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

Percentage Accurate: 65.7% → 99.8%

Time: 9.6s

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: 65.7% 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: 99.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11500:\\ \;\;\;\;\left(x - \left(\frac{-1}{{y}^{3}} - \frac{1}{y}\right)\right) + \left(\frac{x}{{y}^{2}} + \left(\frac{-1}{{y}^{2}} - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)\right)\\ \mathbf{elif}\;y \leq 180000000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{1}{y} + -1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -11500.0)
   (+
    (- x (- (/ -1.0 (pow y 3.0)) (/ 1.0 y)))
    (+
     (/ x (pow y 2.0))
     (- (/ -1.0 (pow y 2.0)) (+ (/ x y) (/ x (pow y 3.0))))))
   (if (<= y 180000000.0)
     (+ 1.0 (/ (* y (- 1.0 x)) (- -1.0 y)))
     (- x (/ (+ (/ 1.0 y) -1.0) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -11500.0) {
		tmp = (x - ((-1.0 / pow(y, 3.0)) - (1.0 / y))) + ((x / pow(y, 2.0)) + ((-1.0 / pow(y, 2.0)) - ((x / y) + (x / pow(y, 3.0)))));
	} else if (y <= 180000000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x - (((1.0 / 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 <= (-11500.0d0)) then
        tmp = (x - (((-1.0d0) / (y ** 3.0d0)) - (1.0d0 / y))) + ((x / (y ** 2.0d0)) + (((-1.0d0) / (y ** 2.0d0)) - ((x / y) + (x / (y ** 3.0d0)))))
    else if (y <= 180000000.0d0) then
        tmp = 1.0d0 + ((y * (1.0d0 - x)) / ((-1.0d0) - y))
    else
        tmp = x - (((1.0d0 / y) + (-1.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -11500.0) {
		tmp = (x - ((-1.0 / Math.pow(y, 3.0)) - (1.0 / y))) + ((x / Math.pow(y, 2.0)) + ((-1.0 / Math.pow(y, 2.0)) - ((x / y) + (x / Math.pow(y, 3.0)))));
	} else if (y <= 180000000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x - (((1.0 / y) + -1.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -11500.0:
		tmp = (x - ((-1.0 / math.pow(y, 3.0)) - (1.0 / y))) + ((x / math.pow(y, 2.0)) + ((-1.0 / math.pow(y, 2.0)) - ((x / y) + (x / math.pow(y, 3.0)))))
	elif y <= 180000000.0:
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y))
	else:
		tmp = x - (((1.0 / y) + -1.0) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -11500.0)
		tmp = Float64(Float64(x - Float64(Float64(-1.0 / (y ^ 3.0)) - Float64(1.0 / y))) + Float64(Float64(x / (y ^ 2.0)) + Float64(Float64(-1.0 / (y ^ 2.0)) - Float64(Float64(x / y) + Float64(x / (y ^ 3.0))))));
	elseif (y <= 180000000.0)
		tmp = Float64(1.0 + Float64(Float64(y * Float64(1.0 - x)) / Float64(-1.0 - y)));
	else
		tmp = Float64(x - Float64(Float64(Float64(1.0 / y) + -1.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11500.0)
		tmp = (x - ((-1.0 / (y ^ 3.0)) - (1.0 / y))) + ((x / (y ^ 2.0)) + ((-1.0 / (y ^ 2.0)) - ((x / y) + (x / (y ^ 3.0)))));
	elseif (y <= 180000000.0)
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	else
		tmp = x - (((1.0 / y) + -1.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -11500.0], N[(N[(x - N[(N[(-1.0 / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] - N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] + N[(x / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 180000000.0], N[(1.0 + N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -11500

   1. Initial program 34.9%

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

      1. associate-/l* 53.2%

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

      2. remove-double-neg 53.2%

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

      3. remove-double-neg 53.2%

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

      4. +-commutative 53.2%

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

   3. Simplified 53.2%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -11500 < y < 1.8e8

   1. Initial program 100.0%

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

   if 1.8e8 < y

   1. Initial program 27.6%

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

      1. associate-/l* 46.2%

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

      2. remove-double-neg 46.2%

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

      3. remove-double-neg 46.2%

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

      4. +-commutative 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11500:\\ \;\;\;\;\left(x - \left(\frac{-1}{{y}^{3}} - \frac{1}{y}\right)\right) + \left(\frac{x}{{y}^{2}} + \left(\frac{-1}{{y}^{2}} - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)\right)\\ \mathbf{elif}\;y \leq 180000000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{1}{y} + -1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{-8} \lor \neg \left(t\_0 \leq 5\right):\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{1}{y} + -1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 2e-8) (not (<= t_0 5.0)))
     (+ 1.0 (* (+ x -1.0) (/ y (+ y 1.0))))
     (- x (/ (+ (/ 1.0 y) -1.0) y)))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 2e-8) || !(t_0 <= 5.0)) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x - (((1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 2d-8) .or. (.not. (t_0 <= 5.0d0))) then
        tmp = 1.0d0 + ((x + (-1.0d0)) * (y / (y + 1.0d0)))
    else
        tmp = x - (((1.0d0 / y) + (-1.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 2e-8) || !(t_0 <= 5.0)) {
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	} else {
		tmp = x - (((1.0 / y) + -1.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 2e-8) or not (t_0 <= 5.0):
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)))
	else:
		tmp = x - (((1.0 / y) + -1.0) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))
	tmp = 0.0
	if ((t_0 <= 2e-8) || !(t_0 <= 5.0))
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x - Float64(Float64(Float64(1.0 / y) + -1.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (y + 1.0);
	tmp = 0.0;
	if ((t_0 <= 2e-8) || ~((t_0 <= 5.0)))
		tmp = 1.0 + ((x + -1.0) * (y / (y + 1.0)));
	else
		tmp = x - (((1.0 / y) + -1.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 2e-8], N[Not[LessEqual[t$95$0, 5.0]], $MachinePrecision]], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 2e-8 or 5 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 87.2%

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

   if 2e-8 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 5

   1. Initial program 9.1%

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

      1. associate-/l* 9.1%

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

      2. remove-double-neg 9.1%

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

      3. remove-double-neg 9.1%

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

      4. +-commutative 9.1%

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

   3. Simplified 9.1%

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

   5. Taylor expanded in y around -inf 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around 0 99.6%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 2 \cdot 10^{-8} \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 5\right):\\ \;\;\;\;1 + \left(x + -1\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{1}{y} + -1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11500:\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{\left(x + -1\right) - \frac{x + -1}{y}}{y}}{y}\\ \mathbf{elif}\;y \leq 62000000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{1}{y} + -1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -11500.0)
   (- x (/ (- (+ x -1.0) (/ (- (+ x -1.0) (/ (+ x -1.0) y)) y)) y))
   (if (<= y 62000000.0)
     (+ 1.0 (/ (* y (- 1.0 x)) (- -1.0 y)))
     (- x (/ (+ (/ 1.0 y) -1.0) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -11500.0) {
		tmp = x - (((x + -1.0) - (((x + -1.0) - ((x + -1.0) / y)) / y)) / y);
	} else if (y <= 62000000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x - (((1.0 / 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 <= (-11500.0d0)) then
        tmp = x - (((x + (-1.0d0)) - (((x + (-1.0d0)) - ((x + (-1.0d0)) / y)) / y)) / y)
    else if (y <= 62000000.0d0) then
        tmp = 1.0d0 + ((y * (1.0d0 - x)) / ((-1.0d0) - y))
    else
        tmp = x - (((1.0d0 / y) + (-1.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -11500.0) {
		tmp = x - (((x + -1.0) - (((x + -1.0) - ((x + -1.0) / y)) / y)) / y);
	} else if (y <= 62000000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x - (((1.0 / y) + -1.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -11500.0:
		tmp = x - (((x + -1.0) - (((x + -1.0) - ((x + -1.0) / y)) / y)) / y)
	elif y <= 62000000.0:
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y))
	else:
		tmp = x - (((1.0 / y) + -1.0) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -11500.0)
		tmp = Float64(x - Float64(Float64(Float64(x + -1.0) - Float64(Float64(Float64(x + -1.0) - Float64(Float64(x + -1.0) / y)) / y)) / y));
	elseif (y <= 62000000.0)
		tmp = Float64(1.0 + Float64(Float64(y * Float64(1.0 - x)) / Float64(-1.0 - y)));
	else
		tmp = Float64(x - Float64(Float64(Float64(1.0 / y) + -1.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11500.0)
		tmp = x - (((x + -1.0) - (((x + -1.0) - ((x + -1.0) / y)) / y)) / y);
	elseif (y <= 62000000.0)
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	else
		tmp = x - (((1.0 / y) + -1.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -11500.0], N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] - N[(N[(N[(x + -1.0), $MachinePrecision] - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 62000000.0], N[(1.0 + N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -11500

   1. Initial program 34.9%

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

      1. associate-/l* 53.2%

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

      2. remove-double-neg 53.2%

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

      3. remove-double-neg 53.2%

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

      4. +-commutative 53.2%

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

   3. Simplified 53.2%

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

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

   if -11500 < y < 6.2e7

   1. Initial program 100.0%

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

   if 6.2e7 < y

   1. Initial program 27.6%

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

      1. associate-/l* 46.2%

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

      2. remove-double-neg 46.2%

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

      3. remove-double-neg 46.2%

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

      4. +-commutative 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11500:\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{\left(x + -1\right) - \frac{x + -1}{y}}{y}}{y}\\ \mathbf{elif}\;y \leq 62000000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{1}{y} + -1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10.5:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+70}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 2.75e-67)
     1.0
     (if (<= y 10.5) (* y x) (if (<= y 2.55e+70) (/ 1.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 2.75e-67) {
		tmp = 1.0;
	} else if (y <= 10.5) {
		tmp = y * x;
	} else if (y <= 2.55e+70) {
		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 <= 2.75d-67) then
        tmp = 1.0d0
    else if (y <= 10.5d0) then
        tmp = y * x
    else if (y <= 2.55d+70) 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 <= 2.75e-67) {
		tmp = 1.0;
	} else if (y <= 10.5) {
		tmp = y * x;
	} else if (y <= 2.55e+70) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 2.75e-67:
		tmp = 1.0
	elif y <= 10.5:
		tmp = y * x
	elif y <= 2.55e+70:
		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 <= 2.75e-67)
		tmp = 1.0;
	elseif (y <= 10.5)
		tmp = Float64(y * x);
	elseif (y <= 2.55e+70)
		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 <= 2.75e-67)
		tmp = 1.0;
	elseif (y <= 10.5)
		tmp = y * x;
	elseif (y <= 2.55e+70)
		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, 2.75e-67], 1.0, If[LessEqual[y, 10.5], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.55e+70], N[(1.0 / y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1 or 2.55000000000000007e70 < y

   1. Initial program 32.2%

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

      1. associate-/l* 52.9%

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

      2. remove-double-neg 52.9%

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

      3. remove-double-neg 52.9%

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

      4. +-commutative 52.9%

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

   3. Simplified 52.9%

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

   5. Taylor expanded in y around inf 76.9%

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

   if -1 < y < 2.7500000000000001e-67

   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 99.9%

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

   6. Taylor expanded in y around 0 82.4%

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

   if 2.7500000000000001e-67 < y < 10.5

   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 0 100.0%

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

   6. Taylor expanded in x around inf 63.0%

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

      1. *-commutative 63.0%

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

   8. Simplified 63.0%

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

   if 10.5 < y < 2.55000000000000007e70

   1. Initial program 22.6%

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

      1. associate-/l* 22.7%

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

      2. remove-double-neg 22.7%

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

      3. remove-double-neg 22.7%

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

      4. +-commutative 22.7%

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

   3. Simplified 22.7%

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

   5. Taylor expanded in y around -inf 97.2%

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

      1. mul-1-neg 97.2%

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

      2. distribute-frac-neg 97.2%

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

      3. neg-sub0 97.2%

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

      4. associate-+l- 97.2%

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

      5. neg-sub0 97.2%

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

      6. +-commutative 97.2%

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

      7. sub-neg 97.2%

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

   7. Simplified 97.2%

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

   8. Taylor expanded in x around 0 83.7%

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

Alternative 5: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -260000:\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{x + -1}{y}}{y}\\ \mathbf{elif}\;y \leq 26500000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{1}{y} + -1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -260000.0)
   (- x (/ (- (+ x -1.0) (/ (+ x -1.0) y)) y))
   (if (<= y 26500000.0)
     (+ 1.0 (/ (* y (- 1.0 x)) (- -1.0 y)))
     (- x (/ (+ (/ 1.0 y) -1.0) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -260000.0) {
		tmp = x - (((x + -1.0) - ((x + -1.0) / y)) / y);
	} else if (y <= 26500000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x - (((1.0 / 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 <= (-260000.0d0)) then
        tmp = x - (((x + (-1.0d0)) - ((x + (-1.0d0)) / y)) / y)
    else if (y <= 26500000.0d0) then
        tmp = 1.0d0 + ((y * (1.0d0 - x)) / ((-1.0d0) - y))
    else
        tmp = x - (((1.0d0 / y) + (-1.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -260000.0) {
		tmp = x - (((x + -1.0) - ((x + -1.0) / y)) / y);
	} else if (y <= 26500000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x - (((1.0 / y) + -1.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -260000.0:
		tmp = x - (((x + -1.0) - ((x + -1.0) / y)) / y)
	elif y <= 26500000.0:
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y))
	else:
		tmp = x - (((1.0 / y) + -1.0) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -260000.0)
		tmp = Float64(x - Float64(Float64(Float64(x + -1.0) - Float64(Float64(x + -1.0) / y)) / y));
	elseif (y <= 26500000.0)
		tmp = Float64(1.0 + Float64(Float64(y * Float64(1.0 - x)) / Float64(-1.0 - y)));
	else
		tmp = Float64(x - Float64(Float64(Float64(1.0 / y) + -1.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -260000.0)
		tmp = x - (((x + -1.0) - ((x + -1.0) / y)) / y);
	elseif (y <= 26500000.0)
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	else
		tmp = x - (((1.0 / y) + -1.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -260000.0], N[(x - N[(N[(N[(x + -1.0), $MachinePrecision] - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 26500000.0], N[(1.0 + N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e5

   1. Initial program 34.9%

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

      1. associate-/l* 53.2%

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

      2. remove-double-neg 53.2%

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

      3. remove-double-neg 53.2%

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

      4. +-commutative 53.2%

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

   3. Simplified 53.2%

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

   5. Taylor expanded in y around -inf 99.5%

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

   7. Simplified 99.5%

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

   if -2.6e5 < y < 2.65e7

   1. Initial program 100.0%

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

   if 2.65e7 < y

   1. Initial program 27.6%

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

      1. associate-/l* 46.2%

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

      2. remove-double-neg 46.2%

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

      3. remove-double-neg 46.2%

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

      4. +-commutative 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -260000:\\ \;\;\;\;x - \frac{\left(x + -1\right) - \frac{x + -1}{y}}{y}\\ \mathbf{elif}\;y \leq 26500000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{1}{y} + -1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-70}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.039:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (/ 1.0 y))))
   (if (<= y -1.0) t_0 (if (<= y 8.5e-70) 1.0 (if (<= y 0.039) (* y x) t_0)))))

C

double code(double x, double y) {
	double t_0 = x + (1.0 / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 8.5e-70) {
		tmp = 1.0;
	} else if (y <= 0.039) {
		tmp = y * x;
	} 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 = x + (1.0d0 / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 8.5d-70) then
        tmp = 1.0d0
    else if (y <= 0.039d0) then
        tmp = y * x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + (1.0 / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 8.5e-70) {
		tmp = 1.0;
	} else if (y <= 0.039) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + (1.0 / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 8.5e-70:
		tmp = 1.0
	elif y <= 0.039:
		tmp = y * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(1.0 / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 8.5e-70)
		tmp = 1.0;
	elseif (y <= 0.039)
		tmp = Float64(y * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + (1.0 / y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 8.5e-70)
		tmp = 1.0;
	elseif (y <= 0.039)
		tmp = y * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 8.5e-70], 1.0, If[LessEqual[y, 0.039], N[(y * x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.0389999999999999999 < y

   1. Initial program 31.2%

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

      1. associate-/l* 49.6%

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

      2. remove-double-neg 49.6%

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

      3. remove-double-neg 49.6%

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

      4. +-commutative 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in y around -inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-frac-neg 98.8%

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

      3. neg-sub0 98.8%

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

      4. associate-+l- 98.8%

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

      5. neg-sub0 98.8%

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

      6. +-commutative 98.8%

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

      7. sub-neg 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around 0 98.6%

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

   if -1 < y < 8.5000000000000002e-70

   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 99.9%

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

   6. Taylor expanded in y around 0 82.4%

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

   if 8.5000000000000002e-70 < y < 0.0389999999999999999

   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 0 100.0%

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

   6. Taylor expanded in x around inf 63.0%

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

      1. *-commutative 63.0%

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

   8. Simplified 63.0%

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

Alternative 7: 98.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.2)) {
		tmp = x - (((1.0 / y) + -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 <= 1.2d0))) then
        tmp = x - (((1.0d0 / y) + (-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 <= 1.2)) {
		tmp = x - (((1.0 / y) + -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 <= 1.2):
		tmp = x - (((1.0 / y) + -1.0) / y)
	else:
		tmp = 1.0 + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.2))
		tmp = Float64(x - Float64(Float64(Float64(1.0 / y) + -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 <= 1.2)))
		tmp = x - (((1.0 / y) + -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, 1.2]], $MachinePrecision]], N[(x - N[(N[(N[(1.0 / y), $MachinePrecision] + -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 1.19999999999999996 < y

   1. Initial program 31.2%

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

      1. associate-/l* 49.6%

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

      2. remove-double-neg 49.6%

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

      3. remove-double-neg 49.6%

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

      4. +-commutative 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in y around -inf 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 99.6%

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

   if -1 < y < 1.19999999999999996

   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 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. neg-mul-1 99.9%

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

   8. Simplified 99.9%

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

      1. cancel-sign-sub 99.9%

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

      2. +-commutative 99.9%

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

   10. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

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

Alternative 8: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 120000000000:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 9.6e-71) 1.0 (if (<= y 120000000000.0) (* y x) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 9.6e-71) {
		tmp = 1.0;
	} else if (y <= 120000000000.0) {
		tmp = 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 <= 9.6d-71) then
        tmp = 1.0d0
    else if (y <= 120000000000.0d0) then
        tmp = 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 <= 9.6e-71) {
		tmp = 1.0;
	} else if (y <= 120000000000.0) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 9.6e-71:
		tmp = 1.0
	elif y <= 120000000000.0:
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 9.6e-71)
		tmp = 1.0;
	elseif (y <= 120000000000.0)
		tmp = 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 <= 9.6e-71)
		tmp = 1.0;
	elseif (y <= 120000000000.0)
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 9.6e-71], 1.0, If[LessEqual[y, 120000000000.0], N[(y * x), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.2e11 < y

   1. Initial program 31.0%

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

      1. associate-/l* 49.6%

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

      2. remove-double-neg 49.6%

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

      3. remove-double-neg 49.6%

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

      4. +-commutative 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in y around inf 71.1%

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

   if -1 < y < 9.6e-71

   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 99.9%

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

   6. Taylor expanded in y around 0 82.4%

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

   if 9.6e-71 < y < 1.2e11

   1. Initial program 97.4%

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

      1. associate-/l* 97.4%

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

      2. remove-double-neg 97.4%

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

      3. remove-double-neg 97.4%

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

      4. +-commutative 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 95.1%

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

   6. Taylor expanded in x around inf 60.1%

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

      1. *-commutative 60.1%

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

   8. Simplified 60.1%

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

Alternative 9: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.3\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.3))) (+ x (/ (- 1.0 x) y)) (+ 1.0 (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.3)) {
		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 <= 1.3d0))) 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 <= 1.3)) {
		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 <= 1.3):
		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 <= 1.3))
		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 <= 1.3)))
		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, 1.3]], $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 1.30000000000000004 < y

   1. Initial program 31.2%

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

      1. associate-/l* 49.6%

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

      2. remove-double-neg 49.6%

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

      3. remove-double-neg 49.6%

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

      4. +-commutative 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in y around -inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-frac-neg 98.8%

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

      3. neg-sub0 98.8%

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

      4. associate-+l- 98.8%

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

      5. neg-sub0 98.8%

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

      6. +-commutative 98.8%

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

      7. sub-neg 98.8%

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

   7. Simplified 98.8%

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

   if -1 < y < 1.30000000000000004

   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 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. neg-mul-1 99.9%

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

   8. Simplified 99.9%

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

      1. cancel-sign-sub 99.9%

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

      2. +-commutative 99.9%

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

   10. Applied egg-rr 99.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.3\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% 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 31.2%

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

      1. associate-/l* 49.6%

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

      2. remove-double-neg 49.6%

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

      3. remove-double-neg 49.6%

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

      4. +-commutative 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in y around -inf 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-frac-neg 98.8%

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

      3. neg-sub0 98.8%

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

      4. associate-+l- 98.8%

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

      5. neg-sub0 98.8%

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

      6. +-commutative 98.8%

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

      7. sub-neg 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around 0 98.6%

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

   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. Taylor expanded in y around 0 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

      1. neg-mul-1 99.9%

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

   8. Simplified 99.9%

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

      1. cancel-sign-sub 99.9%

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

      2. +-commutative 99.9%

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

   10. Applied egg-rr 99.9%

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

4. Final simplification 99.3%

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

Alternative 11: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6600000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 6600000000000.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 6600000000000.0) {
		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 <= 6600000000000.0d0) 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 <= 6600000000000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 6600000000000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 6600000000000.0)
		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 <= 6600000000000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 6600000000000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 6.6e12 < y

   1. Initial program 31.0%

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

      1. associate-/l* 49.7%

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

      2. remove-double-neg 49.7%

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

      3. remove-double-neg 49.7%

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

      4. +-commutative 49.7%

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

   3. Simplified 49.7%

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

   5. Taylor expanded in y around inf 71.6%

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

   if -1 < y < 6.6e12

   1. Initial program 99.1%

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

      1. associate-/l* 99.1%

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

      2. remove-double-neg 99.1%

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

      3. remove-double-neg 99.1%

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

      4. +-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 98.4%

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

   6. Taylor expanded in y around 0 74.9%

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

Alternative 12: 38.7% 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 65.6%

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

   1. associate-/l* 74.8%

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

   2. remove-double-neg 74.8%

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

   3. remove-double-neg 74.8%

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

   4. +-commutative 74.8%

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

3. Simplified 74.8%

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

5. Taylor expanded in y around 0 51.2%

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

6. Taylor expanded in y around 0 40.0%

   \[\leadsto \color{blue}{1} \]
7. 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 2024157 
(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))))