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

Percentage Accurate: 99.4% → 99.4%

Time: 6.6s

Alternatives: 7

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, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   3. lift-*.f64 N/A

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

   4. associate-*r* N/A

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

   5. lower-*.f64 N/A

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

4. Applied rewrites 99.4%

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

5. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lower--.f64 N/A

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

   4. associate-*r/ N/A

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

   5. metadata-eval N/A

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

   6. lower-/.f64 99.5

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

7. Applied rewrites 99.5%

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

8. Taylor expanded in y around 0

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

10. Applied rewrites 99.5%

    \[\leadsto \mathsf{fma}\left(3, \color{blue}{y}, \frac{0.3333333333333333}{x} - 3\right) \cdot \sqrt{x} \]
11. Add Preprocessing

Alternative 2: 86.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{-35}:\\ \;\;\;\;\sqrt{{x}^{-1}} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \mathsf{fma}\left(3, y, -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.5e-35)
   (* (sqrt (pow x -1.0)) 0.3333333333333333)
   (* (sqrt x) (fma 3.0 y -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.5e-35) {
		tmp = sqrt(pow(x, -1.0)) * 0.3333333333333333;
	} else {
		tmp = sqrt(x) * fma(3.0, y, -3.0);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.5e-35)
		tmp = Float64(sqrt((x ^ -1.0)) * 0.3333333333333333);
	else
		tmp = Float64(sqrt(x) * fma(3.0, y, -3.0));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.5e-35], N[(N[Sqrt[N[Power[x, -1.0], $MachinePrecision]], $MachinePrecision] * 0.3333333333333333), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.49999999999999994e-35

   1. Initial program 99.1%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 85.6

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

   5. Applied rewrites 85.6%

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

   if 1.49999999999999994e-35 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 95.1%

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

   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. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-out-- N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sqrt.f64 N/A

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

      12. lower-/.f64 94.4

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

   7. Applied rewrites 94.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 95.2%

       \[\leadsto \sqrt{x} \cdot \color{blue}{\mathsf{fma}\left(3, y, -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{-35}:\\ \;\;\;\;\sqrt{{x}^{-1}} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \mathsf{fma}\left(3, y, -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 5.9 \cdot 10^{-7}\right):\\ \;\;\;\;\left(\sqrt{x} \cdot 3\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 5.9e-7)))
   (* (* (sqrt x) 3.0) y)
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 5.9e-7)) {
		tmp = (sqrt(x) * 3.0) * y;
	} else {
		tmp = sqrt(x) * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 5.9d-7))) then
        tmp = (sqrt(x) * 3.0d0) * y
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 5.9e-7)) {
		tmp = (Math.sqrt(x) * 3.0) * y;
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 5.9e-7):
		tmp = (math.sqrt(x) * 3.0) * y
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 5.9e-7))
		tmp = Float64(Float64(sqrt(x) * 3.0) * y);
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 5.9e-7)))
		tmp = (sqrt(x) * 3.0) * y;
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 5.9e-7]], $MachinePrecision]], N[(N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 5.89999999999999963e-7 < 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 69.8

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

   5. Applied rewrites 69.8%

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

   7. Applied rewrites 69.8%

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

   if -1 < y < 5.89999999999999963e-7

   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 57.1%

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

   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. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-out-- N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sqrt.f64 N/A

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

      12. lower-/.f64 57.1

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

   7. Applied rewrites 57.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 56.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 5.9 \cdot 10^{-7}\right):\\ \;\;\;\;\left(\sqrt{x} \cdot 3\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\left(\sqrt{x} \cdot 3\right) \cdot y\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(3 \cdot y\right) \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (* (* (sqrt x) 3.0) y)
   (if (<= y 5.9e-7) (* (sqrt x) -3.0) (* (* 3.0 y) (sqrt x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = (sqrt(x) * 3.0) * y;
	} else if (y <= 5.9e-7) {
		tmp = sqrt(x) * -3.0;
	} else {
		tmp = (3.0 * y) * sqrt(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = (sqrt(x) * 3.0d0) * y
    else if (y <= 5.9d-7) then
        tmp = sqrt(x) * (-3.0d0)
    else
        tmp = (3.0d0 * y) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = (Math.sqrt(x) * 3.0) * y;
	} else if (y <= 5.9e-7) {
		tmp = Math.sqrt(x) * -3.0;
	} else {
		tmp = (3.0 * y) * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = (math.sqrt(x) * 3.0) * y
	elif y <= 5.9e-7:
		tmp = math.sqrt(x) * -3.0
	else:
		tmp = (3.0 * y) * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(Float64(sqrt(x) * 3.0) * y);
	elseif (y <= 5.9e-7)
		tmp = Float64(sqrt(x) * -3.0);
	else
		tmp = Float64(Float64(3.0 * y) * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = (sqrt(x) * 3.0) * y;
	elseif (y <= 5.9e-7)
		tmp = sqrt(x) * -3.0;
	else
		tmp = (3.0 * y) * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 5.9e-7], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], N[(N[(3.0 * y), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   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 67.7

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

   5. Applied rewrites 67.7%

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

   7. Applied rewrites 67.8%

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

   if -1 < y < 5.89999999999999963e-7

   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 57.1%

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

   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. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-out-- N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sqrt.f64 N/A

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

      12. lower-/.f64 57.1

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

   7. Applied rewrites 57.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 56.4%

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

   if 5.89999999999999963e-7 < 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. 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. *-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 72.1

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

   7. Applied rewrites 72.1%

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

Alternative 5: 61.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\left(\sqrt{x} \cdot 3\right) \cdot y\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot y\right) \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (* (* (sqrt x) 3.0) y)
   (if (<= y 5.9e-7) (* (sqrt x) -3.0) (* (* (sqrt x) y) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = (sqrt(x) * 3.0) * y;
	} else if (y <= 5.9e-7) {
		tmp = sqrt(x) * -3.0;
	} else {
		tmp = (sqrt(x) * 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 (y <= (-1.0d0)) then
        tmp = (sqrt(x) * 3.0d0) * y
    else if (y <= 5.9d-7) then
        tmp = sqrt(x) * (-3.0d0)
    else
        tmp = (sqrt(x) * y) * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = (Math.sqrt(x) * 3.0) * y;
	} else if (y <= 5.9e-7) {
		tmp = Math.sqrt(x) * -3.0;
	} else {
		tmp = (Math.sqrt(x) * y) * 3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = (math.sqrt(x) * 3.0) * y
	elif y <= 5.9e-7:
		tmp = math.sqrt(x) * -3.0
	else:
		tmp = (math.sqrt(x) * y) * 3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(Float64(sqrt(x) * 3.0) * y);
	elseif (y <= 5.9e-7)
		tmp = Float64(sqrt(x) * -3.0);
	else
		tmp = Float64(Float64(sqrt(x) * y) * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = (sqrt(x) * 3.0) * y;
	elseif (y <= 5.9e-7)
		tmp = sqrt(x) * -3.0;
	else
		tmp = (sqrt(x) * y) * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 5.9e-7], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], N[(N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision] * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   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 67.7

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

   5. Applied rewrites 67.7%

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

   7. Applied rewrites 67.8%

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

   if -1 < y < 5.89999999999999963e-7

   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 57.1%

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

   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. fp-cancel-sign-sub-inv N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-out-- N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-sqrt.f64 N/A

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

      12. lower-/.f64 57.1

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

   7. Applied rewrites 57.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 56.4%

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

   if 5.89999999999999963e-7 < 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 72.1

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

   5. Applied rewrites 72.1%

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

Alternative 6: 62.2% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_] := N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y + -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
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 63.2%

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

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. fp-cancel-sign-sub-inv N/A

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

   4. metadata-eval N/A

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

   5. distribute-lft-out-- N/A

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

   6. lower-*.f64 N/A

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

   7. lower--.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. lower-*.f64 N/A

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

   11. lower-sqrt.f64 N/A

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

   12. lower-/.f64 61.6

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

7. Applied rewrites 61.6%

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

8. Taylor expanded in x around 0

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

10. Applied rewrites 63.7%

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

Alternative 7: 25.4% accurate, 2.7× 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%

   \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
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 63.2%

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

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. fp-cancel-sign-sub-inv N/A

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

   4. metadata-eval N/A

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

   5. distribute-lft-out-- N/A

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

   6. lower-*.f64 N/A

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

   7. lower--.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. lower-*.f64 N/A

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

   11. lower-sqrt.f64 N/A

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

   12. lower-/.f64 61.6

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

7. Applied rewrites 61.6%

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

8. Taylor expanded in y around 0

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

10. Applied rewrites 31.4%

    \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]
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 2024320 
(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)))