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

Percentage Accurate: 65.6% → 76.9%

Time: 1.4s

Alternatives: 6

Speedup: 1.1×

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 65.6% 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: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \left(1 - x\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{+18}:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (- 1.0 x))))
   (if (<= y -2.9e+19)
     t_0
     (if (<= y 1.62e+18) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (1.0 - x);
	double tmp;
	if (y <= -2.9e+19) {
		tmp = t_0;
	} else if (y <= 1.62e+18) {
		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 - (1.0d0 - x)
    if (y <= (-2.9d+19)) then
        tmp = t_0
    else if (y <= 1.62d+18) 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 - (1.0 - x);
	double tmp;
	if (y <= -2.9e+19) {
		tmp = t_0;
	} else if (y <= 1.62e+18) {
		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 - (1.0 - x)
	tmp = 0
	if y <= -2.9e+19:
		tmp = t_0
	elif y <= 1.62e+18:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(1.0 - x))
	tmp = 0.0
	if (y <= -2.9e+19)
		tmp = t_0;
	elseif (y <= 1.62e+18)
		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 - (1.0 - x);
	tmp = 0.0;
	if (y <= -2.9e+19)
		tmp = t_0;
	elseif (y <= 1.62e+18)
		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[(1.0 - N[(1.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+19], t$95$0, If[LessEqual[y, 1.62e+18], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e19 or 1.62e18 < y

   1. Initial program 25.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 51.3%

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

   if -2.9e19 < y < 1.62e18

   1. Initial program 98.9%

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

Alternative 2: 61.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{y + 1}\\ t_1 := 1 - \left(1 - x\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.9999995:\\ \;\;\;\;y + 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ y 1.0))) (t_1 (- 1.0 (- 1.0 x))))
   (if (<= t_0 -1e+20) t_1 (if (<= t_0 0.9999995) (+ y 1.0) t_1))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (y + 1.0);
	double t_1 = 1.0 - (1.0 - x);
	double tmp;
	if (t_0 <= -1e+20) {
		tmp = t_1;
	} else if (t_0 <= 0.9999995) {
		tmp = y + 1.0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (y + 1.0d0)
    t_1 = 1.0d0 - (1.0d0 - x)
    if (t_0 <= (-1d+20)) then
        tmp = t_1
    else if (t_0 <= 0.9999995d0) then
        tmp = y + 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (y + 1.0);
	double t_1 = 1.0 - (1.0 - x);
	double tmp;
	if (t_0 <= -1e+20) {
		tmp = t_1;
	} else if (t_0 <= 0.9999995) {
		tmp = y + 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (y + 1.0)
	t_1 = 1.0 - (1.0 - x)
	tmp = 0
	if t_0 <= -1e+20:
		tmp = t_1
	elif t_0 <= 0.9999995:
		tmp = y + 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0))
	t_1 = Float64(1.0 - Float64(1.0 - x))
	tmp = 0.0
	if (t_0 <= -1e+20)
		tmp = t_1;
	elseif (t_0 <= 0.9999995)
		tmp = Float64(y + 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (y + 1.0);
	t_1 = 1.0 - (1.0 - x);
	tmp = 0.0;
	if (t_0 <= -1e+20)
		tmp = t_1;
	elseif (t_0 <= 0.9999995)
		tmp = y + 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(1.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+20], t$95$1, If[LessEqual[t$95$0, 0.9999995], N[(y + 1.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < -1e20 or 0.999999500000000041 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 40.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 43.5%

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

   if -1e20 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.999999500000000041

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 4.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 94.5%

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

Alternative 3: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \left(1 - x\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+14}:\\ \;\;\;\;\frac{1 - \left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (- 1.0 x))))
   (if (<= y -5e+39)
     t_0
     (if (<= y 3.3e+14) (/ (- 1.0 (* (- 1.0 x) y)) (+ y 1.0)) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (1.0 - x);
	double tmp;
	if (y <= -5e+39) {
		tmp = t_0;
	} else if (y <= 3.3e+14) {
		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 - (1.0d0 - x)
    if (y <= (-5d+39)) then
        tmp = t_0
    else if (y <= 3.3d+14) 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 - (1.0 - x);
	double tmp;
	if (y <= -5e+39) {
		tmp = t_0;
	} else if (y <= 3.3e+14) {
		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 - (1.0 - x)
	tmp = 0
	if y <= -5e+39:
		tmp = t_0
	elif y <= 3.3e+14:
		tmp = (1.0 - ((1.0 - x) * y)) / (y + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(1.0 - x))
	tmp = 0.0
	if (y <= -5e+39)
		tmp = t_0;
	elseif (y <= 3.3e+14)
		tmp = Float64(Float64(1.0 - 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 - (1.0 - x);
	tmp = 0.0;
	if (y <= -5e+39)
		tmp = t_0;
	elseif (y <= 3.3e+14)
		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[(1.0 - N[(1.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+39], t$95$0, If[LessEqual[y, 3.3e+14], N[(N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000015e39 or 3.3e14 < y

   1. Initial program 25.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 51.3%

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

   if -5.00000000000000015e39 < y < 3.3e14

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 3.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 96.4%

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

Alternative 4: 74.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 29.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 51.2%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.2%

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

Alternative 5: 38.5% accurate, 6.5× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ y 1.0))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y + 1.0

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 3.0%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 37.9%

   \[\leadsto \color{blue}{y + 1} \]
9. Add Preprocessing

Alternative 6: 26.0% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.2%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 3.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 25.1%

   \[\leadsto 1 - \color{blue}{x} \]
9. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.6× 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 2024321 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64
  :pre (TRUE)

  :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))))