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

Percentage Accurate: 66.8% → 99.9%

Time: 13.9s

Alternatives: 12

Speedup: 2.1×

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: 66.8% 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, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -1}{y}\\ \mathbf{if}\;y \leq -60000000000:\\ \;\;\;\;x + \frac{t_0 + \left(1 - x\right)}{y}\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;1 - \frac{y}{y + 1} \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{x + -1}{{y}^{2}} - \left(t_0 + \frac{x + -1}{{y}^{3}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ x -1.0) y)))
   (if (<= y -60000000000.0)
     (+ x (/ (+ t_0 (- 1.0 x)) y))
     (if (<= y 14000.0)
       (- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))
       (+
        x
        (- (/ (+ x -1.0) (pow y 2.0)) (+ t_0 (/ (+ x -1.0) (pow y 3.0)))))))))

C

double code(double x, double y) {
	double t_0 = (x + -1.0) / y;
	double tmp;
	if (y <= -60000000000.0) {
		tmp = x + ((t_0 + (1.0 - x)) / y);
	} else if (y <= 14000.0) {
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x));
	} else {
		tmp = x + (((x + -1.0) / pow(y, 2.0)) - (t_0 + ((x + -1.0) / pow(y, 3.0))));
	}
	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 <= (-60000000000.0d0)) then
        tmp = x + ((t_0 + (1.0d0 - x)) / y)
    else if (y <= 14000.0d0) then
        tmp = 1.0d0 - ((y / (y + 1.0d0)) * (1.0d0 - x))
    else
        tmp = x + (((x + (-1.0d0)) / (y ** 2.0d0)) - (t_0 + ((x + (-1.0d0)) / (y ** 3.0d0))))
    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 <= -60000000000.0) {
		tmp = x + ((t_0 + (1.0 - x)) / y);
	} else if (y <= 14000.0) {
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x));
	} else {
		tmp = x + (((x + -1.0) / Math.pow(y, 2.0)) - (t_0 + ((x + -1.0) / Math.pow(y, 3.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + -1.0) / y
	tmp = 0
	if y <= -60000000000.0:
		tmp = x + ((t_0 + (1.0 - x)) / y)
	elif y <= 14000.0:
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x))
	else:
		tmp = x + (((x + -1.0) / math.pow(y, 2.0)) - (t_0 + ((x + -1.0) / math.pow(y, 3.0))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + -1.0) / y)
	tmp = 0.0
	if (y <= -60000000000.0)
		tmp = Float64(x + Float64(Float64(t_0 + Float64(1.0 - x)) / y));
	elseif (y <= 14000.0)
		tmp = Float64(1.0 - Float64(Float64(y / Float64(y + 1.0)) * Float64(1.0 - x)));
	else
		tmp = Float64(x + Float64(Float64(Float64(x + -1.0) / (y ^ 2.0)) - Float64(t_0 + Float64(Float64(x + -1.0) / (y ^ 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + -1.0) / y;
	tmp = 0.0;
	if (y <= -60000000000.0)
		tmp = x + ((t_0 + (1.0 - x)) / y);
	elseif (y <= 14000.0)
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x));
	else
		tmp = x + (((x + -1.0) / (y ^ 2.0)) - (t_0 + ((x + -1.0) / (y ^ 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -60000000000.0], N[(x + N[(N[(t$95$0 + N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 14000.0], N[(1.0 - N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] - N[(t$95$0 + N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -60000000000 \lor \neg \left(y \leq 400000\right):\\ \;\;\;\;x + \frac{\frac{x + -1}{y} + \left(1 - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{y + 1} \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -60000000000.0) (not (<= y 400000.0)))
   (+ x (/ (+ (/ (+ x -1.0) y) (- 1.0 x)) y))
   (- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -60000000000.0) || !(y <= 400000.0)) {
		tmp = x + ((((x + -1.0) / y) + (1.0 - x)) / y);
	} else {
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - 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 <= (-60000000000.0d0)) .or. (.not. (y <= 400000.0d0))) then
        tmp = x + ((((x + (-1.0d0)) / y) + (1.0d0 - x)) / y)
    else
        tmp = 1.0d0 - ((y / (y + 1.0d0)) * (1.0d0 - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -60000000000.0) || !(y <= 400000.0)) {
		tmp = x + ((((x + -1.0) / y) + (1.0 - x)) / y);
	} else {
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -60000000000.0) or not (y <= 400000.0):
		tmp = x + ((((x + -1.0) / y) + (1.0 - x)) / y)
	else:
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -60000000000.0) || !(y <= 400000.0))
		tmp = Float64(x + Float64(Float64(Float64(Float64(x + -1.0) / y) + Float64(1.0 - x)) / y));
	else
		tmp = Float64(1.0 - Float64(Float64(y / Float64(y + 1.0)) * Float64(1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -60000000000.0) || ~((y <= 400000.0)))
		tmp = x + ((((x + -1.0) / y) + (1.0 - x)) / y);
	else
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -60000000000.0], N[Not[LessEqual[y, 400000.0]], $MachinePrecision]], N[(x + N[(N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] + N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+100}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-56}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 0.108:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.05e+123)
   x
   (if (<= y -7e+100)
     (/ 1.0 y)
     (if (<= y -1.0)
       x
       (if (<= y 7.5e-56)
         (- 1.0 y)
         (if (<= y 2.2e-37) (* y x) (if (<= y 0.108) (- 1.0 y) x)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.05e+123) {
		tmp = x;
	} else if (y <= -7e+100) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = x;
	} else if (y <= 7.5e-56) {
		tmp = 1.0 - y;
	} else if (y <= 2.2e-37) {
		tmp = y * x;
	} else if (y <= 0.108) {
		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 <= (-1.05d+123)) then
        tmp = x
    else if (y <= (-7d+100)) then
        tmp = 1.0d0 / y
    else if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 7.5d-56) then
        tmp = 1.0d0 - y
    else if (y <= 2.2d-37) then
        tmp = y * x
    else if (y <= 0.108d0) 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 <= -1.05e+123) {
		tmp = x;
	} else if (y <= -7e+100) {
		tmp = 1.0 / y;
	} else if (y <= -1.0) {
		tmp = x;
	} else if (y <= 7.5e-56) {
		tmp = 1.0 - y;
	} else if (y <= 2.2e-37) {
		tmp = y * x;
	} else if (y <= 0.108) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.05e+123:
		tmp = x
	elif y <= -7e+100:
		tmp = 1.0 / y
	elif y <= -1.0:
		tmp = x
	elif y <= 7.5e-56:
		tmp = 1.0 - y
	elif y <= 2.2e-37:
		tmp = y * x
	elif y <= 0.108:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.05e+123)
		tmp = x;
	elseif (y <= -7e+100)
		tmp = Float64(1.0 / y);
	elseif (y <= -1.0)
		tmp = x;
	elseif (y <= 7.5e-56)
		tmp = Float64(1.0 - y);
	elseif (y <= 2.2e-37)
		tmp = Float64(y * x);
	elseif (y <= 0.108)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.05e+123)
		tmp = x;
	elseif (y <= -7e+100)
		tmp = 1.0 / y;
	elseif (y <= -1.0)
		tmp = x;
	elseif (y <= 7.5e-56)
		tmp = 1.0 - y;
	elseif (y <= 2.2e-37)
		tmp = y * x;
	elseif (y <= 0.108)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.05e+123], x, If[LessEqual[y, -7e+100], N[(1.0 / y), $MachinePrecision], If[LessEqual[y, -1.0], x, If[LessEqual[y, 7.5e-56], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 2.2e-37], N[(y * x), $MachinePrecision], If[LessEqual[y, 0.108], N[(1.0 - y), $MachinePrecision], x]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -98000000000:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 230000000:\\ \;\;\;\;1 - \frac{y}{y + 1} \cdot \left(1 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -98000000000.0)
   (- x (/ -1.0 y))
   (if (<= y 230000000.0)
     (- 1.0 (* (/ y (+ y 1.0)) (- 1.0 x)))
     (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -98000000000.0) {
		tmp = x - (-1.0 / y);
	} else if (y <= 230000000.0) {
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-98000000000.0d0)) then
        tmp = x - ((-1.0d0) / y)
    else if (y <= 230000000.0d0) then
        tmp = 1.0d0 - ((y / (y + 1.0d0)) * (1.0d0 - x))
    else
        tmp = x + ((1.0d0 - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -98000000000.0) {
		tmp = x - (-1.0 / y);
	} else if (y <= 230000000.0) {
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -98000000000.0:
		tmp = x - (-1.0 / y)
	elif y <= 230000000.0:
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -98000000000.0)
		tmp = Float64(x - Float64(-1.0 / y));
	elseif (y <= 230000000.0)
		tmp = Float64(1.0 - Float64(Float64(y / Float64(y + 1.0)) * Float64(1.0 - x)));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -98000000000.0)
		tmp = x - (-1.0 / y);
	elseif (y <= 230000000.0)
		tmp = 1.0 - ((y / (y + 1.0)) * (1.0 - x));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -98000000000.0], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 230000000.0], N[(1.0 - N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{-1}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-58}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-37}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 0.096:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ -1.0 y))))
   (if (<= y -1.0)
     t_0
     (if (<= y 5.2e-58)
       (- 1.0 y)
       (if (<= y 1.5e-37) (* y x) (if (<= y 0.096) (- 1.0 y) 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 <= 5.2e-58) {
		tmp = 1.0 - y;
	} else if (y <= 1.5e-37) {
		tmp = y * x;
	} else if (y <= 0.096) {
		tmp = 1.0 - 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 = x - ((-1.0d0) / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 5.2d-58) then
        tmp = 1.0d0 - y
    else if (y <= 1.5d-37) then
        tmp = y * x
    else if (y <= 0.096d0) then
        tmp = 1.0d0 - y
    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 <= 5.2e-58) {
		tmp = 1.0 - y;
	} else if (y <= 1.5e-37) {
		tmp = y * x;
	} else if (y <= 0.096) {
		tmp = 1.0 - y;
	} 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 <= 5.2e-58:
		tmp = 1.0 - y
	elif y <= 1.5e-37:
		tmp = y * x
	elif y <= 0.096:
		tmp = 1.0 - y
	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 <= 5.2e-58)
		tmp = Float64(1.0 - y);
	elseif (y <= 1.5e-37)
		tmp = Float64(y * x);
	elseif (y <= 0.096)
		tmp = Float64(1.0 - y);
	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 <= 5.2e-58)
		tmp = 1.0 - y;
	elseif (y <= 1.5e-37)
		tmp = y * x;
	elseif (y <= 0.096)
		tmp = 1.0 - y;
	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, 5.2e-58], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 1.5e-37], N[(y * x), $MachinePrecision], If[LessEqual[y, 0.096], N[(1.0 - y), $MachinePrecision], t$95$0]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-55}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-37}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 0.82:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 4.8e-55)
     (- 1.0 y)
     (if (<= y 6.2e-37) (* y x) (if (<= y 0.82) (- 1.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 4.8e-55) {
		tmp = 1.0 - y;
	} else if (y <= 6.2e-37) {
		tmp = y * x;
	} else if (y <= 0.82) {
		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 <= 4.8d-55) then
        tmp = 1.0d0 - y
    else if (y <= 6.2d-37) then
        tmp = y * x
    else if (y <= 0.82d0) 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 <= 4.8e-55) {
		tmp = 1.0 - y;
	} else if (y <= 6.2e-37) {
		tmp = y * x;
	} else if (y <= 0.82) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 4.8e-55:
		tmp = 1.0 - y
	elif y <= 6.2e-37:
		tmp = y * x
	elif y <= 0.82:
		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 <= 4.8e-55)
		tmp = Float64(1.0 - y);
	elseif (y <= 6.2e-37)
		tmp = Float64(y * x);
	elseif (y <= 0.82)
		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 <= 4.8e-55)
		tmp = 1.0 - y;
	elseif (y <= 6.2e-37)
		tmp = y * x;
	elseif (y <= 0.82)
		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, 4.8e-55], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 6.2e-37], N[(y * x), $MachinePrecision], If[LessEqual[y, 0.82], N[(1.0 - y), $MachinePrecision], x]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.84\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.84)))
   (- x (/ -1.0 y))
   (+ 1.0 (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.84)) {
		tmp = 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 <= 0.84d0))) then
        tmp = 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 <= 0.84)) {
		tmp = 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 <= 0.84):
		tmp = 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 <= 0.84))
		tmp = Float64(x - Float64(-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 <= 0.84)))
		tmp = 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, 0.84]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 73.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-58}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-31}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 2.5e-58) 1.0 (if (<= y 5.6e-31) (* y x) (if (<= y 1.0) 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 2.5e-58) {
		tmp = 1.0;
	} else if (y <= 5.6e-31) {
		tmp = y * x;
	} else if (y <= 1.0) {
		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 <= 2.5d-58) then
        tmp = 1.0d0
    else if (y <= 5.6d-31) then
        tmp = y * x
    else if (y <= 1.0d0) 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 <= 2.5e-58) {
		tmp = 1.0;
	} else if (y <= 5.6e-31) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 2.5e-58:
		tmp = 1.0
	elif y <= 5.6e-31:
		tmp = y * x
	elif y <= 1.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 2.5e-58)
		tmp = 1.0;
	elseif (y <= 5.6e-31)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		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 <= 2.5e-58)
		tmp = 1.0;
	elseif (y <= 5.6e-31)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 2.5e-58], 1.0, If[LessEqual[y, 5.6e-31], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], 1.0, x]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 97.8% accurate, 1.2× 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 73.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.066:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 0.066) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.066) {
		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 <= 0.066d0) 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 <= 0.066) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.066:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.066)
		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 <= 0.066)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.066], 1.0, x]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 39.1% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.6% accurate, 0.7× 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 2024003 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (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))))