Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B

Percentage Accurate: 99.4% → 99.4%

Time: 10.2s

Alternatives: 15

Speedup: 0.4×

Specification

Math

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

FPCore

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

C

double code(double x, double y) {
	return (3.0 * sqrt(x)) * ((y + (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 = (3.0d0 * sqrt(x)) * ((y + (1.0d0 / (x * 9.0d0))) - 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	return (3.0 * sqrt(x)) * ((y + (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 = (3.0d0 * sqrt(x)) * ((y + (1.0d0 / (x * 9.0d0))) - 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \sqrt{x} \cdot \mathsf{fma}\left(3, y, -3 + {\left(x \cdot 3\right)}^{-1}\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (sqrt x) (fma 3.0 y (+ -3.0 (pow (* x 3.0) -1.0)))))

C

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

Julia

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right) + \sqrt{x} \cdot \left(3 \cdot y\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x))) (* (sqrt x) (* 3.0 y))))

C

double code(double x, double y) {
	return (sqrt(x) * (-3.0 + (0.3333333333333333 / x))) + (sqrt(x) * (3.0 * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))) + (sqrt(x) * (3.0d0 * y))
end function

Java

public static double code(double x, double y) {
	return (Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))) + (Math.sqrt(x) * (3.0 * y));
}

Python

def code(x, y):
	return (math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))) + (math.sqrt(x) * (3.0 * y))

Julia

function code(x, y)
	return Float64(Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x))) + Float64(sqrt(x) * Float64(3.0 * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (sqrt(x) * (-3.0 + (0.3333333333333333 / x))) + (sqrt(x) * (3.0 * y));
end

Wolfram

code[x_, y_] := N[(N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 3: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \sqrt{x} \cdot \mathsf{fma}\left(3, y, -3 + \frac{0.3333333333333333}{x}\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (sqrt x) (fma 3.0 y (+ -3.0 (/ 0.3333333333333333 x)))))

C

double code(double x, double y) {
	return sqrt(x) * fma(3.0, y, (-3.0 + (0.3333333333333333 / x)));
}

Julia

function code(x, y)
	return Float64(sqrt(x) * fma(3.0, y, Float64(-3.0 + Float64(0.3333333333333333 / x))))
end

Wolfram

code[x_, y_] := N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y + N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 4: 60.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{if}\;x \leq 4 \cdot 10^{-105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.2:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+81} \lor \neg \left(x \leq 2.8 \cdot 10^{+217}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 0.3333333333333333 (sqrt (/ 1.0 x)))))
   (if (<= x 4e-105)
     t_0
     (if (<= x 1.55e-93)
       (* y (* (sqrt x) 3.0))
       (if (<= x 1.15e-34)
         t_0
         (if (<= x 2.2)
           (* 3.0 (* (sqrt x) y))
           (if (or (<= x 3.9e+81) (not (<= x 2.8e+217)))
             (* (sqrt x) -3.0)
             (* (sqrt x) (* 3.0 y)))))))))

C

double code(double x, double y) {
	double t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	double tmp;
	if (x <= 4e-105) {
		tmp = t_0;
	} else if (x <= 1.55e-93) {
		tmp = y * (sqrt(x) * 3.0);
	} else if (x <= 1.15e-34) {
		tmp = t_0;
	} else if (x <= 2.2) {
		tmp = 3.0 * (sqrt(x) * y);
	} else if ((x <= 3.9e+81) || !(x <= 2.8e+217)) {
		tmp = sqrt(x) * -3.0;
	} else {
		tmp = sqrt(x) * (3.0 * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    if (x <= 4d-105) then
        tmp = t_0
    else if (x <= 1.55d-93) then
        tmp = y * (sqrt(x) * 3.0d0)
    else if (x <= 1.15d-34) then
        tmp = t_0
    else if (x <= 2.2d0) then
        tmp = 3.0d0 * (sqrt(x) * y)
    else if ((x <= 3.9d+81) .or. (.not. (x <= 2.8d+217))) then
        tmp = sqrt(x) * (-3.0d0)
    else
        tmp = sqrt(x) * (3.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.3333333333333333 * Math.sqrt((1.0 / x));
	double tmp;
	if (x <= 4e-105) {
		tmp = t_0;
	} else if (x <= 1.55e-93) {
		tmp = y * (Math.sqrt(x) * 3.0);
	} else if (x <= 1.15e-34) {
		tmp = t_0;
	} else if (x <= 2.2) {
		tmp = 3.0 * (Math.sqrt(x) * y);
	} else if ((x <= 3.9e+81) || !(x <= 2.8e+217)) {
		tmp = Math.sqrt(x) * -3.0;
	} else {
		tmp = Math.sqrt(x) * (3.0 * y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.3333333333333333 * math.sqrt((1.0 / x))
	tmp = 0
	if x <= 4e-105:
		tmp = t_0
	elif x <= 1.55e-93:
		tmp = y * (math.sqrt(x) * 3.0)
	elif x <= 1.15e-34:
		tmp = t_0
	elif x <= 2.2:
		tmp = 3.0 * (math.sqrt(x) * y)
	elif (x <= 3.9e+81) or not (x <= 2.8e+217):
		tmp = math.sqrt(x) * -3.0
	else:
		tmp = math.sqrt(x) * (3.0 * y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)))
	tmp = 0.0
	if (x <= 4e-105)
		tmp = t_0;
	elseif (x <= 1.55e-93)
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	elseif (x <= 1.15e-34)
		tmp = t_0;
	elseif (x <= 2.2)
		tmp = Float64(3.0 * Float64(sqrt(x) * y));
	elseif ((x <= 3.9e+81) || !(x <= 2.8e+217))
		tmp = Float64(sqrt(x) * -3.0);
	else
		tmp = Float64(sqrt(x) * Float64(3.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	tmp = 0.0;
	if (x <= 4e-105)
		tmp = t_0;
	elseif (x <= 1.55e-93)
		tmp = y * (sqrt(x) * 3.0);
	elseif (x <= 1.15e-34)
		tmp = t_0;
	elseif (x <= 2.2)
		tmp = 3.0 * (sqrt(x) * y);
	elseif ((x <= 3.9e+81) || ~((x <= 2.8e+217)))
		tmp = sqrt(x) * -3.0;
	else
		tmp = sqrt(x) * (3.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4e-105], t$95$0, If[LessEqual[x, 1.55e-93], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-34], t$95$0, If[LessEqual[x, 2.2], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.9e+81], N[Not[LessEqual[x, 2.8e+217]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{if}\;x \leq 3.9 \cdot 10^{-103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-34}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 0.3333333333333333 (sqrt (/ 1.0 x)))))
   (if (<= x 3.9e-103)
     t_0
     (if (<= x 1.55e-93)
       (* y (* (sqrt x) 3.0))
       (if (<= x 1.22e-34) t_0 (* 3.0 (* (sqrt x) (+ y -1.0))))))))

C

double code(double x, double y) {
	double t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	double tmp;
	if (x <= 3.9e-103) {
		tmp = t_0;
	} else if (x <= 1.55e-93) {
		tmp = y * (sqrt(x) * 3.0);
	} else if (x <= 1.22e-34) {
		tmp = t_0;
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	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 = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    if (x <= 3.9d-103) then
        tmp = t_0
    else if (x <= 1.55d-93) then
        tmp = y * (sqrt(x) * 3.0d0)
    else if (x <= 1.22d-34) then
        tmp = t_0
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.3333333333333333 * Math.sqrt((1.0 / x));
	double tmp;
	if (x <= 3.9e-103) {
		tmp = t_0;
	} else if (x <= 1.55e-93) {
		tmp = y * (Math.sqrt(x) * 3.0);
	} else if (x <= 1.22e-34) {
		tmp = t_0;
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.3333333333333333 * math.sqrt((1.0 / x))
	tmp = 0
	if x <= 3.9e-103:
		tmp = t_0
	elif x <= 1.55e-93:
		tmp = y * (math.sqrt(x) * 3.0)
	elif x <= 1.22e-34:
		tmp = t_0
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)))
	tmp = 0.0
	if (x <= 3.9e-103)
		tmp = t_0;
	elseif (x <= 1.55e-93)
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	elseif (x <= 1.22e-34)
		tmp = t_0;
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	tmp = 0.0;
	if (x <= 3.9e-103)
		tmp = t_0;
	elseif (x <= 1.55e-93)
		tmp = y * (sqrt(x) * 3.0);
	elseif (x <= 1.22e-34)
		tmp = t_0;
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 3.9e-103], t$95$0, If[LessEqual[x, 1.55e-93], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.22e-34], t$95$0, N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 6: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + \frac{0.1111111111111111}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = 3.0 * (sqrt(x) * (y + (0.1111111111111111 / x)));
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -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 = 3.0d0 * (sqrt(x) * (y + (0.1111111111111111d0 / x)))
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = 3.0 * (Math.sqrt(x) * (y + (0.1111111111111111 / x)));
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.11:
		tmp = 3.0 * (math.sqrt(x) * (y + (0.1111111111111111 / x)))
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.11)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + Float64(0.1111111111111111 / x))));
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.11)
		tmp = 3.0 * (sqrt(x) * (y + (0.1111111111111111 / x)));
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.11], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.2:\\ \;\;\;\;\left(y + \frac{0.1111111111111111}{x}\right) \cdot \sqrt{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.2)
   (* (+ y (/ 0.1111111111111111 x)) (sqrt (* x 9.0)))
   (* 3.0 (* (sqrt x) (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.2) {
		tmp = (y + (0.1111111111111111 / x)) * sqrt((x * 9.0));
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -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 <= 1.2d0) then
        tmp = (y + (0.1111111111111111d0 / x)) * sqrt((x * 9.0d0))
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.2) {
		tmp = (y + (0.1111111111111111 / x)) * Math.sqrt((x * 9.0));
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.2:
		tmp = (y + (0.1111111111111111 / x)) * math.sqrt((x * 9.0))
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.2)
		tmp = Float64(Float64(y + Float64(0.1111111111111111 / x)) * sqrt(Float64(x * 9.0)));
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.2)
		tmp = (y + (0.1111111111111111 / x)) * sqrt((x * 9.0));
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.2], N[(N[(y + N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 9: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 10: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 11: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -10000 \lor \neg \left(y \leq 3.5 \cdot 10^{-26}\right):\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -10000.0) (not (<= y 3.5e-26)))
   (* 3.0 (* (sqrt x) y))
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -10000.0) || !(y <= 3.5e-26)) {
		tmp = 3.0 * (sqrt(x) * y);
	} else {
		tmp = 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 <= (-10000.0d0)) .or. (.not. (y <= 3.5d-26))) then
        tmp = 3.0d0 * (sqrt(x) * y)
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -10000.0) || !(y <= 3.5e-26)) {
		tmp = 3.0 * (Math.sqrt(x) * y);
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -10000.0) or not (y <= 3.5e-26):
		tmp = 3.0 * (math.sqrt(x) * y)
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -10000.0) || !(y <= 3.5e-26))
		tmp = Float64(3.0 * Float64(sqrt(x) * y));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -10000.0) || ~((y <= 3.5e-26)))
		tmp = 3.0 * (sqrt(x) * y);
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -10000.0], N[Not[LessEqual[y, 3.5e-26]], $MachinePrecision]], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

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

Alternative 12: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -10000 \lor \neg \left(y \leq 3.5 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -10000.0) (not (<= y 3.5e-26)))
   (* y (* (sqrt x) 3.0))
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -10000.0) || !(y <= 3.5e-26)) {
		tmp = y * (sqrt(x) * 3.0);
	} else {
		tmp = 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 <= (-10000.0d0)) .or. (.not. (y <= 3.5d-26))) then
        tmp = y * (sqrt(x) * 3.0d0)
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -10000.0) || !(y <= 3.5e-26)) {
		tmp = y * (Math.sqrt(x) * 3.0);
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -10000.0) or not (y <= 3.5e-26):
		tmp = y * (math.sqrt(x) * 3.0)
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -10000.0) || !(y <= 3.5e-26))
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -10000.0) || ~((y <= 3.5e-26)))
		tmp = y * (sqrt(x) * 3.0);
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -10000.0], N[Not[LessEqual[y, 3.5e-26]], $MachinePrecision]], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

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

Alternative 13: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -10000:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-26}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -10000.0)
   (* y (* (sqrt x) 3.0))
   (if (<= y 3.5e-26) (* (sqrt x) -3.0) (* (sqrt x) (* 3.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -10000.0) {
		tmp = y * (sqrt(x) * 3.0);
	} else if (y <= 3.5e-26) {
		tmp = sqrt(x) * -3.0;
	} else {
		tmp = sqrt(x) * (3.0 * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-10000.0d0)) then
        tmp = y * (sqrt(x) * 3.0d0)
    else if (y <= 3.5d-26) then
        tmp = sqrt(x) * (-3.0d0)
    else
        tmp = sqrt(x) * (3.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -10000.0) {
		tmp = y * (Math.sqrt(x) * 3.0);
	} else if (y <= 3.5e-26) {
		tmp = Math.sqrt(x) * -3.0;
	} else {
		tmp = Math.sqrt(x) * (3.0 * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -10000.0:
		tmp = y * (math.sqrt(x) * 3.0)
	elif y <= 3.5e-26:
		tmp = math.sqrt(x) * -3.0
	else:
		tmp = math.sqrt(x) * (3.0 * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -10000.0)
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	elseif (y <= 3.5e-26)
		tmp = Float64(sqrt(x) * -3.0);
	else
		tmp = Float64(sqrt(x) * Float64(3.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -10000.0)
		tmp = y * (sqrt(x) * 3.0);
	elseif (y <= 3.5e-26)
		tmp = sqrt(x) * -3.0;
	else
		tmp = sqrt(x) * (3.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -10000.0], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-26], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 14: 3.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{x \cdot 9} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt (* x 9.0)))

C

double code(double x, double y) {
	return sqrt((x * 9.0));
}

Fortran

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

Java

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

Python

def code(x, y):
	return math.sqrt((x * 9.0))

Julia

function code(x, y)
	return sqrt(Float64(x * 9.0))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt((x * 9.0));
end

Wolfram

code[x_, y_] := N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]

Derivation

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

Alternative 15: 26.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{x} \cdot -3 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024008 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

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

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