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

Percentage Accurate: 99.7% → 99.7%

Time: 14.1s

Alternatives: 14

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

1. Initial program 99.8%

   \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+23}:\\ \;\;\;\;1 - \frac{y}{3 \cdot \sqrt{x}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{-1}{x \cdot 9} + 1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y}{\sqrt{x}}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.45e+23)
   (- 1.0 (/ y (* 3.0 (sqrt x))))
   (if (<= y 1.5e+60)
     (+ (/ -1.0 (* x 9.0)) 1.0)
     (- 1.0 (/ (/ y (sqrt x)) 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.45e+23) {
		tmp = 1.0 - (y / (3.0 * sqrt(x)));
	} else if (y <= 1.5e+60) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = 1.0 - ((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 <= (-1.45d+23)) then
        tmp = 1.0d0 - (y / (3.0d0 * sqrt(x)))
    else if (y <= 1.5d+60) then
        tmp = ((-1.0d0) / (x * 9.0d0)) + 1.0d0
    else
        tmp = 1.0d0 - ((y / sqrt(x)) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.45e+23) {
		tmp = 1.0 - (y / (3.0 * Math.sqrt(x)));
	} else if (y <= 1.5e+60) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = 1.0 - ((y / Math.sqrt(x)) / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.45e+23:
		tmp = 1.0 - (y / (3.0 * math.sqrt(x)))
	elif y <= 1.5e+60:
		tmp = (-1.0 / (x * 9.0)) + 1.0
	else:
		tmp = 1.0 - ((y / math.sqrt(x)) / 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.45e+23)
		tmp = Float64(1.0 - Float64(y / Float64(3.0 * sqrt(x))));
	elseif (y <= 1.5e+60)
		tmp = Float64(Float64(-1.0 / Float64(x * 9.0)) + 1.0);
	else
		tmp = Float64(1.0 - Float64(Float64(y / sqrt(x)) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.45e+23)
		tmp = 1.0 - (y / (3.0 * sqrt(x)));
	elseif (y <= 1.5e+60)
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	else
		tmp = 1.0 - ((y / sqrt(x)) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.45e+23], N[(1.0 - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+60], N[(N[(-1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 - N[(N[(y / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45000000000000006e23

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.45000000000000006e23 < y < 1.4999999999999999e60

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.4999999999999999e60 < y

   1. Initial program 99.7%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{y}{3 \cdot \sqrt{x}}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+23}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+60}:\\ \;\;\;\;\frac{-1}{x \cdot 9} + 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ y (* 3.0 (sqrt x))))))
   (if (<= y -1.35e+23)
     t_0
     (if (<= y 3.8e+60) (+ (/ -1.0 (* x 9.0)) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (y / (3.0 * sqrt(x)));
	double tmp;
	if (y <= -1.35e+23) {
		tmp = t_0;
	} else if (y <= 3.8e+60) {
		tmp = (-1.0 / (x * 9.0)) + 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 / (3.0d0 * sqrt(x)))
    if (y <= (-1.35d+23)) then
        tmp = t_0
    else if (y <= 3.8d+60) then
        tmp = ((-1.0d0) / (x * 9.0d0)) + 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 / (3.0 * Math.sqrt(x)));
	double tmp;
	if (y <= -1.35e+23) {
		tmp = t_0;
	} else if (y <= 3.8e+60) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (y / (3.0 * math.sqrt(x)))
	tmp = 0
	if y <= -1.35e+23:
		tmp = t_0
	elif y <= 3.8e+60:
		tmp = (-1.0 / (x * 9.0)) + 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(y / Float64(3.0 * sqrt(x))))
	tmp = 0.0
	if (y <= -1.35e+23)
		tmp = t_0;
	elseif (y <= 3.8e+60)
		tmp = Float64(Float64(-1.0 / Float64(x * 9.0)) + 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (y / (3.0 * sqrt(x)));
	tmp = 0.0;
	if (y <= -1.35e+23)
		tmp = t_0;
	elseif (y <= 3.8e+60)
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+23], t$95$0, If[LessEqual[y, 3.8e+60], N[(N[(-1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3499999999999999e23 or 3.80000000000000009e60 < y

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.3499999999999999e23 < y < 3.80000000000000009e60

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+23}:\\ \;\;\;\;1 + \frac{y \cdot -0.3333333333333333}{\sqrt{x}}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+60}:\\ \;\;\;\;\frac{-1}{x \cdot 9} + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{y}{-3}}{\sqrt{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.45e+23)
   (+ 1.0 (/ (* y -0.3333333333333333) (sqrt x)))
   (if (<= y 1.52e+60)
     (+ (/ -1.0 (* x 9.0)) 1.0)
     (+ 1.0 (/ (/ y -3.0) (sqrt x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.45e+23) {
		tmp = 1.0 + ((y * -0.3333333333333333) / sqrt(x));
	} else if (y <= 1.52e+60) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = 1.0 + ((y / -3.0) / sqrt(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 <= (-1.45d+23)) then
        tmp = 1.0d0 + ((y * (-0.3333333333333333d0)) / sqrt(x))
    else if (y <= 1.52d+60) then
        tmp = ((-1.0d0) / (x * 9.0d0)) + 1.0d0
    else
        tmp = 1.0d0 + ((y / (-3.0d0)) / sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.45e+23) {
		tmp = 1.0 + ((y * -0.3333333333333333) / Math.sqrt(x));
	} else if (y <= 1.52e+60) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = 1.0 + ((y / -3.0) / Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.45e+23:
		tmp = 1.0 + ((y * -0.3333333333333333) / math.sqrt(x))
	elif y <= 1.52e+60:
		tmp = (-1.0 / (x * 9.0)) + 1.0
	else:
		tmp = 1.0 + ((y / -3.0) / math.sqrt(x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.45e+23)
		tmp = Float64(1.0 + Float64(Float64(y * -0.3333333333333333) / sqrt(x)));
	elseif (y <= 1.52e+60)
		tmp = Float64(Float64(-1.0 / Float64(x * 9.0)) + 1.0);
	else
		tmp = Float64(1.0 + Float64(Float64(y / -3.0) / sqrt(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.45e+23)
		tmp = 1.0 + ((y * -0.3333333333333333) / sqrt(x));
	elseif (y <= 1.52e+60)
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	else
		tmp = 1.0 + ((y / -3.0) / sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.45e+23], N[(1.0 + N[(N[(y * -0.3333333333333333), $MachinePrecision] / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e+60], N[(N[(-1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(1.0 + N[(N[(y / -3.0), $MachinePrecision] / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45000000000000006e23

   1. Initial program 99.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -1.45000000000000006e23 < y < 1.52e60

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.52e60 < y

   1. Initial program 99.7%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{y \cdot -0.3333333333333333}{\sqrt{x}}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+60}:\\ \;\;\;\;\frac{-1}{x \cdot 9} + 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* y -0.3333333333333333) (sqrt x)))))
   (if (<= y -6.6e+22)
     t_0
     (if (<= y 1.15e+60) (+ (/ -1.0 (* x 9.0)) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((y * -0.3333333333333333) / sqrt(x));
	double tmp;
	if (y <= -6.6e+22) {
		tmp = t_0;
	} else if (y <= 1.15e+60) {
		tmp = (-1.0 / (x * 9.0)) + 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 * (-0.3333333333333333d0)) / sqrt(x))
    if (y <= (-6.6d+22)) then
        tmp = t_0
    else if (y <= 1.15d+60) then
        tmp = ((-1.0d0) / (x * 9.0d0)) + 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 * -0.3333333333333333) / Math.sqrt(x));
	double tmp;
	if (y <= -6.6e+22) {
		tmp = t_0;
	} else if (y <= 1.15e+60) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((y * -0.3333333333333333) / math.sqrt(x))
	tmp = 0
	if y <= -6.6e+22:
		tmp = t_0
	elif y <= 1.15e+60:
		tmp = (-1.0 / (x * 9.0)) + 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(y * -0.3333333333333333) / sqrt(x)))
	tmp = 0.0
	if (y <= -6.6e+22)
		tmp = t_0;
	elseif (y <= 1.15e+60)
		tmp = Float64(Float64(-1.0 / Float64(x * 9.0)) + 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((y * -0.3333333333333333) / sqrt(x));
	tmp = 0.0;
	if (y <= -6.6e+22)
		tmp = t_0;
	elseif (y <= 1.15e+60)
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(y * -0.3333333333333333), $MachinePrecision] / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+22], t$95$0, If[LessEqual[y, 1.15e+60], N[(N[(-1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999996e22 or 1.15000000000000008e60 < y

   1. Initial program 99.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -6.5999999999999996e22 < y < 1.15000000000000008e60

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\frac{1}{x}} \cdot \left(-0.3333333333333333 \cdot y\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+49}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{-1}{x \cdot 9} + 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt (/ 1.0 x)) (* -0.3333333333333333 y))))
   (if (<= y -6.2e+49)
     t_0
     (if (<= y 4.2e+98) (+ (/ -1.0 (* x 9.0)) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = sqrt((1.0 / x)) * (-0.3333333333333333 * y);
	double tmp;
	if (y <= -6.2e+49) {
		tmp = t_0;
	} else if (y <= 4.2e+98) {
		tmp = (-1.0 / (x * 9.0)) + 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 = sqrt((1.0d0 / x)) * ((-0.3333333333333333d0) * y)
    if (y <= (-6.2d+49)) then
        tmp = t_0
    else if (y <= 4.2d+98) then
        tmp = ((-1.0d0) / (x * 9.0d0)) + 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt((1.0 / x)) * (-0.3333333333333333 * y);
	double tmp;
	if (y <= -6.2e+49) {
		tmp = t_0;
	} else if (y <= 4.2e+98) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt((1.0 / x)) * (-0.3333333333333333 * y)
	tmp = 0
	if y <= -6.2e+49:
		tmp = t_0
	elif y <= 4.2e+98:
		tmp = (-1.0 / (x * 9.0)) + 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(Float64(1.0 / x)) * Float64(-0.3333333333333333 * y))
	tmp = 0.0
	if (y <= -6.2e+49)
		tmp = t_0;
	elseif (y <= 4.2e+98)
		tmp = Float64(Float64(-1.0 / Float64(x * 9.0)) + 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt((1.0 / x)) * (-0.3333333333333333 * y);
	tmp = 0.0;
	if (y <= -6.2e+49)
		tmp = t_0;
	elseif (y <= 4.2e+98)
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision] * N[(-0.3333333333333333 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+49], t$95$0, If[LessEqual[y, 4.2e+98], N[(N[(-1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999985e49 or 4.20000000000000008e98 < y

   1. Initial program 99.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -6.19999999999999985e49 < y < 4.20000000000000008e98

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.4:\\ \;\;\;\;\frac{-0.1111111111111111}{x} - \frac{y}{3 \cdot \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y}{\sqrt{x}}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6.4)
   (- (/ -0.1111111111111111 x) (/ y (* 3.0 (sqrt x))))
   (- 1.0 (/ (/ y (sqrt x)) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6.4) {
		tmp = (-0.1111111111111111 / x) - (y / (3.0 * sqrt(x)));
	} else {
		tmp = 1.0 - ((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 (x <= 6.4d0) then
        tmp = ((-0.1111111111111111d0) / x) - (y / (3.0d0 * sqrt(x)))
    else
        tmp = 1.0d0 - ((y / sqrt(x)) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6.4) {
		tmp = (-0.1111111111111111 / x) - (y / (3.0 * Math.sqrt(x)));
	} else {
		tmp = 1.0 - ((y / Math.sqrt(x)) / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6.4:
		tmp = (-0.1111111111111111 / x) - (y / (3.0 * math.sqrt(x)))
	else:
		tmp = 1.0 - ((y / math.sqrt(x)) / 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6.4)
		tmp = Float64(Float64(-0.1111111111111111 / x) - Float64(y / Float64(3.0 * sqrt(x))));
	else
		tmp = Float64(1.0 - Float64(Float64(y / sqrt(x)) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6.4)
		tmp = (-0.1111111111111111 / x) - (y / (3.0 * sqrt(x)));
	else
		tmp = 1.0 - ((y / sqrt(x)) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6.4], N[(N[(-0.1111111111111111 / x), $MachinePrecision] - N[(y / N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.4000000000000004

   1. Initial program 99.6%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 6.4000000000000004 < x

   1. Initial program 99.9%

      \[\left(1 - \frac{1}{x \cdot 9}\right) - \frac{y}{3 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Alternative 9: 65.1% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.56 \cdot 10^{+135}:\\ \;\;\;\;\frac{-1}{x \cdot 9} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{-0.0013717421124828531}{x}}{x \cdot x}}{\frac{0.012345679012345678}{x}} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.56e+135)
   (+ (/ -1.0 (* x 9.0)) 1.0)
   (*
    (/ (/ (/ -0.0013717421124828531 x) (* x x)) (/ 0.012345679012345678 x))
    x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.56e+135) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = (((-0.0013717421124828531 / x) / (x * x)) / (0.012345679012345678 / x)) * 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 <= 1.56d+135) then
        tmp = ((-1.0d0) / (x * 9.0d0)) + 1.0d0
    else
        tmp = ((((-0.0013717421124828531d0) / x) / (x * x)) / (0.012345679012345678d0 / x)) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.56e+135) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = (((-0.0013717421124828531 / x) / (x * x)) / (0.012345679012345678 / x)) * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.56e+135:
		tmp = (-1.0 / (x * 9.0)) + 1.0
	else:
		tmp = (((-0.0013717421124828531 / x) / (x * x)) / (0.012345679012345678 / x)) * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.56e+135)
		tmp = Float64(Float64(-1.0 / Float64(x * 9.0)) + 1.0);
	else
		tmp = Float64(Float64(Float64(Float64(-0.0013717421124828531 / x) / Float64(x * x)) / Float64(0.012345679012345678 / x)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.56e+135)
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	else
		tmp = (((-0.0013717421124828531 / x) / (x * x)) / (0.012345679012345678 / x)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.56e+135], N[(N[(-1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(N[(N[(-0.0013717421124828531 / x), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision] / N[(0.012345679012345678 / x), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.55999999999999993e135

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.55999999999999993e135 < y

   1. Initial program 99.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 64.7% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.06 \cdot 10^{+137}:\\ \;\;\;\;\frac{-1}{x \cdot 9} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{0.012345679012345678}{x}}{x}}{\frac{-0.1111111111111111}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.06e+137)
   (+ (/ -1.0 (* x 9.0)) 1.0)
   (/ (/ (/ 0.012345679012345678 x) x) (/ -0.1111111111111111 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.06e+137) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = ((0.012345679012345678 / x) / x) / (-0.1111111111111111 / 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 <= 1.06d+137) then
        tmp = ((-1.0d0) / (x * 9.0d0)) + 1.0d0
    else
        tmp = ((0.012345679012345678d0 / x) / x) / ((-0.1111111111111111d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.06e+137) {
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	} else {
		tmp = ((0.012345679012345678 / x) / x) / (-0.1111111111111111 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.06e+137:
		tmp = (-1.0 / (x * 9.0)) + 1.0
	else:
		tmp = ((0.012345679012345678 / x) / x) / (-0.1111111111111111 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.06e+137)
		tmp = Float64(Float64(-1.0 / Float64(x * 9.0)) + 1.0);
	else
		tmp = Float64(Float64(Float64(0.012345679012345678 / x) / x) / Float64(-0.1111111111111111 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.06e+137)
		tmp = (-1.0 / (x * 9.0)) + 1.0;
	else
		tmp = ((0.012345679012345678 / x) / x) / (-0.1111111111111111 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.06e+137], N[(N[(-1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(N[(N[(0.012345679012345678 / x), $MachinePrecision] / x), $MachinePrecision] / N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.06000000000000006e137

   1. Initial program 99.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.06000000000000006e137 < y

   1. Initial program 99.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 61.2% accurate, 14.1× 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

1. Split input into 2 regimes

2. if x < 0.110000000000000001

   1. Initial program 99.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 0.110000000000000001 < x

   1. Initial program 99.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 62.2% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \frac{-1}{x \cdot 9} + 1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return (-1.0 / (x * 9.0)) + 1.0;
}

Python

def code(x, y):
	return (-1.0 / (x * 9.0)) + 1.0

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in y around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

9. Applied egg-rr 0

   \[\leadsto expr\]
10. Add Preprocessing

Alternative 13: 62.2% accurate, 22.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in y around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Alternative 14: 31.5% 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

1. Initial program 99.8%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in y around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

8. Taylor expanded in x around inf 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]
11. 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 2024110 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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