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

Percentage Accurate: 99.4% → 99.4%

Time: 15.7s

Alternatives: 17

Speedup: 1.0×

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, 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]

Derivation

1. Initial program 99.4%

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

Alternative 2: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot \sqrt{x}\right) \cdot y\\ t_1 := \frac{1}{\frac{\sqrt{x}}{0.3333333333333333}}\\ \mathbf{if}\;y \leq -380:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-290}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* 3.0 (sqrt x)) y))
        (t_1 (/ 1.0 (/ (sqrt x) 0.3333333333333333))))
   (if (<= y -380.0)
     t_0
     (if (<= y -1.32e-226)
       t_1
       (if (<= y 3.1e-290) (* (sqrt x) -3.0) (if (<= y 9e+64) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = (3.0 * sqrt(x)) * y;
	double t_1 = 1.0 / (sqrt(x) / 0.3333333333333333);
	double tmp;
	if (y <= -380.0) {
		tmp = t_0;
	} else if (y <= -1.32e-226) {
		tmp = t_1;
	} else if (y <= 3.1e-290) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 9e+64) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (3.0d0 * sqrt(x)) * y
    t_1 = 1.0d0 / (sqrt(x) / 0.3333333333333333d0)
    if (y <= (-380.0d0)) then
        tmp = t_0
    else if (y <= (-1.32d-226)) then
        tmp = t_1
    else if (y <= 3.1d-290) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 9d+64) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (3.0 * Math.sqrt(x)) * y;
	double t_1 = 1.0 / (Math.sqrt(x) / 0.3333333333333333);
	double tmp;
	if (y <= -380.0) {
		tmp = t_0;
	} else if (y <= -1.32e-226) {
		tmp = t_1;
	} else if (y <= 3.1e-290) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 9e+64) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (3.0 * math.sqrt(x)) * y
	t_1 = 1.0 / (math.sqrt(x) / 0.3333333333333333)
	tmp = 0
	if y <= -380.0:
		tmp = t_0
	elif y <= -1.32e-226:
		tmp = t_1
	elif y <= 3.1e-290:
		tmp = math.sqrt(x) * -3.0
	elif y <= 9e+64:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(3.0 * sqrt(x)) * y)
	t_1 = Float64(1.0 / Float64(sqrt(x) / 0.3333333333333333))
	tmp = 0.0
	if (y <= -380.0)
		tmp = t_0;
	elseif (y <= -1.32e-226)
		tmp = t_1;
	elseif (y <= 3.1e-290)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 9e+64)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (3.0 * sqrt(x)) * y;
	t_1 = 1.0 / (sqrt(x) / 0.3333333333333333);
	tmp = 0.0;
	if (y <= -380.0)
		tmp = t_0;
	elseif (y <= -1.32e-226)
		tmp = t_1;
	elseif (y <= 3.1e-290)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 9e+64)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 / N[(N[Sqrt[x], $MachinePrecision] / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -380.0], t$95$0, If[LessEqual[y, -1.32e-226], t$95$1, If[LessEqual[y, 3.1e-290], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 9e+64], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -380 or 8.99999999999999946e64 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -380 < y < -1.32e-226 or 3.0999999999999999e-290 < y < 8.99999999999999946e64

   1. Initial program 99.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]

   if -1.32e-226 < y < 3.0999999999999999e-290

   1. Initial program 99.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around inf 0

       \[\leadsto expr\]

   12. Simplified 0

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

Alternative 3: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot \sqrt{x}\right) \cdot y\\ \mathbf{if}\;y \leq -340:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-227}:\\ \;\;\;\;\frac{0.3333333333333333}{\sqrt{x}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-290}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+66}:\\ \;\;\;\;{x}^{-0.5} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* 3.0 (sqrt x)) y)))
   (if (<= y -340.0)
     t_0
     (if (<= y -4.1e-227)
       (/ 0.3333333333333333 (sqrt x))
       (if (<= y 2.8e-290)
         (* (sqrt x) -3.0)
         (if (<= y 2.8e+66) (* (pow x -0.5) 0.3333333333333333) t_0))))))

C

double code(double x, double y) {
	double t_0 = (3.0 * sqrt(x)) * y;
	double tmp;
	if (y <= -340.0) {
		tmp = t_0;
	} else if (y <= -4.1e-227) {
		tmp = 0.3333333333333333 / sqrt(x);
	} else if (y <= 2.8e-290) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 2.8e+66) {
		tmp = pow(x, -0.5) * 0.3333333333333333;
	} 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 = (3.0d0 * sqrt(x)) * y
    if (y <= (-340.0d0)) then
        tmp = t_0
    else if (y <= (-4.1d-227)) then
        tmp = 0.3333333333333333d0 / sqrt(x)
    else if (y <= 2.8d-290) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 2.8d+66) then
        tmp = (x ** (-0.5d0)) * 0.3333333333333333d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (3.0 * Math.sqrt(x)) * y;
	double tmp;
	if (y <= -340.0) {
		tmp = t_0;
	} else if (y <= -4.1e-227) {
		tmp = 0.3333333333333333 / Math.sqrt(x);
	} else if (y <= 2.8e-290) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 2.8e+66) {
		tmp = Math.pow(x, -0.5) * 0.3333333333333333;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (3.0 * math.sqrt(x)) * y
	tmp = 0
	if y <= -340.0:
		tmp = t_0
	elif y <= -4.1e-227:
		tmp = 0.3333333333333333 / math.sqrt(x)
	elif y <= 2.8e-290:
		tmp = math.sqrt(x) * -3.0
	elif y <= 2.8e+66:
		tmp = math.pow(x, -0.5) * 0.3333333333333333
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(3.0 * sqrt(x)) * y)
	tmp = 0.0
	if (y <= -340.0)
		tmp = t_0;
	elseif (y <= -4.1e-227)
		tmp = Float64(0.3333333333333333 / sqrt(x));
	elseif (y <= 2.8e-290)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 2.8e+66)
		tmp = Float64((x ^ -0.5) * 0.3333333333333333);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (3.0 * sqrt(x)) * y;
	tmp = 0.0;
	if (y <= -340.0)
		tmp = t_0;
	elseif (y <= -4.1e-227)
		tmp = 0.3333333333333333 / sqrt(x);
	elseif (y <= 2.8e-290)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 2.8e+66)
		tmp = (x ^ -0.5) * 0.3333333333333333;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -340.0], t$95$0, If[LessEqual[y, -4.1e-227], N[(0.3333333333333333 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-290], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 2.8e+66], N[(N[Power[x, -0.5], $MachinePrecision] * 0.3333333333333333), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -340 or 2.8000000000000001e66 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -340 < y < -4.10000000000000009e-227

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -4.10000000000000009e-227 < y < 2.79999999999999997e-290

   1. Initial program 99.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around inf 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   if 2.79999999999999997e-290 < y < 2.8000000000000001e66

   1. Initial program 99.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

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

Alternative 4: 61.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{if}\;y \leq -380:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-225}:\\ \;\;\;\;\frac{0.3333333333333333}{\sqrt{x}}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-290}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+65}:\\ \;\;\;\;{x}^{-0.5} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 3.0 (* (sqrt x) y))))
   (if (<= y -380.0)
     t_0
     (if (<= y -4.3e-225)
       (/ 0.3333333333333333 (sqrt x))
       (if (<= y 2.35e-290)
         (* (sqrt x) -3.0)
         (if (<= y 3.9e+65) (* (pow x -0.5) 0.3333333333333333) t_0))))))

C

double code(double x, double y) {
	double t_0 = 3.0 * (sqrt(x) * y);
	double tmp;
	if (y <= -380.0) {
		tmp = t_0;
	} else if (y <= -4.3e-225) {
		tmp = 0.3333333333333333 / sqrt(x);
	} else if (y <= 2.35e-290) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 3.9e+65) {
		tmp = pow(x, -0.5) * 0.3333333333333333;
	} 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 = 3.0d0 * (sqrt(x) * y)
    if (y <= (-380.0d0)) then
        tmp = t_0
    else if (y <= (-4.3d-225)) then
        tmp = 0.3333333333333333d0 / sqrt(x)
    else if (y <= 2.35d-290) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 3.9d+65) then
        tmp = (x ** (-0.5d0)) * 0.3333333333333333d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 3.0 * (Math.sqrt(x) * y);
	double tmp;
	if (y <= -380.0) {
		tmp = t_0;
	} else if (y <= -4.3e-225) {
		tmp = 0.3333333333333333 / Math.sqrt(x);
	} else if (y <= 2.35e-290) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 3.9e+65) {
		tmp = Math.pow(x, -0.5) * 0.3333333333333333;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 3.0 * (math.sqrt(x) * y)
	tmp = 0
	if y <= -380.0:
		tmp = t_0
	elif y <= -4.3e-225:
		tmp = 0.3333333333333333 / math.sqrt(x)
	elif y <= 2.35e-290:
		tmp = math.sqrt(x) * -3.0
	elif y <= 3.9e+65:
		tmp = math.pow(x, -0.5) * 0.3333333333333333
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(3.0 * Float64(sqrt(x) * y))
	tmp = 0.0
	if (y <= -380.0)
		tmp = t_0;
	elseif (y <= -4.3e-225)
		tmp = Float64(0.3333333333333333 / sqrt(x));
	elseif (y <= 2.35e-290)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 3.9e+65)
		tmp = Float64((x ^ -0.5) * 0.3333333333333333);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 3.0 * (sqrt(x) * y);
	tmp = 0.0;
	if (y <= -380.0)
		tmp = t_0;
	elseif (y <= -4.3e-225)
		tmp = 0.3333333333333333 / sqrt(x);
	elseif (y <= 2.35e-290)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 3.9e+65)
		tmp = (x ^ -0.5) * 0.3333333333333333;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -380.0], t$95$0, If[LessEqual[y, -4.3e-225], N[(0.3333333333333333 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e-290], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 3.9e+65], N[(N[Power[x, -0.5], $MachinePrecision] * 0.3333333333333333), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -380 or 3.8999999999999998e65 < y

   1. Initial program 99.5%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -380 < y < -4.29999999999999979e-225

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -4.29999999999999979e-225 < y < 2.3500000000000001e-290

   1. Initial program 99.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around inf 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   if 2.3500000000000001e-290 < y < 3.8999999999999998e65

   1. Initial program 99.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

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

Alternative 5: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 195:\\ \;\;\;\;\left(\frac{0.1111111111111111}{x} + y\right) \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 195.0)
   (* (+ (/ 0.1111111111111111 x) y) (* 3.0 (sqrt x)))
   (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 195.0) {
		tmp = ((0.1111111111111111 / x) + y) * (3.0 * sqrt(x));
	} else {
		tmp = sqrt(x) * ((3.0 * y) + -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 <= 195.0d0) then
        tmp = ((0.1111111111111111d0 / x) + y) * (3.0d0 * sqrt(x))
    else
        tmp = sqrt(x) * ((3.0d0 * y) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 195.0) {
		tmp = ((0.1111111111111111 / x) + y) * (3.0 * Math.sqrt(x));
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 195.0:
		tmp = ((0.1111111111111111 / x) + y) * (3.0 * math.sqrt(x))
	else:
		tmp = math.sqrt(x) * ((3.0 * y) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 195.0)
		tmp = Float64(Float64(Float64(0.1111111111111111 / x) + y) * Float64(3.0 * sqrt(x)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 195.0)
		tmp = ((0.1111111111111111 / x) + y) * (3.0 * sqrt(x));
	else
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 195.0], N[(N[(N[(0.1111111111111111 / x), $MachinePrecision] + y), $MachinePrecision] * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 195

   1. Initial program 99.3%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   if 195 < x

   1. Initial program 99.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 6: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.11)
   (* (sqrt x) (+ (* 3.0 y) (/ 0.3333333333333333 x)))
   (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = sqrt(x) * ((3.0 * y) + (0.3333333333333333 / x));
	} else {
		tmp = sqrt(x) * ((3.0 * y) + -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 <= 0.11d0) then
        tmp = sqrt(x) * ((3.0d0 * y) + (0.3333333333333333d0 / x))
    else
        tmp = sqrt(x) * ((3.0d0 * y) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = Math.sqrt(x) * ((3.0 * y) + (0.3333333333333333 / x));
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.11:
		tmp = math.sqrt(x) * ((3.0 * y) + (0.3333333333333333 / x))
	else:
		tmp = math.sqrt(x) * ((3.0 * y) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.11)
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + Float64(0.3333333333333333 / x)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.11)
		tmp = sqrt(x) * ((3.0 * y) + (0.3333333333333333 / x));
	else
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.11], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.110000000000000001

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 0.110000000000000001 < x

   1. Initial program 99.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 7: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0042)
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))
   (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = sqrt(x) * ((3.0 * y) + -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 <= 0.0042d0) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    else
        tmp = sqrt(x) * ((3.0d0 * y) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0042:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	else:
		tmp = math.sqrt(x) * ((3.0 * y) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0042)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0042)
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	else
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0042], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.00419999999999999974

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 0.00419999999999999974 < x

   1. Initial program 99.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 8: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\frac{\sqrt{x}}{0.3333333333333333}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.2e-13)
   (/ 1.0 (/ (sqrt x) 0.3333333333333333))
   (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.2e-13) {
		tmp = 1.0 / (sqrt(x) / 0.3333333333333333);
	} else {
		tmp = sqrt(x) * ((3.0 * y) + -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 <= 3.2d-13) then
        tmp = 1.0d0 / (sqrt(x) / 0.3333333333333333d0)
    else
        tmp = sqrt(x) * ((3.0d0 * y) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 3.2e-13) {
		tmp = 1.0 / (Math.sqrt(x) / 0.3333333333333333);
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.2e-13:
		tmp = 1.0 / (math.sqrt(x) / 0.3333333333333333)
	else:
		tmp = math.sqrt(x) * ((3.0 * y) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.2e-13)
		tmp = Float64(1.0 / Float64(sqrt(x) / 0.3333333333333333));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 3.2e-13)
		tmp = 1.0 / (sqrt(x) / 0.3333333333333333);
	else
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.2e-13], N[(1.0 / N[(N[Sqrt[x], $MachinePrecision] / 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.2e-13

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]

   if 3.2e-13 < x

   1. Initial program 99.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 9: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{\frac{\sqrt{x}}{0.3333333333333333}}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.1e-12)
   (/ 1.0 (/ (sqrt x) 0.3333333333333333))
   (* 3.0 (* (sqrt x) (+ -1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.1e-12) {
		tmp = 1.0 / (sqrt(x) / 0.3333333333333333);
	} else {
		tmp = 3.0 * (sqrt(x) * (-1.0 + y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 3.1d-12) then
        tmp = 1.0d0 / (sqrt(x) / 0.3333333333333333d0)
    else
        tmp = 3.0d0 * (sqrt(x) * ((-1.0d0) + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 3.1e-12) {
		tmp = 1.0 / (Math.sqrt(x) / 0.3333333333333333);
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (-1.0 + y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.1e-12:
		tmp = 1.0 / (math.sqrt(x) / 0.3333333333333333)
	else:
		tmp = 3.0 * (math.sqrt(x) * (-1.0 + y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.1e-12)
		tmp = Float64(1.0 / Float64(sqrt(x) / 0.3333333333333333));
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(-1.0 + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 3.1e-12)
		tmp = 1.0 / (sqrt(x) / 0.3333333333333333);
	else
		tmp = 3.0 * (sqrt(x) * (-1.0 + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.1e-12], N[(1.0 / N[(N[Sqrt[x], $MachinePrecision] / 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.1000000000000001e-12

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]

   if 3.1000000000000001e-12 < x

   1. Initial program 99.5%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 10: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

4. Applied egg-rr 0

   \[\leadsto expr\]

6. Applied egg-rr 0

   \[\leadsto expr\]

8. Applied egg-rr 0

   \[\leadsto expr\]
9. Add Preprocessing

Alternative 11: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 12: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 13: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Simplified 0

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

Alternative 14: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 400000000:\\ \;\;\;\;{x}^{-0.5} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 400000000.0) (* (pow x -0.5) 0.3333333333333333) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 400000000.0) {
		tmp = pow(x, -0.5) * 0.3333333333333333;
	} 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 (x <= 400000000.0d0) then
        tmp = (x ** (-0.5d0)) * 0.3333333333333333d0
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 400000000.0) {
		tmp = Math.pow(x, -0.5) * 0.3333333333333333;
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 400000000.0:
		tmp = math.pow(x, -0.5) * 0.3333333333333333
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 400000000.0)
		tmp = Float64((x ^ -0.5) * 0.3333333333333333);
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 400000000.0)
		tmp = (x ^ -0.5) * 0.3333333333333333;
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 400000000.0], N[(N[Power[x, -0.5], $MachinePrecision] * 0.3333333333333333), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4e8

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 4e8 < x

   1. Initial program 99.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around inf 0

       \[\leadsto expr\]

   12. Simplified 0

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

Alternative 15: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 400000000:\\ \;\;\;\;\frac{0.3333333333333333}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 400000000.0) (/ 0.3333333333333333 (sqrt x)) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 400000000.0) {
		tmp = 0.3333333333333333 / sqrt(x);
	} 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 (x <= 400000000.0d0) then
        tmp = 0.3333333333333333d0 / sqrt(x)
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 400000000.0) {
		tmp = 0.3333333333333333 / Math.sqrt(x);
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 400000000.0:
		tmp = 0.3333333333333333 / math.sqrt(x)
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 400000000.0)
		tmp = Float64(0.3333333333333333 / sqrt(x));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 400000000.0)
		tmp = 0.3333333333333333 / sqrt(x);
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 400000000.0], N[(0.3333333333333333 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4e8

   1. Initial program 99.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 4e8 < x

   1. Initial program 99.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   7. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   9. Simplified 0

      \[\leadsto expr\]

   10. Taylor expanded in x around inf 0

       \[\leadsto expr\]

   12. Simplified 0

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

Alternative 16: 25.6% 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

1. Initial program 99.4%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

7. Taylor expanded in y around 0 0

   \[\leadsto expr\]

9. Simplified 0

   \[\leadsto expr\]

10. Taylor expanded in x around inf 0

    \[\leadsto expr\]

12. Simplified 0

    \[\leadsto expr\]
13. Add Preprocessing

Alternative 17: 3.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

7. Taylor expanded in y around 0 0

   \[\leadsto expr\]

9. Simplified 0

   \[\leadsto expr\]

10. Taylor expanded in x around -inf 0

    \[\leadsto expr\]

12. Simplified 0

    \[\leadsto expr\]
13. 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 2024110 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (* 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)))