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

Percentage Accurate: 99.4% → 99.4%

Time: 7.4s

Alternatives: 12

Speedup: N/A×

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, 0.9× speedup

Math

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

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(Float64(-1.0 / 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[(N[(-1.0 / x), $MachinePrecision] / -9.0), $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. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/r* N/A

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

   4. frac-2neg N/A

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{\mathsf{neg}\left(\frac{1}{x}\right)}{\mathsf{neg}\left(9\right)}}\right) - 1\right) \]

   5. lower-/.f64 N/A

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{\mathsf{neg}\left(\frac{1}{x}\right)}{\mathsf{neg}\left(9\right)}}\right) - 1\right) \]

   6. distribute-neg-frac N/A

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\color{blue}{\frac{\mathsf{neg}\left(1\right)}{x}}}{\mathsf{neg}\left(9\right)}\right) - 1\right) \]

   7. metadata-eval N/A

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{\color{blue}{-1}}{x}}{\mathsf{neg}\left(9\right)}\right) - 1\right) \]

   8. lower-/.f64 N/A

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\color{blue}{\frac{-1}{x}}}{\mathsf{neg}\left(9\right)}\right) - 1\right) \]

   9. metadata-eval 99.4

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

4. Applied rewrites 99.4%

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

Alternative 2: 91.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right)\\ \mathbf{if}\;t\_0 \leq -100:\\ \;\;\;\;\left(\left(y - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\sqrt{{x}^{-1}} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* 3.0 (sqrt x)) (- (+ y (pow (* x 9.0) -1.0)) 1.0))))
   (if (<= t_0 -100.0)
     (* (* (- y 1.0) (sqrt x)) 3.0)
     (if (<= t_0 2e+151)
       (* (sqrt (pow x -1.0)) 0.3333333333333333)
       (* (* y 3.0) (sqrt x))))))

C

double code(double x, double y) {
	double t_0 = (3.0 * sqrt(x)) * ((y + pow((x * 9.0), -1.0)) - 1.0);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = ((y - 1.0) * sqrt(x)) * 3.0;
	} else if (t_0 <= 2e+151) {
		tmp = sqrt(pow(x, -1.0)) * 0.3333333333333333;
	} else {
		tmp = (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) :: t_0
    real(8) :: tmp
    t_0 = (3.0d0 * sqrt(x)) * ((y + ((x * 9.0d0) ** (-1.0d0))) - 1.0d0)
    if (t_0 <= (-100.0d0)) then
        tmp = ((y - 1.0d0) * sqrt(x)) * 3.0d0
    else if (t_0 <= 2d+151) then
        tmp = sqrt((x ** (-1.0d0))) * 0.3333333333333333d0
    else
        tmp = (y * 3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (3.0 * Math.sqrt(x)) * ((y + Math.pow((x * 9.0), -1.0)) - 1.0);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = ((y - 1.0) * Math.sqrt(x)) * 3.0;
	} else if (t_0 <= 2e+151) {
		tmp = Math.sqrt(Math.pow(x, -1.0)) * 0.3333333333333333;
	} else {
		tmp = (y * 3.0) * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (3.0 * math.sqrt(x)) * ((y + math.pow((x * 9.0), -1.0)) - 1.0)
	tmp = 0
	if t_0 <= -100.0:
		tmp = ((y - 1.0) * math.sqrt(x)) * 3.0
	elif t_0 <= 2e+151:
		tmp = math.sqrt(math.pow(x, -1.0)) * 0.3333333333333333
	else:
		tmp = (y * 3.0) * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(3.0 * sqrt(x)) * Float64(Float64(y + (Float64(x * 9.0) ^ -1.0)) - 1.0))
	tmp = 0.0
	if (t_0 <= -100.0)
		tmp = Float64(Float64(Float64(y - 1.0) * sqrt(x)) * 3.0);
	elseif (t_0 <= 2e+151)
		tmp = Float64(sqrt((x ^ -1.0)) * 0.3333333333333333);
	else
		tmp = Float64(Float64(y * 3.0) * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (3.0 * sqrt(x)) * ((y + ((x * 9.0) ^ -1.0)) - 1.0);
	tmp = 0.0;
	if (t_0 <= -100.0)
		tmp = ((y - 1.0) * sqrt(x)) * 3.0;
	elseif (t_0 <= 2e+151)
		tmp = sqrt((x ^ -1.0)) * 0.3333333333333333;
	else
		tmp = (y * 3.0) * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[Power[N[(x * 9.0), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -100.0], N[(N[(N[(y - 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision], If[LessEqual[t$95$0, 2e+151], N[(N[Sqrt[N[Power[x, -1.0], $MachinePrecision]], $MachinePrecision] * 0.3333333333333333), $MachinePrecision], N[(N[(y * 3.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) < -100

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\left(\left(\left(y - \frac{-0.1111111111111111}{x}\right) - 1\right) \cdot \sqrt{x}\right) \cdot 3} \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]
   6. Step-by-step derivation

      1. lower--.f64 98.2

         \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   7. Applied rewrites 98.2%

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   if -100 < (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) < 2.00000000000000003e151

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \sqrt{\frac{1}{x}}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot \frac{1}{3}} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot \frac{1}{3}} \]

      3. lower-sqrt.f64 N/A

         \[\leadsto \color{blue}{\sqrt{\frac{1}{x}}} \cdot \frac{1}{3} \]

      4. lower-/.f64 82.8

         \[\leadsto \sqrt{\color{blue}{\frac{1}{x}}} \cdot 0.3333333333333333 \]

   5. Applied rewrites 82.8%

      \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot 0.3333333333333333} \]

   if 2.00000000000000003e151 < (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64)))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 99.8

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.8%

      \[\leadsto \left(y \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right) \leq -100:\\ \;\;\;\;\left(\left(y - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right) \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\sqrt{{x}^{-1}} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right)\\ \mathbf{if}\;t\_0 \leq -1.32 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(y - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(\left(\frac{0.1111111111111111}{x} - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* 3.0 (sqrt x)) (- (+ y (pow (* x 9.0) -1.0)) 1.0))))
   (if (<= t_0 -1.32e+19)
     (* (* (- y 1.0) (sqrt x)) 3.0)
     (if (<= t_0 2e+151)
       (* (* (- (/ 0.1111111111111111 x) 1.0) (sqrt x)) 3.0)
       (* (* y 3.0) (sqrt x))))))

C

double code(double x, double y) {
	double t_0 = (3.0 * sqrt(x)) * ((y + pow((x * 9.0), -1.0)) - 1.0);
	double tmp;
	if (t_0 <= -1.32e+19) {
		tmp = ((y - 1.0) * sqrt(x)) * 3.0;
	} else if (t_0 <= 2e+151) {
		tmp = (((0.1111111111111111 / x) - 1.0) * sqrt(x)) * 3.0;
	} else {
		tmp = (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) :: t_0
    real(8) :: tmp
    t_0 = (3.0d0 * sqrt(x)) * ((y + ((x * 9.0d0) ** (-1.0d0))) - 1.0d0)
    if (t_0 <= (-1.32d+19)) then
        tmp = ((y - 1.0d0) * sqrt(x)) * 3.0d0
    else if (t_0 <= 2d+151) then
        tmp = (((0.1111111111111111d0 / x) - 1.0d0) * sqrt(x)) * 3.0d0
    else
        tmp = (y * 3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (3.0 * Math.sqrt(x)) * ((y + Math.pow((x * 9.0), -1.0)) - 1.0);
	double tmp;
	if (t_0 <= -1.32e+19) {
		tmp = ((y - 1.0) * Math.sqrt(x)) * 3.0;
	} else if (t_0 <= 2e+151) {
		tmp = (((0.1111111111111111 / x) - 1.0) * Math.sqrt(x)) * 3.0;
	} else {
		tmp = (y * 3.0) * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (3.0 * math.sqrt(x)) * ((y + math.pow((x * 9.0), -1.0)) - 1.0)
	tmp = 0
	if t_0 <= -1.32e+19:
		tmp = ((y - 1.0) * math.sqrt(x)) * 3.0
	elif t_0 <= 2e+151:
		tmp = (((0.1111111111111111 / x) - 1.0) * math.sqrt(x)) * 3.0
	else:
		tmp = (y * 3.0) * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(3.0 * sqrt(x)) * Float64(Float64(y + (Float64(x * 9.0) ^ -1.0)) - 1.0))
	tmp = 0.0
	if (t_0 <= -1.32e+19)
		tmp = Float64(Float64(Float64(y - 1.0) * sqrt(x)) * 3.0);
	elseif (t_0 <= 2e+151)
		tmp = Float64(Float64(Float64(Float64(0.1111111111111111 / x) - 1.0) * sqrt(x)) * 3.0);
	else
		tmp = Float64(Float64(y * 3.0) * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (3.0 * sqrt(x)) * ((y + ((x * 9.0) ^ -1.0)) - 1.0);
	tmp = 0.0;
	if (t_0 <= -1.32e+19)
		tmp = ((y - 1.0) * sqrt(x)) * 3.0;
	elseif (t_0 <= 2e+151)
		tmp = (((0.1111111111111111 / x) - 1.0) * sqrt(x)) * 3.0;
	else
		tmp = (y * 3.0) * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[Power[N[(x * 9.0), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1.32e+19], N[(N[(N[(y - 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision], If[LessEqual[t$95$0, 2e+151], N[(N[(N[(N[(0.1111111111111111 / x), $MachinePrecision] - 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision], N[(N[(y * 3.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) < -1.32e19

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\left(\left(\left(y - \frac{-0.1111111111111111}{x}\right) - 1\right) \cdot \sqrt{x}\right) \cdot 3} \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]
   6. Step-by-step derivation

      1. lower--.f64 99.1

         \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   7. Applied rewrites 99.1%

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   if -1.32e19 < (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) < 2.00000000000000003e151

   1. Initial program 99.2%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\left(\left(\left(y - \frac{-0.1111111111111111}{x}\right) - 1\right) \cdot \sqrt{x}\right) \cdot 3} \]

   5. Taylor expanded in y around 0

      \[\leadsto \left(\color{blue}{\left(\frac{1}{9} \cdot \frac{1}{x} - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 84.3

         \[\leadsto \left(\left(\color{blue}{\frac{0.1111111111111111}{x}} - 1\right) \cdot \sqrt{x}\right) \cdot 3 \]

   7. Applied rewrites 84.3%

      \[\leadsto \left(\color{blue}{\left(\frac{0.1111111111111111}{x} - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   if 2.00000000000000003e151 < (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64)))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 99.8

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.8%

      \[\leadsto \left(y \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right) \leq -1.32 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(y - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right) \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(\left(\frac{0.1111111111111111}{x} - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right)\\ \mathbf{if}\;t\_0 \leq -1.32 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(y - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(\left(\frac{0.1111111111111111}{x} - 1\right) \cdot 3\right) \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* 3.0 (sqrt x)) (- (+ y (pow (* x 9.0) -1.0)) 1.0))))
   (if (<= t_0 -1.32e+19)
     (* (* (- y 1.0) (sqrt x)) 3.0)
     (if (<= t_0 2e+151)
       (* (* (- (/ 0.1111111111111111 x) 1.0) 3.0) (sqrt x))
       (* (* y 3.0) (sqrt x))))))

C

double code(double x, double y) {
	double t_0 = (3.0 * sqrt(x)) * ((y + pow((x * 9.0), -1.0)) - 1.0);
	double tmp;
	if (t_0 <= -1.32e+19) {
		tmp = ((y - 1.0) * sqrt(x)) * 3.0;
	} else if (t_0 <= 2e+151) {
		tmp = (((0.1111111111111111 / x) - 1.0) * 3.0) * sqrt(x);
	} else {
		tmp = (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) :: t_0
    real(8) :: tmp
    t_0 = (3.0d0 * sqrt(x)) * ((y + ((x * 9.0d0) ** (-1.0d0))) - 1.0d0)
    if (t_0 <= (-1.32d+19)) then
        tmp = ((y - 1.0d0) * sqrt(x)) * 3.0d0
    else if (t_0 <= 2d+151) then
        tmp = (((0.1111111111111111d0 / x) - 1.0d0) * 3.0d0) * sqrt(x)
    else
        tmp = (y * 3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (3.0 * Math.sqrt(x)) * ((y + Math.pow((x * 9.0), -1.0)) - 1.0);
	double tmp;
	if (t_0 <= -1.32e+19) {
		tmp = ((y - 1.0) * Math.sqrt(x)) * 3.0;
	} else if (t_0 <= 2e+151) {
		tmp = (((0.1111111111111111 / x) - 1.0) * 3.0) * Math.sqrt(x);
	} else {
		tmp = (y * 3.0) * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (3.0 * math.sqrt(x)) * ((y + math.pow((x * 9.0), -1.0)) - 1.0)
	tmp = 0
	if t_0 <= -1.32e+19:
		tmp = ((y - 1.0) * math.sqrt(x)) * 3.0
	elif t_0 <= 2e+151:
		tmp = (((0.1111111111111111 / x) - 1.0) * 3.0) * math.sqrt(x)
	else:
		tmp = (y * 3.0) * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(3.0 * sqrt(x)) * Float64(Float64(y + (Float64(x * 9.0) ^ -1.0)) - 1.0))
	tmp = 0.0
	if (t_0 <= -1.32e+19)
		tmp = Float64(Float64(Float64(y - 1.0) * sqrt(x)) * 3.0);
	elseif (t_0 <= 2e+151)
		tmp = Float64(Float64(Float64(Float64(0.1111111111111111 / x) - 1.0) * 3.0) * sqrt(x));
	else
		tmp = Float64(Float64(y * 3.0) * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (3.0 * sqrt(x)) * ((y + ((x * 9.0) ^ -1.0)) - 1.0);
	tmp = 0.0;
	if (t_0 <= -1.32e+19)
		tmp = ((y - 1.0) * sqrt(x)) * 3.0;
	elseif (t_0 <= 2e+151)
		tmp = (((0.1111111111111111 / x) - 1.0) * 3.0) * sqrt(x);
	else
		tmp = (y * 3.0) * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[Power[N[(x * 9.0), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1.32e+19], N[(N[(N[(y - 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision], If[LessEqual[t$95$0, 2e+151], N[(N[(N[(N[(0.1111111111111111 / x), $MachinePrecision] - 1.0), $MachinePrecision] * 3.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(N[(y * 3.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) < -1.32e19

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\left(\left(\left(y - \frac{-0.1111111111111111}{x}\right) - 1\right) \cdot \sqrt{x}\right) \cdot 3} \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]
   6. Step-by-step derivation

      1. lower--.f64 99.1

         \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   7. Applied rewrites 99.1%

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   if -1.32e19 < (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) < 2.00000000000000003e151

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(\frac{1}{9} \cdot \frac{1}{x} - 1\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lower-sqrt.f64 84.2

          \[\leadsto \left(\left(\frac{0.1111111111111111}{x} - 1\right) \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]

   5. Applied rewrites 84.2%

      \[\leadsto \color{blue}{\left(\left(\frac{0.1111111111111111}{x} - 1\right) \cdot 3\right) \cdot \sqrt{x}} \]

   if 2.00000000000000003e151 < (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64)))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 99.8

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.8%

      \[\leadsto \left(y \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right) \leq -1.32 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(y - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right) \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(\left(\frac{0.1111111111111111}{x} - 1\right) \cdot 3\right) \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right)\\ \mathbf{if}\;t\_0 \leq -100:\\ \;\;\;\;\left(\left(y - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \sqrt{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* 3.0 (sqrt x)) (- (+ y (pow (* x 9.0) -1.0)) 1.0))))
   (if (<= t_0 -100.0)
     (* (* (- y 1.0) (sqrt x)) 3.0)
     (if (<= t_0 2e+151)
       (/ (* 0.3333333333333333 (sqrt x)) x)
       (* (* y 3.0) (sqrt x))))))

C

double code(double x, double y) {
	double t_0 = (3.0 * sqrt(x)) * ((y + pow((x * 9.0), -1.0)) - 1.0);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = ((y - 1.0) * sqrt(x)) * 3.0;
	} else if (t_0 <= 2e+151) {
		tmp = (0.3333333333333333 * sqrt(x)) / x;
	} else {
		tmp = (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) :: t_0
    real(8) :: tmp
    t_0 = (3.0d0 * sqrt(x)) * ((y + ((x * 9.0d0) ** (-1.0d0))) - 1.0d0)
    if (t_0 <= (-100.0d0)) then
        tmp = ((y - 1.0d0) * sqrt(x)) * 3.0d0
    else if (t_0 <= 2d+151) then
        tmp = (0.3333333333333333d0 * sqrt(x)) / x
    else
        tmp = (y * 3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (3.0 * Math.sqrt(x)) * ((y + Math.pow((x * 9.0), -1.0)) - 1.0);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = ((y - 1.0) * Math.sqrt(x)) * 3.0;
	} else if (t_0 <= 2e+151) {
		tmp = (0.3333333333333333 * Math.sqrt(x)) / x;
	} else {
		tmp = (y * 3.0) * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (3.0 * math.sqrt(x)) * ((y + math.pow((x * 9.0), -1.0)) - 1.0)
	tmp = 0
	if t_0 <= -100.0:
		tmp = ((y - 1.0) * math.sqrt(x)) * 3.0
	elif t_0 <= 2e+151:
		tmp = (0.3333333333333333 * math.sqrt(x)) / x
	else:
		tmp = (y * 3.0) * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(3.0 * sqrt(x)) * Float64(Float64(y + (Float64(x * 9.0) ^ -1.0)) - 1.0))
	tmp = 0.0
	if (t_0 <= -100.0)
		tmp = Float64(Float64(Float64(y - 1.0) * sqrt(x)) * 3.0);
	elseif (t_0 <= 2e+151)
		tmp = Float64(Float64(0.3333333333333333 * sqrt(x)) / x);
	else
		tmp = Float64(Float64(y * 3.0) * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (3.0 * sqrt(x)) * ((y + ((x * 9.0) ^ -1.0)) - 1.0);
	tmp = 0.0;
	if (t_0 <= -100.0)
		tmp = ((y - 1.0) * sqrt(x)) * 3.0;
	elseif (t_0 <= 2e+151)
		tmp = (0.3333333333333333 * sqrt(x)) / x;
	else
		tmp = (y * 3.0) * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[Power[N[(x * 9.0), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -100.0], N[(N[(N[(y - 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision], If[LessEqual[t$95$0, 2e+151], N[(N[(0.3333333333333333 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(y * 3.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) < -100

   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. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\left(\left(\left(y - \frac{-0.1111111111111111}{x}\right) - 1\right) \cdot \sqrt{x}\right) \cdot 3} \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]
   6. Step-by-step derivation

      1. lower--.f64 98.2

         \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   7. Applied rewrites 98.2%

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot \sqrt{x}\right) \cdot 3 \]

   if -100 < (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) < 2.00000000000000003e151

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{\frac{1}{3} \cdot \sqrt{x} + 3 \cdot \left(\sqrt{{x}^{3}} \cdot \left(y - 1\right)\right)}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{3} \cdot \sqrt{x} + 3 \cdot \left(\sqrt{{x}^{3}} \cdot \left(y - 1\right)\right)}{x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{3 \cdot \left(\sqrt{{x}^{3}} \cdot \left(y - 1\right)\right) + \frac{1}{3} \cdot \sqrt{x}}}{x} \]

      3. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(3 \cdot \sqrt{{x}^{3}}\right) \cdot \left(y - 1\right)} + \frac{1}{3} \cdot \sqrt{x}}{x} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(y - 1\right) \cdot \left(3 \cdot \sqrt{{x}^{3}}\right)} + \frac{1}{3} \cdot \sqrt{x}}{x} \]

      5. associate-*r* N/A

         \[\leadsto \frac{\color{blue}{\left(\left(y - 1\right) \cdot 3\right) \cdot \sqrt{{x}^{3}}} + \frac{1}{3} \cdot \sqrt{x}}{x} \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\left(y - 1\right) \cdot 3, \sqrt{{x}^{3}}, \frac{1}{3} \cdot \sqrt{x}\right)}}{x} \]

      7. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(y - 1\right) \cdot 3}, \sqrt{{x}^{3}}, \frac{1}{3} \cdot \sqrt{x}\right)}{x} \]

      8. lower--.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\left(y - 1\right)} \cdot 3, \sqrt{{x}^{3}}, \frac{1}{3} \cdot \sqrt{x}\right)}{x} \]

      9. lower-sqrt.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(y - 1\right) \cdot 3, \color{blue}{\sqrt{{x}^{3}}}, \frac{1}{3} \cdot \sqrt{x}\right)}{x} \]

      10. lower-pow.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y - 1\right) \cdot 3, \sqrt{\color{blue}{{x}^{3}}}, \frac{1}{3} \cdot \sqrt{x}\right)}{x} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y - 1\right) \cdot 3, \sqrt{{x}^{3}}, \color{blue}{\sqrt{x} \cdot \frac{1}{3}}\right)}{x} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y - 1\right) \cdot 3, \sqrt{{x}^{3}}, \color{blue}{\sqrt{x} \cdot \frac{1}{3}}\right)}{x} \]

      13. lower-sqrt.f64 92.3

          \[\leadsto \frac{\mathsf{fma}\left(\left(y - 1\right) \cdot 3, \sqrt{{x}^{3}}, \color{blue}{\sqrt{x}} \cdot 0.3333333333333333\right)}{x} \]

   5. Applied rewrites 92.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\left(y - 1\right) \cdot 3, \sqrt{{x}^{3}}, \sqrt{x} \cdot 0.3333333333333333\right)}{x}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{1}{3} \cdot \sqrt{x}}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 82.8%

      \[\leadsto \frac{0.3333333333333333 \cdot \sqrt{x}}{x} \]

   if 2.00000000000000003e151 < (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64)))

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 99.8

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.8%

      \[\leadsto \left(y \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right) \leq -100:\\ \;\;\;\;\left(\left(y - 1\right) \cdot \sqrt{x}\right) \cdot 3\\ \mathbf{elif}\;\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + {\left(x \cdot 9\right)}^{-1}\right) - 1\right) \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \sqrt{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.4% accurate, 1.1× speedup

Math

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

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(Float64(Float64(y - Float64(-0.1111111111111111 / x)) - 1.0) * 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[(N[(N[(y - N[(-0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] * N[Sqrt[x], $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
3. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-*l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

4. Applied rewrites 99.4%

   \[\leadsto \color{blue}{\left(\left(\left(y - \frac{-0.1111111111111111}{x}\right) - 1\right) \cdot \sqrt{x}\right) \cdot 3} \]
5. Add Preprocessing

Alternative 7: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -25000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -25000.0) (not (<= y 1.0)))
   (* (* y 3.0) (sqrt x))
   (* -3.0 (sqrt x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -25000.0) || !(y <= 1.0)) {
		tmp = (y * 3.0) * sqrt(x);
	} else {
		tmp = -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 <= (-25000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = (y * 3.0d0) * sqrt(x)
    else
        tmp = (-3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -25000.0) || !(y <= 1.0)) {
		tmp = (y * 3.0) * Math.sqrt(x);
	} else {
		tmp = -3.0 * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -25000.0) or not (y <= 1.0):
		tmp = (y * 3.0) * math.sqrt(x)
	else:
		tmp = -3.0 * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -25000.0) || !(y <= 1.0))
		tmp = Float64(Float64(y * 3.0) * sqrt(x));
	else
		tmp = Float64(-3.0 * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -25000.0) || ~((y <= 1.0)))
		tmp = (y * 3.0) * sqrt(x);
	else
		tmp = -3.0 * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -25000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(N[(y * 3.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(-3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -25000 or 1 < y

   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. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 72.0

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 72.0%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 72.0%

      \[\leadsto \left(y \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]

   if -25000 < y < 1

   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
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate--l+ N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}, 3, \left(3 \cdot \sqrt{x}\right) \cdot y\right)} \]

   4. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{-0.1111111111111111}{x} - 1\right) \cdot \sqrt{x}, 3, y \cdot \left(\sqrt{x} \cdot 3\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-3 \cdot \sqrt{\frac{1}{x}} + 3 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. distribute-rgt-out N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-fma.f64 48.6

          \[\leadsto \left(\sqrt{\frac{1}{x}} \cdot \color{blue}{\mathsf{fma}\left(3, y, -3\right)}\right) \cdot x \]

   7. Applied rewrites 48.6%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot \mathsf{fma}\left(3, y, -3\right)\right) \cdot x} \]

   8. Taylor expanded in y around 0

      \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]
   9. Step-by-step derivation

   10. Applied rewrites 47.6%

       \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -25000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -25000:\\ \;\;\;\;\left(\sqrt{x} \cdot y\right) \cdot 3\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -25000.0)
   (* (* (sqrt x) y) 3.0)
   (if (<= y 1.0) (* -3.0 (sqrt x)) (* (* y 3.0) (sqrt x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -25000.0) {
		tmp = (sqrt(x) * y) * 3.0;
	} else if (y <= 1.0) {
		tmp = -3.0 * sqrt(x);
	} else {
		tmp = (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 <= (-25000.0d0)) then
        tmp = (sqrt(x) * y) * 3.0d0
    else if (y <= 1.0d0) then
        tmp = (-3.0d0) * sqrt(x)
    else
        tmp = (y * 3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -25000.0) {
		tmp = (Math.sqrt(x) * y) * 3.0;
	} else if (y <= 1.0) {
		tmp = -3.0 * Math.sqrt(x);
	} else {
		tmp = (y * 3.0) * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -25000.0:
		tmp = (math.sqrt(x) * y) * 3.0
	elif y <= 1.0:
		tmp = -3.0 * math.sqrt(x)
	else:
		tmp = (y * 3.0) * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -25000.0)
		tmp = Float64(Float64(sqrt(x) * y) * 3.0);
	elseif (y <= 1.0)
		tmp = Float64(-3.0 * sqrt(x));
	else
		tmp = Float64(Float64(y * 3.0) * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -25000.0)
		tmp = (sqrt(x) * y) * 3.0;
	elseif (y <= 1.0)
		tmp = -3.0 * sqrt(x);
	else
		tmp = (y * 3.0) * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -25000.0], N[(N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision] * 3.0), $MachinePrecision], If[LessEqual[y, 1.0], N[(-3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(N[(y * 3.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -25000

   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. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 69.2

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 69.2%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

   if -25000 < y < 1

   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
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate--l+ N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}, 3, \left(3 \cdot \sqrt{x}\right) \cdot y\right)} \]

   4. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{-0.1111111111111111}{x} - 1\right) \cdot \sqrt{x}, 3, y \cdot \left(\sqrt{x} \cdot 3\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-3 \cdot \sqrt{\frac{1}{x}} + 3 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. distribute-rgt-out N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-fma.f64 48.6

          \[\leadsto \left(\sqrt{\frac{1}{x}} \cdot \color{blue}{\mathsf{fma}\left(3, y, -3\right)}\right) \cdot x \]

   7. Applied rewrites 48.6%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot \mathsf{fma}\left(3, y, -3\right)\right) \cdot x} \]

   8. Taylor expanded in y around 0

      \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]
   9. Step-by-step derivation

   10. Applied rewrites 47.6%

       \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]

   if 1 < 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

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 74.4

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 74.5%

      \[\leadsto \left(y \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 61.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -25000:\\ \;\;\;\;\left(\sqrt{x} \cdot 3\right) \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3\right) \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -25000.0)
   (* (* (sqrt x) 3.0) y)
   (if (<= y 1.0) (* -3.0 (sqrt x)) (* (* y 3.0) (sqrt x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -25000.0) {
		tmp = (sqrt(x) * 3.0) * y;
	} else if (y <= 1.0) {
		tmp = -3.0 * sqrt(x);
	} else {
		tmp = (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 <= (-25000.0d0)) then
        tmp = (sqrt(x) * 3.0d0) * y
    else if (y <= 1.0d0) then
        tmp = (-3.0d0) * sqrt(x)
    else
        tmp = (y * 3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -25000.0) {
		tmp = (Math.sqrt(x) * 3.0) * y;
	} else if (y <= 1.0) {
		tmp = -3.0 * Math.sqrt(x);
	} else {
		tmp = (y * 3.0) * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -25000.0:
		tmp = (math.sqrt(x) * 3.0) * y
	elif y <= 1.0:
		tmp = -3.0 * math.sqrt(x)
	else:
		tmp = (y * 3.0) * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -25000.0)
		tmp = Float64(Float64(sqrt(x) * 3.0) * y);
	elseif (y <= 1.0)
		tmp = Float64(-3.0 * sqrt(x));
	else
		tmp = Float64(Float64(y * 3.0) * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -25000.0)
		tmp = (sqrt(x) * 3.0) * y;
	elseif (y <= 1.0)
		tmp = -3.0 * sqrt(x);
	else
		tmp = (y * 3.0) * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -25000.0], N[(N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 1.0], N[(-3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(N[(y * 3.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -25000

   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. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 69.2

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 69.2%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 69.2%

      \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \color{blue}{y} \]

   if -25000 < y < 1

   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
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. associate--l+ N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*r* N/A

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

      11. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}, 3, \left(3 \cdot \sqrt{x}\right) \cdot y\right)} \]

   4. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{-0.1111111111111111}{x} - 1\right) \cdot \sqrt{x}, 3, y \cdot \left(\sqrt{x} \cdot 3\right)\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(-3 \cdot \sqrt{\frac{1}{x}} + 3 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. distribute-rgt-out N/A

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

      7. lower-*.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-fma.f64 48.6

          \[\leadsto \left(\sqrt{\frac{1}{x}} \cdot \color{blue}{\mathsf{fma}\left(3, y, -3\right)}\right) \cdot x \]

   7. Applied rewrites 48.6%

      \[\leadsto \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot \mathsf{fma}\left(3, y, -3\right)\right) \cdot x} \]

   8. Taylor expanded in y around 0

      \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]
   9. Step-by-step derivation

   10. Applied rewrites 47.6%

       \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]

   if 1 < 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

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right)} \cdot 3 \]

      4. lower-sqrt.f64 74.4

         \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot y\right) \cdot 3 \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot y\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 74.5%

      \[\leadsto \left(y \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 62.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(y - 1\right)\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \left(y - 1\right)\right) \cdot 3} \]

   2. associate-*l* N/A

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\left(y - 1\right) \cdot 3\right)} \]

   3. *-commutative N/A

      \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot 3\right) \cdot \sqrt{x}} \]

   4. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot 3\right) \cdot \sqrt{x}} \]

   5. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot 3\right)} \cdot \sqrt{x} \]

   6. lower--.f64 N/A

      \[\leadsto \left(\color{blue}{\left(y - 1\right)} \cdot 3\right) \cdot \sqrt{x} \]

   7. lower-sqrt.f64 60.9

      \[\leadsto \left(\left(y - 1\right) \cdot 3\right) \cdot \color{blue}{\sqrt{x}} \]

5. Applied rewrites 60.9%

   \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot 3\right) \cdot \sqrt{x}} \]
6. Add Preprocessing

Alternative 11: 62.7% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. associate--l+ N/A

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

   5. +-commutative N/A

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

   6. distribute-lft-in N/A

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

   7. *-commutative N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

   10. associate-*r* N/A

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

   11. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}, 3, \left(3 \cdot \sqrt{x}\right) \cdot y\right)} \]

4. Applied rewrites 60.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{-0.1111111111111111}{x} - 1\right) \cdot \sqrt{x}, 3, y \cdot \left(\sqrt{x} \cdot 3\right)\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(-3 \cdot \sqrt{\frac{1}{x}} + 3 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)\right)} \]
6. Step-by-step derivation

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. associate-*r* N/A

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

   6. distribute-rgt-out N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. lower-fma.f64 57.4

       \[\leadsto \left(\sqrt{\frac{1}{x}} \cdot \color{blue}{\mathsf{fma}\left(3, y, -3\right)}\right) \cdot x \]

7. Applied rewrites 57.4%

   \[\leadsto \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot \mathsf{fma}\left(3, y, -3\right)\right) \cdot x} \]
8. Step-by-step derivation

9. Applied rewrites 60.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3, y, -3\right) \cdot \sqrt{x}} \]
10. Add Preprocessing

Alternative 12: 25.7% accurate, 2.7× 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%

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

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. associate--l+ N/A

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

   5. +-commutative N/A

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

   6. distribute-lft-in N/A

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

   7. *-commutative N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

   10. associate-*r* N/A

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

   11. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}, 3, \left(3 \cdot \sqrt{x}\right) \cdot y\right)} \]

4. Applied rewrites 60.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\frac{-0.1111111111111111}{x} - 1\right) \cdot \sqrt{x}, 3, y \cdot \left(\sqrt{x} \cdot 3\right)\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(-3 \cdot \sqrt{\frac{1}{x}} + 3 \cdot \left(\sqrt{\frac{1}{x}} \cdot y\right)\right)} \]
6. Step-by-step derivation

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. associate-*r* N/A

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

   6. distribute-rgt-out N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. lower-fma.f64 57.4

       \[\leadsto \left(\sqrt{\frac{1}{x}} \cdot \color{blue}{\mathsf{fma}\left(3, y, -3\right)}\right) \cdot x \]

7. Applied rewrites 57.4%

   \[\leadsto \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot \mathsf{fma}\left(3, y, -3\right)\right) \cdot x} \]

8. Taylor expanded in y around 0

   \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]
9. Step-by-step derivation

10. Applied rewrites 24.8%

    \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]
11. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.7× 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 2024337 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x)))))

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