Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D

Percentage Accurate: 99.7% → 99.7%

Time: 9.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (1.0d0 / (x * 9.0d0))) - (y / (3.0d0 * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * Math.sqrt(x)));
}

Python

def code(x, y):
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(1.0 / Float64(x * 9.0))) - Float64(y / Float64(3.0 * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (1.0d0 / (x * 9.0d0))) - (y / (3.0d0 * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * Math.sqrt(x)));
}

Python

def code(x, y):
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(1.0 / Float64(x * 9.0))) - Float64(y / Float64(3.0 * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (1.0d0 / (x * 9.0d0))) - (y / (3.0d0 * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * Math.sqrt(x)));
}

Python

def code(x, y):
	return (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(1.0 / Float64(x * 9.0))) - Float64(y / Float64(3.0 * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (1.0 / (x * 9.0))) - (y / (3.0 * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{0.1111111111111111}{x}\right) + \frac{y}{\sqrt{x}} \cdot -0.3333333333333333 \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- 1.0 (/ 0.1111111111111111 x)) (* (/ y (sqrt x)) -0.3333333333333333)))

C

double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) + ((y / sqrt(x)) * -0.3333333333333333);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (0.1111111111111111d0 / x)) + ((y / sqrt(x)) * (-0.3333333333333333d0))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) + ((y / Math.sqrt(x)) * -0.3333333333333333);
}

Python

def code(x, y):
	return (1.0 - (0.1111111111111111 / x)) + ((y / math.sqrt(x)) * -0.3333333333333333)

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(0.1111111111111111 / x)) + Float64(Float64(y / sqrt(x)) * -0.3333333333333333))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (0.1111111111111111 / x)) + ((y / sqrt(x)) * -0.3333333333333333);
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 3: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{0.1111111111111111}{x}\right) + \frac{\frac{y}{-3}}{\sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- 1.0 (/ 0.1111111111111111 x)) (/ (/ y -3.0) (sqrt x))))

C

double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) + ((y / -3.0) / sqrt(x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (0.1111111111111111d0 / x)) + ((y / (-3.0d0)) / sqrt(x))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) + ((y / -3.0) / Math.sqrt(x));
}

Python

def code(x, y):
	return (1.0 - (0.1111111111111111 / x)) + ((y / -3.0) / math.sqrt(x))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(0.1111111111111111 / x)) + Float64(Float64(y / -3.0) / sqrt(x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (0.1111111111111111 / x)) + ((y / -3.0) / sqrt(x));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(y / -3.0), $MachinePrecision] / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{0.1111111111111111}{x}\right) + \frac{\frac{y}{\sqrt{x}}}{-3} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (- 1.0 (/ 0.1111111111111111 x)) (/ (/ y (sqrt x)) -3.0)))

C

double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) + ((y / sqrt(x)) / -3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - (0.1111111111111111d0 / x)) + ((y / sqrt(x)) / (-3.0d0))
end function

Java

public static double code(double x, double y) {
	return (1.0 - (0.1111111111111111 / x)) + ((y / Math.sqrt(x)) / -3.0);
}

Python

def code(x, y):
	return (1.0 - (0.1111111111111111 / x)) + ((y / math.sqrt(x)) / -3.0)

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(0.1111111111111111 / x)) + Float64(Float64(y / sqrt(x)) / -3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - (0.1111111111111111 / x)) + ((y / sqrt(x)) / -3.0);
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 5: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+85} \lor \neg \left(y \leq 7.5 \cdot 10^{+87}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{\sqrt{x}}{y}}\\ \mathbf{else}:\\ \;\;\;\;1 - 0.1111111111111111 \cdot \frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5e+85) (not (<= y 7.5e+87)))
   (/ -0.3333333333333333 (/ (sqrt x) y))
   (- 1.0 (* 0.1111111111111111 (/ 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e+85) || !(y <= 7.5e+87)) {
		tmp = -0.3333333333333333 / (sqrt(x) / y);
	} else {
		tmp = 1.0 - (0.1111111111111111 * (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 <= (-4.5d+85)) .or. (.not. (y <= 7.5d+87))) then
        tmp = (-0.3333333333333333d0) / (sqrt(x) / y)
    else
        tmp = 1.0d0 - (0.1111111111111111d0 * (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e+85) || !(y <= 7.5e+87)) {
		tmp = -0.3333333333333333 / (Math.sqrt(x) / y);
	} else {
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5e+85) or not (y <= 7.5e+87):
		tmp = -0.3333333333333333 / (math.sqrt(x) / y)
	else:
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5e+85) || !(y <= 7.5e+87))
		tmp = Float64(-0.3333333333333333 / Float64(sqrt(x) / y));
	else
		tmp = Float64(1.0 - Float64(0.1111111111111111 * Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.5e+85) || ~((y <= 7.5e+87)))
		tmp = -0.3333333333333333 / (sqrt(x) / y);
	else
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5e+85], N[Not[LessEqual[y, 7.5e+87]], $MachinePrecision]], N[(-0.3333333333333333 / N[(N[Sqrt[x], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+85} \lor \neg \left(y \leq 1.25 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{y}{\sqrt{x} \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;1 - 0.1111111111111111 \cdot \frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9e+85) (not (<= y 1.25e+86)))
   (/ y (* (sqrt x) -3.0))
   (- 1.0 (* 0.1111111111111111 (/ 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9e+85) || !(y <= 1.25e+86)) {
		tmp = y / (sqrt(x) * -3.0);
	} else {
		tmp = 1.0 - (0.1111111111111111 * (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 <= (-9d+85)) .or. (.not. (y <= 1.25d+86))) then
        tmp = y / (sqrt(x) * (-3.0d0))
    else
        tmp = 1.0d0 - (0.1111111111111111d0 * (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -9e+85) || !(y <= 1.25e+86)) {
		tmp = y / (Math.sqrt(x) * -3.0);
	} else {
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9e+85) or not (y <= 1.25e+86):
		tmp = y / (math.sqrt(x) * -3.0)
	else:
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9e+85) || !(y <= 1.25e+86))
		tmp = Float64(y / Float64(sqrt(x) * -3.0));
	else
		tmp = Float64(1.0 - Float64(0.1111111111111111 * Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -9e+85) || ~((y <= 1.25e+86)))
		tmp = y / (sqrt(x) * -3.0);
	else
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9e+85], N[Not[LessEqual[y, 1.25e+86]], $MachinePrecision]], N[(y / N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{y}{-3}}{\sqrt{x}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+84}:\\ \;\;\;\;1 - 0.1111111111111111 \cdot \frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\sqrt{x} \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+85)
   (/ (/ y -3.0) (sqrt x))
   (if (<= y 9e+84)
     (- 1.0 (* 0.1111111111111111 (/ 1.0 x)))
     (/ y (* (sqrt x) -3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+85) {
		tmp = (y / -3.0) / sqrt(x);
	} else if (y <= 9e+84) {
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	} else {
		tmp = y / (sqrt(x) * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.2d+85)) then
        tmp = (y / (-3.0d0)) / sqrt(x)
    else if (y <= 9d+84) then
        tmp = 1.0d0 - (0.1111111111111111d0 * (1.0d0 / x))
    else
        tmp = y / (sqrt(x) * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+85) {
		tmp = (y / -3.0) / Math.sqrt(x);
	} else if (y <= 9e+84) {
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	} else {
		tmp = y / (Math.sqrt(x) * -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+85:
		tmp = (y / -3.0) / math.sqrt(x)
	elif y <= 9e+84:
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x))
	else:
		tmp = y / (math.sqrt(x) * -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+85)
		tmp = Float64(Float64(y / -3.0) / sqrt(x));
	elseif (y <= 9e+84)
		tmp = Float64(1.0 - Float64(0.1111111111111111 * Float64(1.0 / x)));
	else
		tmp = Float64(y / Float64(sqrt(x) * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.2e+85)
		tmp = (y / -3.0) / sqrt(x);
	elseif (y <= 9e+84)
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	else
		tmp = y / (sqrt(x) * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+85], N[(N[(y / -3.0), $MachinePrecision] / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+84], N[(1.0 - N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{y}{-3}}{\sqrt{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+84}:\\ \;\;\;\;1 - 0.1111111111111111 \cdot \frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\sqrt{x}}}{-3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.5e+85)
   (/ (/ y -3.0) (sqrt x))
   (if (<= y 6e+84)
     (- 1.0 (* 0.1111111111111111 (/ 1.0 x)))
     (/ (/ y (sqrt x)) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.5e+85) {
		tmp = (y / -3.0) / sqrt(x);
	} else if (y <= 6e+84) {
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	} else {
		tmp = (y / sqrt(x)) / -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.5d+85)) then
        tmp = (y / (-3.0d0)) / sqrt(x)
    else if (y <= 6d+84) then
        tmp = 1.0d0 - (0.1111111111111111d0 * (1.0d0 / x))
    else
        tmp = (y / sqrt(x)) / (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.5e+85) {
		tmp = (y / -3.0) / Math.sqrt(x);
	} else if (y <= 6e+84) {
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	} else {
		tmp = (y / Math.sqrt(x)) / -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.5e+85:
		tmp = (y / -3.0) / math.sqrt(x)
	elif y <= 6e+84:
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x))
	else:
		tmp = (y / math.sqrt(x)) / -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.5e+85)
		tmp = Float64(Float64(y / -3.0) / sqrt(x));
	elseif (y <= 6e+84)
		tmp = Float64(1.0 - Float64(0.1111111111111111 * Float64(1.0 / x)));
	else
		tmp = Float64(Float64(y / sqrt(x)) / -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.5e+85)
		tmp = (y / -3.0) / sqrt(x);
	elseif (y <= 6e+84)
		tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
	else
		tmp = (y / sqrt(x)) / -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.5e+85], N[(N[(y / -3.0), $MachinePrecision] / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+84], N[(1.0 - N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] / -3.0), $MachinePrecision]]]

Derivation

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

Alternative 9: 62.9% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ 1 - 0.1111111111111111 \cdot \frac{1}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (* 0.1111111111111111 (/ 1.0 x))))

C

double code(double x, double y) {
	return 1.0 - (0.1111111111111111 * (1.0 / x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - (0.1111111111111111d0 * (1.0d0 / x))
end function

Java

public static double code(double x, double y) {
	return 1.0 - (0.1111111111111111 * (1.0 / x));
}

Python

def code(x, y):
	return 1.0 - (0.1111111111111111 * (1.0 / x))

Julia

function code(x, y)
	return Float64(1.0 - Float64(0.1111111111111111 * Float64(1.0 / x)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - (0.1111111111111111 * (1.0 / x));
end

Wolfram

code[x_, y_] := N[(1.0 - N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 10: 61.9% accurate, 22.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\frac{-0.1111111111111111}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.11) (/ -0.1111111111111111 x) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = -0.1111111111111111 / x;
	} else {
		tmp = 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 (x <= 0.11d0) then
        tmp = (-0.1111111111111111d0) / x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = -0.1111111111111111 / x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.11:
		tmp = -0.1111111111111111 / x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.11)
		tmp = Float64(-0.1111111111111111 / x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.11)
		tmp = -0.1111111111111111 / x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.11], N[(-0.1111111111111111 / x), $MachinePrecision], 1.0]

Derivation

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

Alternative 11: 62.9% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ 1 + \frac{-0.1111111111111111}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ 1.0 (/ -0.1111111111111111 x)))

C

double code(double x, double y) {
	return 1.0 + (-0.1111111111111111 / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 + ((-0.1111111111111111d0) / x)
end function

Java

public static double code(double x, double y) {
	return 1.0 + (-0.1111111111111111 / x);
}

Python

def code(x, y):
	return 1.0 + (-0.1111111111111111 / x)

Julia

function code(x, y)
	return Float64(1.0 + Float64(-0.1111111111111111 / x))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 + (-0.1111111111111111 / x);
end

Wolfram

code[x_, y_] := N[(1.0 + N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 12: 31.7% accurate, 113.0× 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: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - \frac{\frac{1}{x}}{9}\right) - \frac{y}{3 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x)))))

C

double code(double x, double y) {
	return (1.0 - ((1.0 / x) / 9.0)) - (y / (3.0 * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - ((1.0d0 / x) / 9.0d0)) - (y / (3.0d0 * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return (1.0 - ((1.0 / x) / 9.0)) - (y / (3.0 * Math.sqrt(x)));
}

Python

def code(x, y):
	return (1.0 - ((1.0 / x) / 9.0)) - (y / (3.0 * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(Float64(1.0 - Float64(Float64(1.0 / x) / 9.0)) - Float64(y / Float64(3.0 * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - ((1.0 / x) / 9.0)) - (y / (3.0 * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - N[(N[(1.0 / x), $MachinePrecision] / 9.0), $MachinePrecision]), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (- (- 1.0 (/ (/ 1.0 x) 9.0)) (/ y (* 3.0 (sqrt x))))

  (- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x)))))