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

Percentage Accurate: 99.4% → 99.5%

Time: 6.5s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{x \cdot 9} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (sqrt (* x 9.0)) (+ y (+ (/ 0.1111111111111111 x) -1.0))))

C

double code(double x, double y) {
	return sqrt((x * 9.0)) * (y + ((0.1111111111111111 / x) + -1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt((x * 9.0d0)) * (y + ((0.1111111111111111d0 / x) + (-1.0d0)))
end function

Java

public static double code(double x, double y) {
	return Math.sqrt((x * 9.0)) * (y + ((0.1111111111111111 / x) + -1.0));
}

Python

def code(x, y):
	return math.sqrt((x * 9.0)) * (y + ((0.1111111111111111 / x) + -1.0))

Julia

function code(x, y)
	return Float64(sqrt(Float64(x * 9.0)) * Float64(y + Float64(Float64(0.1111111111111111 / x) + -1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt((x * 9.0)) * (y + ((0.1111111111111111 / x) + -1.0));
end

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate--l+ 99.4%

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

   2. sub-neg 99.4%

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

   3. *-commutative 99.4%

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

   4. associate-/r* 99.4%

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

   5. metadata-eval 99.4%

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

   6. metadata-eval 99.4%

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

3. Simplified 99.4%

   \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)} \]
4. Step-by-step derivation

   1. expm1-log1p-u 96.3%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   2. expm1-udef 52.1%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

5. Applied egg-rr 52.1%

   \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]
6. Step-by-step derivation

   1. expm1-def 96.3%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   2. expm1-log1p 99.4%

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

   3. rem-square-sqrt 99.0%

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

   4. fabs-sqr 99.0%

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

   5. rem-square-sqrt 99.4%

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

   6. rem-sqrt-square 99.4%

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

   7. swap-sqr 99.3%

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

   8. metadata-eval 99.3%

      \[\leadsto \sqrt{\color{blue}{9} \cdot \left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   9. rem-square-sqrt 99.5%

      \[\leadsto \sqrt{9 \cdot \color{blue}{x}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   10. *-commutative 99.5%

       \[\leadsto \sqrt{\color{blue}{x \cdot 9}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

7. Simplified 99.5%

   \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

8. Final simplification 99.5%

   \[\leadsto \sqrt{x \cdot 9} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

Alternative 2: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.7 \cdot 10^{-8}:\\ \;\;\;\;\sqrt{2 \cdot \left(y + -1\right) + 0.1111111111111111 \cdot \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.7e-8)
   (sqrt (+ (* 2.0 (+ y -1.0)) (* 0.1111111111111111 (/ 1.0 x))))
   (* (sqrt (* x 9.0)) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.7e-8) {
		tmp = sqrt(((2.0 * (y + -1.0)) + (0.1111111111111111 * (1.0 / x))));
	} else {
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 4.7d-8) then
        tmp = sqrt(((2.0d0 * (y + (-1.0d0))) + (0.1111111111111111d0 * (1.0d0 / x))))
    else
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 4.7e-8) {
		tmp = Math.sqrt(((2.0 * (y + -1.0)) + (0.1111111111111111 * (1.0 / x))));
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.7e-8:
		tmp = math.sqrt(((2.0 * (y + -1.0)) + (0.1111111111111111 * (1.0 / x))))
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.7e-8)
		tmp = sqrt(Float64(Float64(2.0 * Float64(y + -1.0)) + Float64(0.1111111111111111 * Float64(1.0 / x))));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.7e-8)
		tmp = sqrt(((2.0 * (y + -1.0)) + (0.1111111111111111 * (1.0 / x))));
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.7e-8], N[Sqrt[N[(N[(2.0 * N[(y + -1.0), $MachinePrecision]), $MachinePrecision] + N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.6999999999999997e-8

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. sub-neg 99.3%

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

      3. *-commutative 99.3%

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

      4. associate-/r* 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)} \]
   4. Step-by-step derivation

      1. expm1-log1p-u 99.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      2. expm1-udef 6.4%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   5. Applied egg-rr 6.4%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]
   6. Step-by-step derivation

      1. expm1-def 99.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      2. expm1-log1p 99.3%

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

      3. rem-square-sqrt 98.8%

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

      4. fabs-sqr 98.8%

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

      5. rem-square-sqrt 99.3%

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

      6. rem-sqrt-square 99.3%

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

      7. swap-sqr 99.2%

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

      8. metadata-eval 99.2%

         \[\leadsto \sqrt{\color{blue}{9} \cdot \left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      9. rem-square-sqrt 99.3%

         \[\leadsto \sqrt{9 \cdot \color{blue}{x}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      10. *-commutative 99.3%

          \[\leadsto \sqrt{\color{blue}{x \cdot 9}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   7. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 88.4%

         \[\leadsto \color{blue}{\sqrt{\sqrt{x \cdot 9} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)} \cdot \sqrt{\sqrt{x \cdot 9} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}} \]

      2. sqrt-unprod 84.9%

         \[\leadsto \color{blue}{\sqrt{\left(\sqrt{x \cdot 9} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)\right) \cdot \left(\sqrt{x \cdot 9} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)\right)}} \]

      3. swap-sqr 35.8%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{x \cdot 9} \cdot \sqrt{x \cdot 9}\right) \cdot \left(\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)\right)}} \]

      4. add-sqr-sqrt 35.9%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot 9\right)} \cdot \left(\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)\right)} \]

      5. pow2 35.9%

         \[\leadsto \sqrt{\left(x \cdot 9\right) \cdot \color{blue}{{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2}}} \]

      6. associate-+r+ 35.9%

         \[\leadsto \sqrt{\left(x \cdot 9\right) \cdot {\color{blue}{\left(\left(y + \frac{0.1111111111111111}{x}\right) + -1\right)}}^{2}} \]

      7. +-commutative 35.9%

         \[\leadsto \sqrt{\left(x \cdot 9\right) \cdot {\left(\color{blue}{\left(\frac{0.1111111111111111}{x} + y\right)} + -1\right)}^{2}} \]

      8. associate-+l+ 35.9%

         \[\leadsto \sqrt{\left(x \cdot 9\right) \cdot {\color{blue}{\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}}^{2}} \]

   9. Applied egg-rr 35.9%

      \[\leadsto \color{blue}{\sqrt{\left(x \cdot 9\right) \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}}} \]

   10. Taylor expanded in x around 0 78.4%

       \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   if 4.6999999999999997e-8 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 98.6%

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

      1. expm1-log1p-u 93.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      2. expm1-udef 93.7%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   4. Applied egg-rr 92.7%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(y - 1\right) \]
   5. Step-by-step derivation

      1. expm1-def 93.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      2. expm1-log1p 99.5%

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

      3. rem-square-sqrt 99.2%

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

      4. fabs-sqr 99.2%

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

      5. rem-square-sqrt 99.5%

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

      6. rem-sqrt-square 99.5%

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

      7. swap-sqr 99.4%

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

      8. metadata-eval 99.4%

         \[\leadsto \sqrt{\color{blue}{9} \cdot \left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      9. rem-square-sqrt 99.7%

         \[\leadsto \sqrt{9 \cdot \color{blue}{x}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      10. *-commutative 99.7%

          \[\leadsto \sqrt{\color{blue}{x \cdot 9}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   6. Simplified 98.8%

      \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot \left(y - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.7 \cdot 10^{-8}:\\ \;\;\;\;\sqrt{2 \cdot \left(y + -1\right) + 0.1111111111111111 \cdot \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 3: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-47}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+150}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+249}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.1e-47)
   (* (sqrt x) (/ 0.3333333333333333 x))
   (if (<= x 3.9e+150)
     (* 3.0 (* y (sqrt x)))
     (if (<= x 3.6e+249) (* (sqrt x) -3.0) (* (sqrt x) (* y 3.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.1e-47) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else if (x <= 3.9e+150) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (x <= 3.6e+249) {
		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 (x <= 2.1d-47) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else if (x <= 3.9d+150) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (x <= 3.6d+249) 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 (x <= 2.1e-47) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else if (x <= 3.9e+150) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (x <= 3.6e+249) {
		tmp = Math.sqrt(x) * -3.0;
	} else {
		tmp = Math.sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.1e-47:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	elif x <= 3.9e+150:
		tmp = 3.0 * (y * math.sqrt(x))
	elif x <= 3.6e+249:
		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 (x <= 2.1e-47)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	elseif (x <= 3.9e+150)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (x <= 3.6e+249)
		tmp = Float64(sqrt(x) * -3.0);
	else
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.1e-47)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	elseif (x <= 3.9e+150)
		tmp = 3.0 * (y * sqrt(x));
	elseif (x <= 3.6e+249)
		tmp = sqrt(x) * -3.0;
	else
		tmp = sqrt(x) * (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.1e-47], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+150], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+249], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 2.1000000000000001e-47

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. +-commutative 99.3%

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

      4. associate--l+ 99.3%

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

      5. +-commutative 99.3%

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

      6. distribute-rgt-in 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. sub-neg 99.3%

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

      10. metadata-eval 99.3%

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

      11. associate-*l/ 99.3%

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

      12. metadata-eval 99.3%

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

      13. *-commutative 99.3%

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

      14. associate-/r* 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 80.6%

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

   if 2.1000000000000001e-47 < x < 3.89999999999999991e150

   1. Initial program 99.4%

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

      1. associate-*l* 99.6%

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

      2. associate--l+ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 61.8%

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

   if 3.89999999999999991e150 < x < 3.5999999999999997e249

   1. Initial program 99.4%

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

   2. Taylor expanded in y around inf 99.4%

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

   3. Taylor expanded in y around 0 66.2%

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

      1. *-commutative 66.2%

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

   5. Simplified 66.2%

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

   if 3.5999999999999997e249 < 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. Step-by-step derivation

      1. *-commutative 99.6%

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

      2. associate-*l* 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-rgt-in 99.7%

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

      7. *-commutative 99.7%

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

      8. fma-def 99.7%

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

      9. sub-neg 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*l/ 99.7%

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

      12. metadata-eval 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 68.4%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-47}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+150}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+249}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

Alternative 4: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+82} \lor \neg \left(y \leq 5.3 \cdot 10^{+16}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.4e+82) (not (<= y 5.3e+16)))
   (* 3.0 (* y (sqrt x)))
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.4e+82) || !(y <= 5.3e+16)) {
		tmp = 3.0 * (y * sqrt(x));
	} else {
		tmp = sqrt(x) * ((0.3333333333333333 / 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 <= (-4.4d+82)) .or. (.not. (y <= 5.3d+16))) then
        tmp = 3.0d0 * (y * sqrt(x))
    else
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.4e+82) || !(y <= 5.3e+16)) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.4e+82) or not (y <= 5.3e+16):
		tmp = 3.0 * (y * math.sqrt(x))
	else:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.4e+82) || !(y <= 5.3e+16))
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.4e+82) || ~((y <= 5.3e+16)))
		tmp = 3.0 * (y * sqrt(x));
	else
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.4e+82], N[Not[LessEqual[y, 5.3e+16]], $MachinePrecision]], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4000000000000002e82 or 5.3e16 < 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. Step-by-step derivation

      1. associate-*l* 99.6%

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

      2. associate--l+ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 84.2%

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

   if -4.4000000000000002e82 < y < 5.3e16

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. +-commutative 99.3%

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

      4. associate--l+ 99.3%

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

      5. +-commutative 99.3%

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

      6. distribute-rgt-in 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. sub-neg 99.3%

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

      10. metadata-eval 99.3%

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

      11. associate-*l/ 99.3%

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

      12. metadata-eval 99.3%

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

      13. *-commutative 99.3%

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

      14. associate-/r* 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 93.9%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. sub-neg 93.9%

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

      2. associate-*r/ 94.0%

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

      3. metadata-eval 94.0%

         \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

      4. metadata-eval 94.0%

         \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

   6. Simplified 94.0%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+82} \lor \neg \left(y \leq 5.3 \cdot 10^{+16}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \]

Alternative 5: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	return 3.0 * ((y + ((0.1111111111111111 / x) + -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 + ((0.1111111111111111d0 / x) + (-1.0d0))) * sqrt(x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-*l* 99.5%

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

   2. associate--l+ 99.5%

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

   3. sub-neg 99.5%

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

   4. *-commutative 99.5%

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

   5. associate-/r* 99.4%

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

   6. metadata-eval 99.4%

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

   7. metadata-eval 99.4%

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

3. Simplified 99.4%

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

4. Final simplification 99.4%

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

Alternative 6: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4 \cdot 10^{-9}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 4e-9)))
   (* 3.0 (* y (sqrt x)))
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 4e-9)) {
		tmp = 3.0 * (y * sqrt(x));
	} else {
		tmp = sqrt(x) * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 4d-9))) then
        tmp = 3.0d0 * (y * sqrt(x))
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 4e-9)) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 4e-9):
		tmp = 3.0 * (y * math.sqrt(x))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 4e-9))
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	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 <= 4e-9)))
		tmp = 3.0 * (y * sqrt(x));
	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, 4e-9]], $MachinePrecision]], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 4.00000000000000025e-9 < 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. Step-by-step derivation

      1. associate-*l* 99.5%

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

      2. associate--l+ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 74.1%

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

   if -1 < y < 4.00000000000000025e-9

   1. Initial program 99.3%

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

   2. Taylor expanded in y around inf 48.3%

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

   3. Taylor expanded in y around 0 46.5%

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

      1. *-commutative 46.5%

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

   5. Simplified 46.5%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 4 \cdot 10^{-9}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 7: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 9.2e-7)
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))
   (* (sqrt (* x 9.0)) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 9.2e-7) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 9.2d-7) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    else
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 9.2e-7) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 9.2e-7:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 9.2e-7)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 9.2e-7)
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 9.2e-7], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.1999999999999998e-7

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. +-commutative 99.3%

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

      4. associate--l+ 99.3%

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

      5. +-commutative 99.3%

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

      6. distribute-rgt-in 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. sub-neg 99.3%

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

      10. metadata-eval 99.3%

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

      11. associate-*l/ 99.3%

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

      12. metadata-eval 99.3%

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

      13. *-commutative 99.3%

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

      14. associate-/r* 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   5. Step-by-step derivation

      1. sub-neg 77.2%

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

      2. associate-*r/ 77.2%

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

      3. metadata-eval 77.2%

         \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

      4. metadata-eval 77.2%

         \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

   6. Simplified 77.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

   if 9.1999999999999998e-7 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 98.6%

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

      1. expm1-log1p-u 93.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      2. expm1-udef 93.7%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   4. Applied egg-rr 92.7%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(y - 1\right) \]
   5. Step-by-step derivation

      1. expm1-def 93.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      2. expm1-log1p 99.5%

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

      3. rem-square-sqrt 99.2%

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

      4. fabs-sqr 99.2%

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

      5. rem-square-sqrt 99.5%

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

      6. rem-sqrt-square 99.5%

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

      7. swap-sqr 99.4%

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

      8. metadata-eval 99.4%

         \[\leadsto \sqrt{\color{blue}{9} \cdot \left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      9. rem-square-sqrt 99.7%

         \[\leadsto \sqrt{9 \cdot \color{blue}{x}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

      10. *-commutative 99.7%

          \[\leadsto \sqrt{\color{blue}{x \cdot 9}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   6. Simplified 98.8%

      \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot \left(y - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 8: 25.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

2. Taylor expanded in y around inf 62.4%

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

3. Taylor expanded in y around 0 23.2%

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

   1. *-commutative 23.2%

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

5. Simplified 23.2%

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

6. Final simplification 23.2%

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

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023293 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

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

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