1.0) - ((x + -1.0) / 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 <= -200000.0) || !(y <= 320000.0))
		tmp = Float64(x - Float64(Float64(Float64(x + -1.0) - Float64(Float64(x + -1.0) / 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 <= -200000.0) || ~((y <= 320000.0)))
		tmp = x - (((x + -1.0) - ((x + -1.0) / 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, -200000.0], N[Not[LessEqual[y, 320000.0]], $MachinePrecision]], N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] - N[(N[(x + -1.0), $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 < -2e5 or 3.2e5 < y

   1. Initial program 34.2%

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

      1. associate-/l* 57.1%

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

      2. +-commutative 57.1%

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

   3. Simplified 57.1%

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

   5. Taylor expanded in y around inf 99.8%

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

   7. Simplified 99.8%

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

   if -2e5 < y < 3.2e5

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -200000 \lor \neg \left(y \leq 320000\right):\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{x + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -700000000:\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 320000000:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1 - \frac{-1}{x}}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -700000000.0)
   (- x (/ (+ x -1.0) y))
   (if (<= y 320000000.0)
     (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))
     (* x (+ 1.0 (/ (- -1.0 (/ -1.0 x)) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -700000000.0) {
		tmp = x - ((x + -1.0) / y);
	} else if (y <= 320000000.0) {
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	} else {
		tmp = x * (1.0 + ((-1.0 - (-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 <= (-700000000.0d0)) then
        tmp = x - ((x + (-1.0d0)) / y)
    else if (y <= 320000000.0d0) then
        tmp = 1.0d0 - ((y * (1.0d0 - x)) / (y + 1.0d0))
    else
        tmp = x * (1.0d0 + (((-1.0d0) - ((-1.0d0) / x)) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -700000000.0) {
		tmp = x - ((x + -1.0) / y);
	} else if (y <= 320000000.0) {
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	} else {
		tmp = x * (1.0 + ((-1.0 - (-1.0 / x)) / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -700000000.0:
		tmp = x - ((x + -1.0) / y)
	elif y <= 320000000.0:
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0))
	else:
		tmp = x * (1.0 + ((-1.0 - (-1.0 / x)) / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -700000000.0)
		tmp = Float64(x - Float64(Float64(x + -1.0) / y));
	elseif (y <= 320000000.0)
		tmp = Float64(1.0 - Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -700000000.0)
		tmp = x - ((x + -1.0) / y);
	elseif (y <= 320000000.0)
		tmp = 1.0 - ((y * (1.0 - x)) / (y + 1.0));
	else
		tmp = x * (1.0 + ((-1.0 - (-1.0 / x)) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -700000000.0], N[(x - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 320000000.0], N[(1.0 - N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e8

   1. Initial program 34.5%

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

      1. associate-/l* 56.7%

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

      2. +-commutative 56.7%

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

   3. Simplified 56.7%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   if -7e8 < y < 3.2e8

   1. Initial program 99.6%

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

   if 3.2e8 < y

   1. Initial program 30.8%

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

      1. associate-/l* 55.9%

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

      2. +-commutative 55.9%

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

   3. Simplified 55.9%

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

   5. Taylor expanded in x around inf 56.3%

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

   6. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. distribute-neg-frac 99.9%

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

      5. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -700000000:\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 320000000:\\ \;\;\;\;1 - \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1 - \frac{-1}{x}}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13500000000:\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 130000000:\\ \;\;\;\;1 - y \cdot \frac{1 - x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1 - \frac{-1}{x}}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -13500000000.0)
   (- x (/ (+ x -1.0) y))
   (if (<= y 130000000.0)
     (- 1.0 (* y (/ (- 1.0 x) (+ y 1.0))))
     (* x (+ 1.0 (/ (- -1.0 (/ -1.0 x)) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -13500000000.0) {
		tmp = x - ((x + -1.0) / y);
	} else if (y <= 130000000.0) {
		tmp = 1.0 - (y * ((1.0 - x) / (y + 1.0)));
	} else {
		tmp = x * (1.0 + ((-1.0 - (-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 <= (-13500000000.0d0)) then
        tmp = x - ((x + (-1.0d0)) / y)
    else if (y <= 130000000.0d0) then
        tmp = 1.0d0 - (y * ((1.0d0 - x) / (y + 1.0d0)))
    else
        tmp = x * (1.0d0 + (((-1.0d0) - ((-1.0d0) / x)) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -13500000000.0) {
		tmp = x - ((x + -1.0) / y);
	} else if (y <= 130000000.0) {
		tmp = 1.0 - (y * ((1.0 - x) / (y + 1.0)));
	} else {
		tmp = x * (1.0 + ((-1.0 - (-1.0 / x)) / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -13500000000.0:
		tmp = x - ((x + -1.0) / y)
	elif y <= 130000000.0:
		tmp = 1.0 - (y * ((1.0 - x) / (y + 1.0)))
	else:
		tmp = x * (1.0 + ((-1.0 - (-1.0 / x)) / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -13500000000.0)
		tmp = Float64(x - Float64(Float64(x + -1.0) / y));
	elseif (y <= 130000000.0)
		tmp = Float64(1.0 - Float64(y * Float64(Float64(1.0 - x) / Float64(y + 1.0))));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -13500000000.0)
		tmp = x - ((x + -1.0) / y);
	elseif (y <= 130000000.0)
		tmp = 1.0 - (y * ((1.0 - x) / (y + 1.0)));
	else
		tmp = x * (1.0 + ((-1.0 - (-1.0 / x)) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -13500000000.0], N[(x - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 130000000.0], N[(1.0 - N[(y * N[(N[(1.0 - x), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35e10

   1. Initial program 33.5%

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

      1. associate-/l* 56.0%

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

      2. +-commutative 56.0%

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

   3. Simplified 56.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   if -1.35e10 < y < 1.3e8

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. +-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. associate-/l* 99.6%

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

      2. associate-*r* 99.6%

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

      3. neg-mul-1 99.6%

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

      4. distribute-lft1-in 99.6%

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

      5. +-commutative 99.6%

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

      6. sub-neg 99.6%

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

      7. associate-*r/ 99.6%

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

      8. associate-*l/ 99.6%

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

      9. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   if 1.3e8 < y

   1. Initial program 30.8%

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

      1. associate-/l* 55.9%

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

      2. +-commutative 55.9%

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

   3. Simplified 55.9%

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

   5. Taylor expanded in x around inf 56.3%

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

   6. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. sub-neg 99.9%

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

      4. distribute-neg-frac 99.9%

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

      5. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13500000000:\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{elif}\;y \leq 130000000:\\ \;\;\;\;1 - y \cdot \frac{1 - x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1 - \frac{-1}{x}}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5500 \lor \neg \left(y \leq 400\right):\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5500.0) (not (<= y 400.0)))
   (- x (/ (+ x -1.0) y))
   (+ 1.0 (/ (* y x) (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5500.0) || !(y <= 400.0)) {
		tmp = x - ((x + -1.0) / y);
	} else {
		tmp = 1.0 + ((y * 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 <= (-5500.0d0)) .or. (.not. (y <= 400.0d0))) then
        tmp = x - ((x + (-1.0d0)) / y)
    else
        tmp = 1.0d0 + ((y * x) / (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5500.0) || !(y <= 400.0)) {
		tmp = x - ((x + -1.0) / y);
	} else {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5500.0) or not (y <= 400.0):
		tmp = x - ((x + -1.0) / y)
	else:
		tmp = 1.0 + ((y * x) / (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5500.0) || !(y <= 400.0))
		tmp = Float64(x - Float64(Float64(x + -1.0) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * x) / Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5500.0) || ~((y <= 400.0)))
		tmp = x - ((x + -1.0) / y);
	else
		tmp = 1.0 + ((y * x) / (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5500.0], N[Not[LessEqual[y, 400.0]], $MachinePrecision]], N[(x - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * x), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5500 or 400 < y

   1. Initial program 35.0%

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

      1. associate-/l* 57.6%

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

      2. +-commutative 57.6%

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

   3. Simplified 57.6%

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

   5. Taylor expanded in y around inf 98.5%

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

      1. associate--l+ 98.5%

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

      2. div-sub 98.5%

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

   7. Simplified 98.5%

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

   if -5500 < y < 400

   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. +-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 x around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-*r* 100.0%

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

      3. neg-mul-1 100.0%

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

      4. distribute-lft1-in 100.0%

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

      5. +-commutative 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-*r/ 100.0%

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

      8. associate-*l/ 100.0%

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

      9. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. distribute-neg-frac2 98.0%

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

      3. distribute-neg-in 98.0%

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

      4. metadata-eval 98.0%

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

      5. *-commutative 98.0%

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

      6. unsub-neg 98.0%

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

   10. Simplified 98.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5500 \lor \neg \left(y \leq 400\right):\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1400 \lor \neg \left(y \leq 400\right):\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - x \cdot \frac{y}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1400.0) (not (<= y 400.0)))
   (- x (/ (+ x -1.0) y))
   (- 1.0 (* x (/ y (- -1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1400.0) || !(y <= 400.0)) {
		tmp = x - ((x + -1.0) / y);
	} else {
		tmp = 1.0 - (x * (y / (-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 <= (-1400.0d0)) .or. (.not. (y <= 400.0d0))) then
        tmp = x - ((x + (-1.0d0)) / y)
    else
        tmp = 1.0d0 - (x * (y / ((-1.0d0) - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1400.0) || !(y <= 400.0)) {
		tmp = x - ((x + -1.0) / y);
	} else {
		tmp = 1.0 - (x * (y / (-1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1400.0) or not (y <= 400.0):
		tmp = x - ((x + -1.0) / y)
	else:
		tmp = 1.0 - (x * (y / (-1.0 - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1400.0) || !(y <= 400.0))
		tmp = Float64(x - Float64(Float64(x + -1.0) / y));
	else
		tmp = Float64(1.0 - Float64(x * Float64(y / Float64(-1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1400.0) || ~((y <= 400.0)))
		tmp = x - ((x + -1.0) / y);
	else
		tmp = 1.0 - (x * (y / (-1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1400.0], N[Not[LessEqual[y, 400.0]], $MachinePrecision]], N[(x - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1400 or 400 < y

   1. Initial program 35.0%

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

      1. associate-/l* 57.6%

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

      2. +-commutative 57.6%

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

   3. Simplified 57.6%

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

   5. Taylor expanded in y around inf 98.5%

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

      1. associate--l+ 98.5%

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

      2. div-sub 98.5%

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

   7. Simplified 98.5%

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

   if -1400 < y < 400

   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. +-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 x around inf 98.0%

      \[\leadsto 1 - \color{blue}{-1 \cdot \frac{x \cdot y}{1 + y}} \]
   6. 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%

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

      3. distribute-rgt-neg-in 98.0%

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

      4. distribute-neg-frac2 98.0%

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

      5. distribute-neg-in 98.0%

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

      6. metadata-eval 98.0%

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

      7. sub-neg 98.0%

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

   7. Simplified 98.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1400 \lor \neg \left(y \leq 400\right):\\ \;\;\;\;x - \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - x \cdot \frac{y}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = x - ((x + -1.0) / y);
	else
		tmp = 1.0 + ((y * x) - y);
	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[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 36.6%

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

      1. associate-/l* 58.6%

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

      2. +-commutative 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in y around inf 96.8%

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

      1. associate--l+ 96.8%

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

      2. div-sub 96.8%

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

   7. Simplified 96.8%

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

   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. +-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. Step-by-step derivation

      1. *-commutative 98.2%

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

      2. sub-neg 98.2%

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

      3. distribute-rgt-in 98.2%

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

      4. *-un-lft-identity 98.2%

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

   7. Applied egg-rr 98.2%

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

4. Final simplification 97.5%

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

Alternative 8: 98.4% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0)))
   (- x (/ (+ x -1.0) 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 - ((x + -1.0) / 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 - ((x + (-1.0d0)) / 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 - ((x + -1.0) / 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 - ((x + -1.0) / 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(x + -1.0) / 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 - ((x + -1.0) / 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[(x + -1.0), $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 36.6%

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

      1. associate-/l* 58.6%

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

      2. +-commutative 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in y around inf 96.8%

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

      1. associate--l+ 96.8%

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

      2. div-sub 96.8%

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

   7. Simplified 96.8%

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

   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. +-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%

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

4. Final simplification 97.5%

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

Alternative 9: 98.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.15)) {
		tmp = x - ((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 <= 1.15d0))) then
        tmp = x - ((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 <= 1.15)) {
		tmp = x - ((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 <= 1.15):
		tmp = x - ((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 <= 1.15))
		tmp = Float64(x - Float64(Float64(x + -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 <= 1.15)))
		tmp = x - ((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, 1.15]], $MachinePrecision]], N[(x - N[(N[(x + -1.0), $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 36.6%

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

      1. associate-/l* 58.6%

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

      2. +-commutative 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in y around inf 96.8%

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

      1. associate--l+ 96.8%

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

      2. div-sub 96.8%

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

   7. Simplified 96.8%

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

   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. +-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 x around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-*r* 100.0%

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

      3. neg-mul-1 100.0%

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

      4. distribute-lft1-in 100.0%

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

      5. +-commutative 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-*r/ 100.0%

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

      8. associate-*l/ 100.0%

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

      9. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. distribute-neg-frac2 98.6%

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

      3. distribute-neg-in 98.6%

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

      4. metadata-eval 98.6%

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

      5. *-commutative 98.6%

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

      6. unsub-neg 98.6%

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

   10. Simplified 98.6%

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

   11. Taylor expanded in y around 0 97.4%

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

       1. mul-1-neg 97.4%

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

       2. distribute-rgt-neg-out 97.4%

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

   13. Simplified 97.4%

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

4. Final simplification 97.1%

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

Alternative 10: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.9\right):\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.9))) (- x (/ x y)) (+ 1.0 (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.9)) {
		tmp = x - (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 <= 1.9d0))) then
        tmp = x - (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 <= 1.9)) {
		tmp = x - (x / y);
	} else {
		tmp = 1.0 + (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.9):
		tmp = x - (x / y)
	else:
		tmp = 1.0 + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.9))
		tmp = Float64(x - Float64(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 <= 1.9)))
		tmp = x - (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, 1.9]], $MachinePrecision]], N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.8999999999999999 < y

   1. Initial program 36.1%

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

      1. associate-/l* 58.3%

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

      2. +-commutative 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in x around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/l* 65.9%

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

   7. Simplified 65.9%

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

   8. Taylor expanded in y around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

   10. Simplified 79.5%

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

   if -1 < y < 1.8999999999999999

   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. +-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 x around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-*r* 100.0%

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

      3. neg-mul-1 100.0%

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

      4. distribute-lft1-in 100.0%

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

      5. +-commutative 100.0%

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

      6. sub-neg 100.0%

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

      7. associate-*r/ 100.0%

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

      8. associate-*l/ 100.0%

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

      9. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. distribute-neg-frac2 97.9%

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

      3. distribute-neg-in 97.9%

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

      4. metadata-eval 97.9%

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

      5. *-commutative 97.9%

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

      6. unsub-neg 97.9%

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

   10. Simplified 97.9%

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

   11. Taylor expanded in y around 0 96.8%

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

       1. mul-1-neg 96.8%

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

       2. distribute-rgt-neg-out 96.8%

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

   13. Simplified 96.8%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.9\right):\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = x - (x / y);
	else
		tmp = 1.0 - y;
	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[(x / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 36.6%

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

      1. associate-/l* 58.6%

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

      2. +-commutative 58.6%

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

   3. Simplified 58.6%

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

   5. Taylor expanded in x around inf 57.9%

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

      1. *-commutative 57.9%

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

      2. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

   8. Taylor expanded in y around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. unsub-neg 78.9%

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

   10. Simplified 78.9%

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

   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. +-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 x around 0 75.7%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. neg-mul-1 75.3%

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

      2. sub-neg 75.3%

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

   8. Simplified 75.3%

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

4. Final simplification 77.1%

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

Alternative 12: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0045:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.0045) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.0045) {
		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 <= 0.0045d0) 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 <= 0.0045) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.0045:
		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 <= 0.0045)
		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 <= 0.0045)
		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, 0.0045], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.00449999999999999966 < y

   1. Initial program 37.0%

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

      1. associate-/l* 58.9%

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

      2. +-commutative 58.9%

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

   3. Simplified 58.9%

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

   5. Taylor expanded in y around inf 77.5%

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

   if -1 < y < 0.00449999999999999966

   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. +-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 x around 0 76.2%

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

   6. Taylor expanded in y around 0 75.9%

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

      1. neg-mul-1 75.9%

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

      2. sub-neg 75.9%

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

   8. Simplified 75.9%

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

Alternative 13: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 1.25) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 1.25) {
		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 <= 1.25d0) 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 <= 1.25) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 1.25:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 1.25)
		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 <= 1.25)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 1.25], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.25 < y

   1. Initial program 36.1%

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

      1. associate-/l* 58.3%

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

      2. +-commutative 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in y around inf 78.6%

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

   if -1 < y < 1.25

   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. +-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 74.0%

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

Alternative 14: 38.3% 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 68.3%

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

   1. associate-/l* 79.3%

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

   2. +-commutative 79.3%

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

3. Simplified 79.3%

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

5. Taylor expanded in y around 0 39.2%

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

Developer target: 99.6% 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 2024098 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

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