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

Percentage Accurate: 99.4% → 99.4%

Time: 15.4s

Alternatives: 14

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. *-commutative 99.5%

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

   2. associate-*l* 99.4%

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

   3. sub-neg 99.4%

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

   4. +-commutative 99.4%

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

   5. distribute-lft-in 99.4%

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

   6. metadata-eval 99.4%

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

   7. metadata-eval 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. fma-def 99.4%

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

   10. *-commutative 99.4%

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

   11. associate-/r* 99.5%

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

   12. associate-*r/ 99.5%

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

   13. metadata-eval 99.5%

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

   14. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ t_1 := \sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{if}\;x \leq 3.2 \cdot 10^{-94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.00275:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x)))
        (t_1 (* (sqrt x) (* 3.0 y))))
   (if (<= x 3.2e-94)
     t_0
     (if (<= x 1.26e-42)
       t_1
       (if (<= x 0.00275) t_0 (if (<= x 2.3e+93) t_1 (* (sqrt x) -3.0)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double t_1 = sqrt(x) * (3.0 * y);
	double tmp;
	if (x <= 3.2e-94) {
		tmp = t_0;
	} else if (x <= 1.26e-42) {
		tmp = t_1;
	} else if (x <= 0.00275) {
		tmp = t_0;
	} else if (x <= 2.3e+93) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    t_1 = sqrt(x) * (3.0d0 * y)
    if (x <= 3.2d-94) then
        tmp = t_0
    else if (x <= 1.26d-42) then
        tmp = t_1
    else if (x <= 0.00275d0) then
        tmp = t_0
    else if (x <= 2.3d+93) then
        tmp = t_1
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (0.3333333333333333 / x);
	double t_1 = Math.sqrt(x) * (3.0 * y);
	double tmp;
	if (x <= 3.2e-94) {
		tmp = t_0;
	} else if (x <= 1.26e-42) {
		tmp = t_1;
	} else if (x <= 0.00275) {
		tmp = t_0;
	} else if (x <= 2.3e+93) {
		tmp = t_1;
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	t_1 = math.sqrt(x) * (3.0 * y)
	tmp = 0
	if x <= 3.2e-94:
		tmp = t_0
	elif x <= 1.26e-42:
		tmp = t_1
	elif x <= 0.00275:
		tmp = t_0
	elif x <= 2.3e+93:
		tmp = t_1
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	t_1 = Float64(sqrt(x) * Float64(3.0 * y))
	tmp = 0.0
	if (x <= 3.2e-94)
		tmp = t_0;
	elseif (x <= 1.26e-42)
		tmp = t_1;
	elseif (x <= 0.00275)
		tmp = t_0;
	elseif (x <= 2.3e+93)
		tmp = t_1;
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	t_1 = sqrt(x) * (3.0 * y);
	tmp = 0.0;
	if (x <= 3.2e-94)
		tmp = t_0;
	elseif (x <= 1.26e-42)
		tmp = t_1;
	elseif (x <= 0.00275)
		tmp = t_0;
	elseif (x <= 2.3e+93)
		tmp = t_1;
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 3.2e-94], t$95$0, If[LessEqual[x, 1.26e-42], t$95$1, If[LessEqual[x, 0.00275], t$95$0, If[LessEqual[x, 2.3e+93], t$95$1, N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 3.19999999999999997e-94 or 1.26e-42 < x < 0.0027499999999999998

   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* 99.2%

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

      3. sub-neg 99.2%

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

      4. +-commutative 99.2%

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

      5. distribute-lft-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. metadata-eval 99.2%

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

      8. distribute-lft-in 99.2%

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

      9. fma-def 99.2%

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

      10. *-commutative 99.2%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 79.7%

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

   if 3.19999999999999997e-94 < x < 1.26e-42 or 0.0027499999999999998 < x < 2.3000000000000002e93

   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* 99.5%

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

      3. sub-neg 99.5%

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

      4. +-commutative 99.5%

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

      5. distribute-lft-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. fma-def 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 66.4%

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

      1. associate-*r* 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.5%

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

   6. Simplified 66.5%

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

   if 2.3000000000000002e93 < 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. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-lft-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-in 99.7%

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

      9. fma-def 99.7%

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

      10. *-commutative 99.7%

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

      11. associate-/r* 99.7%

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

      12. associate-*r/ 99.7%

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

      13. metadata-eval 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. metadata-eval 62.8%

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

      3. sub-neg 62.8%

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

      4. metadata-eval 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in x around inf 62.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{-94}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-42}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 0.00275:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 3: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ t_1 := y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{if}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.00275:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x)))
        (t_1 (* y (* (sqrt x) 3.0))))
   (if (<= x 4e-94)
     t_0
     (if (<= x 1.26e-42)
       t_1
       (if (<= x 0.00275) t_0 (if (<= x 2.7e+93) t_1 (* (sqrt x) -3.0)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double t_1 = y * (sqrt(x) * 3.0);
	double tmp;
	if (x <= 4e-94) {
		tmp = t_0;
	} else if (x <= 1.26e-42) {
		tmp = t_1;
	} else if (x <= 0.00275) {
		tmp = t_0;
	} else if (x <= 2.7e+93) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    t_1 = y * (sqrt(x) * 3.0d0)
    if (x <= 4d-94) then
        tmp = t_0
    else if (x <= 1.26d-42) then
        tmp = t_1
    else if (x <= 0.00275d0) then
        tmp = t_0
    else if (x <= 2.7d+93) then
        tmp = t_1
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (0.3333333333333333 / x);
	double t_1 = y * (Math.sqrt(x) * 3.0);
	double tmp;
	if (x <= 4e-94) {
		tmp = t_0;
	} else if (x <= 1.26e-42) {
		tmp = t_1;
	} else if (x <= 0.00275) {
		tmp = t_0;
	} else if (x <= 2.7e+93) {
		tmp = t_1;
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	t_1 = y * (math.sqrt(x) * 3.0)
	tmp = 0
	if x <= 4e-94:
		tmp = t_0
	elif x <= 1.26e-42:
		tmp = t_1
	elif x <= 0.00275:
		tmp = t_0
	elif x <= 2.7e+93:
		tmp = t_1
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	t_1 = Float64(y * Float64(sqrt(x) * 3.0))
	tmp = 0.0
	if (x <= 4e-94)
		tmp = t_0;
	elseif (x <= 1.26e-42)
		tmp = t_1;
	elseif (x <= 0.00275)
		tmp = t_0;
	elseif (x <= 2.7e+93)
		tmp = t_1;
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	t_1 = y * (sqrt(x) * 3.0);
	tmp = 0.0;
	if (x <= 4e-94)
		tmp = t_0;
	elseif (x <= 1.26e-42)
		tmp = t_1;
	elseif (x <= 0.00275)
		tmp = t_0;
	elseif (x <= 2.7e+93)
		tmp = t_1;
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4e-94], t$95$0, If[LessEqual[x, 1.26e-42], t$95$1, If[LessEqual[x, 0.00275], t$95$0, If[LessEqual[x, 2.7e+93], t$95$1, N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 3.9999999999999998e-94 or 1.26e-42 < x < 0.0027499999999999998

   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* 99.2%

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

      3. sub-neg 99.2%

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

      4. +-commutative 99.2%

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

      5. distribute-lft-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. metadata-eval 99.2%

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

      8. distribute-lft-in 99.2%

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

      9. fma-def 99.2%

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

      10. *-commutative 99.2%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 79.7%

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

   if 3.9999999999999998e-94 < x < 1.26e-42 or 0.0027499999999999998 < x < 2.6999999999999999e93

   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. associate-*l* 99.2%

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

      2. +-commutative 99.2%

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

      3. associate--l+ 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 99.2%

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

      1. distribute-lft-out 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

      6. +-commutative 99.3%

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

      7. distribute-lft-out 99.3%

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

      8. associate-+r+ 99.3%

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

      9. +-commutative 99.3%

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

      10. associate-*r* 99.6%

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

      11. *-commutative 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in y around inf 66.6%

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

   if 2.6999999999999999e93 < 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. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-lft-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-in 99.7%

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

      9. fma-def 99.7%

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

      10. *-commutative 99.7%

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

      11. associate-/r* 99.7%

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

      12. associate-*r/ 99.7%

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

      13. metadata-eval 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. metadata-eval 62.8%

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

      3. sub-neg 62.8%

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

      4. metadata-eval 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in x around inf 62.8%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.00275:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 4: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sqrt{x}}{x \cdot 3}\\ t_1 := y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{if}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.00275:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sqrt x) (* x 3.0))) (t_1 (* y (* (sqrt x) 3.0))))
   (if (<= x 4e-94)
     t_0
     (if (<= x 1.3e-42)
       t_1
       (if (<= x 0.00275) t_0 (if (<= x 1.22e+92) t_1 (* (sqrt x) -3.0)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) / (x * 3.0);
	double t_1 = y * (sqrt(x) * 3.0);
	double tmp;
	if (x <= 4e-94) {
		tmp = t_0;
	} else if (x <= 1.3e-42) {
		tmp = t_1;
	} else if (x <= 0.00275) {
		tmp = t_0;
	} else if (x <= 1.22e+92) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) / (x * 3.0d0)
    t_1 = y * (sqrt(x) * 3.0d0)
    if (x <= 4d-94) then
        tmp = t_0
    else if (x <= 1.3d-42) then
        tmp = t_1
    else if (x <= 0.00275d0) then
        tmp = t_0
    else if (x <= 1.22d+92) then
        tmp = t_1
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) / (x * 3.0);
	double t_1 = y * (Math.sqrt(x) * 3.0);
	double tmp;
	if (x <= 4e-94) {
		tmp = t_0;
	} else if (x <= 1.3e-42) {
		tmp = t_1;
	} else if (x <= 0.00275) {
		tmp = t_0;
	} else if (x <= 1.22e+92) {
		tmp = t_1;
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) / (x * 3.0)
	t_1 = y * (math.sqrt(x) * 3.0)
	tmp = 0
	if x <= 4e-94:
		tmp = t_0
	elif x <= 1.3e-42:
		tmp = t_1
	elif x <= 0.00275:
		tmp = t_0
	elif x <= 1.22e+92:
		tmp = t_1
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) / Float64(x * 3.0))
	t_1 = Float64(y * Float64(sqrt(x) * 3.0))
	tmp = 0.0
	if (x <= 4e-94)
		tmp = t_0;
	elseif (x <= 1.3e-42)
		tmp = t_1;
	elseif (x <= 0.00275)
		tmp = t_0;
	elseif (x <= 1.22e+92)
		tmp = t_1;
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) / (x * 3.0);
	t_1 = y * (sqrt(x) * 3.0);
	tmp = 0.0;
	if (x <= 4e-94)
		tmp = t_0;
	elseif (x <= 1.3e-42)
		tmp = t_1;
	elseif (x <= 0.00275)
		tmp = t_0;
	elseif (x <= 1.22e+92)
		tmp = t_1;
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] / N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4e-94], t$95$0, If[LessEqual[x, 1.3e-42], t$95$1, If[LessEqual[x, 0.00275], t$95$0, If[LessEqual[x, 1.22e+92], t$95$1, N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 3.9999999999999998e-94 or 1.3e-42 < x < 0.0027499999999999998

   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* 99.2%

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

      3. sub-neg 99.2%

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

      4. +-commutative 99.2%

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

      5. distribute-lft-in 99.2%

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

      6. metadata-eval 99.2%

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

      7. metadata-eval 99.2%

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

      8. distribute-lft-in 99.2%

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

      9. fma-def 99.2%

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

      10. *-commutative 99.2%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(-3 + \mathsf{fma}\left(3, y, \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. flip3-+ 19.1%

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

      2. clear-num 19.1%

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

      3. un-div-inv 19.1%

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

      4. clear-num 19.0%

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

      5. flip3-+ 99.3%

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

      6. +-commutative 99.3%

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

      7. fma-udef 99.3%

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

      8. +-commutative 99.3%

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

      9. associate-+l+ 99.3%

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

      10. fma-def 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in x around 0 79.8%

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

      1. *-commutative 79.8%

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

   8. Simplified 79.8%

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

   if 3.9999999999999998e-94 < x < 1.3e-42 or 0.0027499999999999998 < x < 1.22e92

   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. associate-*l* 99.2%

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

      2. +-commutative 99.2%

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

      3. associate--l+ 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 99.2%

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

      1. distribute-lft-out 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

      6. +-commutative 99.3%

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

      7. distribute-lft-out 99.3%

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

      8. associate-+r+ 99.3%

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

      9. +-commutative 99.3%

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

      10. associate-*r* 99.6%

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

      11. *-commutative 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in y around inf 66.6%

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

   if 1.22e92 < 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. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-lft-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-in 99.7%

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

      9. fma-def 99.7%

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

      10. *-commutative 99.7%

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

      11. associate-/r* 99.7%

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

      12. associate-*r/ 99.7%

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

      13. metadata-eval 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. metadata-eval 62.8%

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

      3. sub-neg 62.8%

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

      4. metadata-eval 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in x around inf 62.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.00275:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 5: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{if}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{{x}^{0.5}}{x}}{3}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.00275:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* (sqrt x) 3.0))))
   (if (<= x 4e-94)
     (/ (/ (pow x 0.5) x) 3.0)
     (if (<= x 1.32e-42)
       t_0
       (if (<= x 0.00275)
         (/ (sqrt x) (* x 3.0))
         (if (<= x 6.5e+92) t_0 (* (sqrt x) -3.0)))))))

C

double code(double x, double y) {
	double t_0 = y * (sqrt(x) * 3.0);
	double tmp;
	if (x <= 4e-94) {
		tmp = (pow(x, 0.5) / x) / 3.0;
	} else if (x <= 1.32e-42) {
		tmp = t_0;
	} else if (x <= 0.00275) {
		tmp = sqrt(x) / (x * 3.0);
	} else if (x <= 6.5e+92) {
		tmp = t_0;
	} else {
		tmp = sqrt(x) * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (sqrt(x) * 3.0d0)
    if (x <= 4d-94) then
        tmp = ((x ** 0.5d0) / x) / 3.0d0
    else if (x <= 1.32d-42) then
        tmp = t_0
    else if (x <= 0.00275d0) then
        tmp = sqrt(x) / (x * 3.0d0)
    else if (x <= 6.5d+92) then
        tmp = t_0
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (Math.sqrt(x) * 3.0);
	double tmp;
	if (x <= 4e-94) {
		tmp = (Math.pow(x, 0.5) / x) / 3.0;
	} else if (x <= 1.32e-42) {
		tmp = t_0;
	} else if (x <= 0.00275) {
		tmp = Math.sqrt(x) / (x * 3.0);
	} else if (x <= 6.5e+92) {
		tmp = t_0;
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (math.sqrt(x) * 3.0)
	tmp = 0
	if x <= 4e-94:
		tmp = (math.pow(x, 0.5) / x) / 3.0
	elif x <= 1.32e-42:
		tmp = t_0
	elif x <= 0.00275:
		tmp = math.sqrt(x) / (x * 3.0)
	elif x <= 6.5e+92:
		tmp = t_0
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(sqrt(x) * 3.0))
	tmp = 0.0
	if (x <= 4e-94)
		tmp = Float64(Float64((x ^ 0.5) / x) / 3.0);
	elseif (x <= 1.32e-42)
		tmp = t_0;
	elseif (x <= 0.00275)
		tmp = Float64(sqrt(x) / Float64(x * 3.0));
	elseif (x <= 6.5e+92)
		tmp = t_0;
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (sqrt(x) * 3.0);
	tmp = 0.0;
	if (x <= 4e-94)
		tmp = ((x ^ 0.5) / x) / 3.0;
	elseif (x <= 1.32e-42)
		tmp = t_0;
	elseif (x <= 0.00275)
		tmp = sqrt(x) / (x * 3.0);
	elseif (x <= 6.5e+92)
		tmp = t_0;
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4e-94], N[(N[(N[Power[x, 0.5], $MachinePrecision] / x), $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 1.32e-42], t$95$0, If[LessEqual[x, 0.00275], N[(N[Sqrt[x], $MachinePrecision] / N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+92], t$95$0, N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 3.9999999999999998e-94

   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* 99.4%

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

      2. +-commutative 99.4%

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

      3. associate--l+ 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 81.7%

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

      1. associate-*r* 81.7%

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

      2. *-commutative 81.7%

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

      3. clear-num 81.6%

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

      4. un-div-inv 81.6%

         \[\leadsto \color{blue}{\frac{\sqrt{x} \cdot 3}{\frac{x}{0.1111111111111111}}} \]

      5. div-inv 81.8%

         \[\leadsto \frac{\sqrt{x} \cdot 3}{\color{blue}{x \cdot \frac{1}{0.1111111111111111}}} \]

      6. metadata-eval 81.8%

         \[\leadsto \frac{\sqrt{x} \cdot 3}{x \cdot \color{blue}{9}} \]

   6. Applied egg-rr 81.8%

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

      1. associate-/l* 81.9%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{\frac{x \cdot 9}{3}}} \]

      2. associate-/l* 81.6%

         \[\leadsto \frac{\sqrt{x}}{\color{blue}{\frac{x}{\frac{3}{9}}}} \]

      3. metadata-eval 81.6%

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

      4. pow1/2 81.6%

         \[\leadsto \frac{\color{blue}{{x}^{0.5}}}{\frac{x}{0.3333333333333333}} \]

      5. sqr-pow 81.5%

         \[\leadsto \frac{\color{blue}{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}}{\frac{x}{0.3333333333333333}} \]

      6. div-inv 81.6%

         \[\leadsto \frac{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}{\color{blue}{x \cdot \frac{1}{0.3333333333333333}}} \]

      7. metadata-eval 81.6%

         \[\leadsto \frac{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}{x \cdot \color{blue}{3}} \]

      8. times-frac 81.7%

         \[\leadsto \color{blue}{\frac{{x}^{\left(\frac{0.5}{2}\right)}}{x} \cdot \frac{{x}^{\left(\frac{0.5}{2}\right)}}{3}} \]

      9. metadata-eval 81.7%

         \[\leadsto \frac{{x}^{\color{blue}{0.25}}}{x} \cdot \frac{{x}^{\left(\frac{0.5}{2}\right)}}{3} \]

      10. metadata-eval 81.7%

          \[\leadsto \frac{{x}^{0.25}}{x} \cdot \frac{{x}^{\color{blue}{0.25}}}{3} \]

   8. Applied egg-rr 81.7%

      \[\leadsto \color{blue}{\frac{{x}^{0.25}}{x} \cdot \frac{{x}^{0.25}}{3}} \]
   9. Step-by-step derivation

      1. associate-*r/ 81.7%

         \[\leadsto \color{blue}{\frac{\frac{{x}^{0.25}}{x} \cdot {x}^{0.25}}{3}} \]

      2. associate-*l/ 81.7%

         \[\leadsto \frac{\color{blue}{\frac{{x}^{0.25} \cdot {x}^{0.25}}{x}}}{3} \]

      3. pow-sqr 81.9%

         \[\leadsto \frac{\frac{\color{blue}{{x}^{\left(2 \cdot 0.25\right)}}}{x}}{3} \]

      4. metadata-eval 81.9%

         \[\leadsto \frac{\frac{{x}^{\color{blue}{0.5}}}{x}}{3} \]

   10. Simplified 81.9%

       \[\leadsto \color{blue}{\frac{\frac{{x}^{0.5}}{x}}{3}} \]

   if 3.9999999999999998e-94 < x < 1.32000000000000006e-42 or 0.0027499999999999998 < x < 6.49999999999999999e92

   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. associate-*l* 99.2%

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

      2. +-commutative 99.2%

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

      3. associate--l+ 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 99.2%

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

      1. distribute-lft-out 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

      6. +-commutative 99.3%

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

      7. distribute-lft-out 99.3%

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

      8. associate-+r+ 99.3%

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

      9. +-commutative 99.3%

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

      10. associate-*r* 99.6%

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

      11. *-commutative 99.6%

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

   6. Simplified 99.6%

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

   7. Taylor expanded in y around inf 66.6%

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

   if 1.32000000000000006e-42 < x < 0.0027499999999999998

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-*l* 98.7%

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

      3. sub-neg 98.7%

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

      4. +-commutative 98.7%

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

      5. distribute-lft-in 98.7%

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

      6. metadata-eval 98.7%

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

      7. metadata-eval 98.7%

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

      8. distribute-lft-in 98.7%

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

      9. fma-def 98.7%

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

      10. *-commutative 98.7%

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

      11. associate-/r* 98.8%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(-3 + \mathsf{fma}\left(3, y, \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. flip3-+ 87.8%

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

      2. clear-num 88.0%

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

      3. un-div-inv 88.1%

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

      4. clear-num 87.8%

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

      5. flip3-+ 99.3%

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

      6. +-commutative 99.3%

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

      7. fma-udef 99.3%

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

      8. +-commutative 99.3%

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

      9. associate-+l+ 99.3%

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

      10. fma-def 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in x around 0 68.7%

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

      1. *-commutative 68.7%

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

   8. Simplified 68.7%

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

   if 6.49999999999999999e92 < 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. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. distribute-lft-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-in 99.7%

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

      9. fma-def 99.7%

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

      10. *-commutative 99.7%

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

      11. associate-/r* 99.7%

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

      12. associate-*r/ 99.7%

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

      13. metadata-eval 99.7%

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

      14. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. metadata-eval 62.8%

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

      3. sub-neg 62.8%

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

      4. metadata-eval 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in x around inf 62.8%

      \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{{x}^{0.5}}{x}}{3}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.00275:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 6: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{{x}^{0.5}}{x}}{3}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.0038:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4e-94)
   (/ (/ (pow x 0.5) x) 3.0)
   (if (<= x 1.32e-42)
     (* y (* (sqrt x) 3.0))
     (if (<= x 0.0038)
       (/ (sqrt x) (* x 3.0))
       (* 3.0 (* (sqrt x) (+ y -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4e-94) {
		tmp = (pow(x, 0.5) / x) / 3.0;
	} else if (x <= 1.32e-42) {
		tmp = y * (sqrt(x) * 3.0);
	} else if (x <= 0.0038) {
		tmp = sqrt(x) / (x * 3.0);
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 4d-94) then
        tmp = ((x ** 0.5d0) / x) / 3.0d0
    else if (x <= 1.32d-42) then
        tmp = y * (sqrt(x) * 3.0d0)
    else if (x <= 0.0038d0) then
        tmp = sqrt(x) / (x * 3.0d0)
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 4e-94) {
		tmp = (Math.pow(x, 0.5) / x) / 3.0;
	} else if (x <= 1.32e-42) {
		tmp = y * (Math.sqrt(x) * 3.0);
	} else if (x <= 0.0038) {
		tmp = Math.sqrt(x) / (x * 3.0);
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4e-94:
		tmp = (math.pow(x, 0.5) / x) / 3.0
	elif x <= 1.32e-42:
		tmp = y * (math.sqrt(x) * 3.0)
	elif x <= 0.0038:
		tmp = math.sqrt(x) / (x * 3.0)
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4e-94)
		tmp = Float64(Float64((x ^ 0.5) / x) / 3.0);
	elseif (x <= 1.32e-42)
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	elseif (x <= 0.0038)
		tmp = Float64(sqrt(x) / Float64(x * 3.0));
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4e-94)
		tmp = ((x ^ 0.5) / x) / 3.0;
	elseif (x <= 1.32e-42)
		tmp = y * (sqrt(x) * 3.0);
	elseif (x <= 0.0038)
		tmp = sqrt(x) / (x * 3.0);
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4e-94], N[(N[(N[Power[x, 0.5], $MachinePrecision] / x), $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 1.32e-42], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0038], N[(N[Sqrt[x], $MachinePrecision] / N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 3.9999999999999998e-94

   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* 99.4%

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

      2. +-commutative 99.4%

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

      3. associate--l+ 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 81.7%

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

      1. associate-*r* 81.7%

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

      2. *-commutative 81.7%

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

      3. clear-num 81.6%

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

      4. un-div-inv 81.6%

         \[\leadsto \color{blue}{\frac{\sqrt{x} \cdot 3}{\frac{x}{0.1111111111111111}}} \]

      5. div-inv 81.8%

         \[\leadsto \frac{\sqrt{x} \cdot 3}{\color{blue}{x \cdot \frac{1}{0.1111111111111111}}} \]

      6. metadata-eval 81.8%

         \[\leadsto \frac{\sqrt{x} \cdot 3}{x \cdot \color{blue}{9}} \]

   6. Applied egg-rr 81.8%

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

      1. associate-/l* 81.9%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{\frac{x \cdot 9}{3}}} \]

      2. associate-/l* 81.6%

         \[\leadsto \frac{\sqrt{x}}{\color{blue}{\frac{x}{\frac{3}{9}}}} \]

      3. metadata-eval 81.6%

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

      4. pow1/2 81.6%

         \[\leadsto \frac{\color{blue}{{x}^{0.5}}}{\frac{x}{0.3333333333333333}} \]

      5. sqr-pow 81.5%

         \[\leadsto \frac{\color{blue}{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}}{\frac{x}{0.3333333333333333}} \]

      6. div-inv 81.6%

         \[\leadsto \frac{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}{\color{blue}{x \cdot \frac{1}{0.3333333333333333}}} \]

      7. metadata-eval 81.6%

         \[\leadsto \frac{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}{x \cdot \color{blue}{3}} \]

      8. times-frac 81.7%

         \[\leadsto \color{blue}{\frac{{x}^{\left(\frac{0.5}{2}\right)}}{x} \cdot \frac{{x}^{\left(\frac{0.5}{2}\right)}}{3}} \]

      9. metadata-eval 81.7%

         \[\leadsto \frac{{x}^{\color{blue}{0.25}}}{x} \cdot \frac{{x}^{\left(\frac{0.5}{2}\right)}}{3} \]

      10. metadata-eval 81.7%

          \[\leadsto \frac{{x}^{0.25}}{x} \cdot \frac{{x}^{\color{blue}{0.25}}}{3} \]

   8. Applied egg-rr 81.7%

      \[\leadsto \color{blue}{\frac{{x}^{0.25}}{x} \cdot \frac{{x}^{0.25}}{3}} \]
   9. Step-by-step derivation

      1. associate-*r/ 81.7%

         \[\leadsto \color{blue}{\frac{\frac{{x}^{0.25}}{x} \cdot {x}^{0.25}}{3}} \]

      2. associate-*l/ 81.7%

         \[\leadsto \frac{\color{blue}{\frac{{x}^{0.25} \cdot {x}^{0.25}}{x}}}{3} \]

      3. pow-sqr 81.9%

         \[\leadsto \frac{\frac{\color{blue}{{x}^{\left(2 \cdot 0.25\right)}}}{x}}{3} \]

      4. metadata-eval 81.9%

         \[\leadsto \frac{\frac{{x}^{\color{blue}{0.5}}}{x}}{3} \]

   10. Simplified 81.9%

       \[\leadsto \color{blue}{\frac{\frac{{x}^{0.5}}{x}}{3}} \]

   if 3.9999999999999998e-94 < x < 1.32000000000000006e-42

   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* 99.0%

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

      2. +-commutative 99.0%

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

      3. associate--l+ 99.0%

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

      4. *-commutative 99.0%

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

      5. associate-/r* 99.2%

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

      6. metadata-eval 99.2%

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

      7. sub-neg 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 99.1%

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

      1. distribute-lft-out 99.2%

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

      2. associate-*r/ 99.2%

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

      3. metadata-eval 99.2%

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

      4. sub-neg 99.2%

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

      5. metadata-eval 99.2%

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

      6. +-commutative 99.2%

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

      7. distribute-lft-out 99.2%

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

      8. associate-+r+ 99.2%

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

      9. +-commutative 99.2%

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

      10. associate-*r* 99.4%

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

      11. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in y around inf 62.7%

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

   if 1.32000000000000006e-42 < x < 0.00379999999999999999

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      2. associate-*l* 98.7%

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

      3. sub-neg 98.7%

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

      4. +-commutative 98.7%

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

      5. distribute-lft-in 98.7%

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

      6. metadata-eval 98.7%

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

      7. metadata-eval 98.7%

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

      8. distribute-lft-in 98.7%

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

      9. fma-def 98.7%

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

      10. *-commutative 98.7%

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

      11. associate-/r* 98.8%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(-3 + \mathsf{fma}\left(3, y, \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. flip3-+ 87.8%

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

      2. clear-num 88.0%

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

      3. un-div-inv 88.1%

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

      4. clear-num 87.8%

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

      5. flip3-+ 99.3%

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

      6. +-commutative 99.3%

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

      7. fma-udef 99.3%

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

      8. +-commutative 99.3%

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

      9. associate-+l+ 99.3%

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

      10. fma-def 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in x around 0 68.7%

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

      1. *-commutative 68.7%

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

   8. Simplified 68.7%

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

   if 0.00379999999999999999 < 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. 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. +-commutative 99.5%

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

      3. associate--l+ 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-/r* 99.5%

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

      6. metadata-eval 99.5%

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

      7. sub-neg 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 98.5%

      \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \color{blue}{\left(y - 1\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{{x}^{0.5}}{x}}{3}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.0038:\\ \;\;\;\;\frac{\sqrt{x}}{x \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 7: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.4 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{{x}^{0.5}}{x}}{3}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.0033:\\ \;\;\;\;3 \cdot \frac{\sqrt{x}}{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6.4e-95)
   (/ (/ (pow x 0.5) x) 3.0)
   (if (<= x 1.26e-42)
     (* y (* (sqrt x) 3.0))
     (if (<= x 0.0033)
       (* 3.0 (/ (sqrt x) (* x 9.0)))
       (* 3.0 (* (sqrt x) (+ y -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6.4e-95) {
		tmp = (pow(x, 0.5) / x) / 3.0;
	} else if (x <= 1.26e-42) {
		tmp = y * (sqrt(x) * 3.0);
	} else if (x <= 0.0033) {
		tmp = 3.0 * (sqrt(x) / (x * 9.0));
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6.4d-95) then
        tmp = ((x ** 0.5d0) / x) / 3.0d0
    else if (x <= 1.26d-42) then
        tmp = y * (sqrt(x) * 3.0d0)
    else if (x <= 0.0033d0) then
        tmp = 3.0d0 * (sqrt(x) / (x * 9.0d0))
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6.4e-95) {
		tmp = (Math.pow(x, 0.5) / x) / 3.0;
	} else if (x <= 1.26e-42) {
		tmp = y * (Math.sqrt(x) * 3.0);
	} else if (x <= 0.0033) {
		tmp = 3.0 * (Math.sqrt(x) / (x * 9.0));
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6.4e-95:
		tmp = (math.pow(x, 0.5) / x) / 3.0
	elif x <= 1.26e-42:
		tmp = y * (math.sqrt(x) * 3.0)
	elif x <= 0.0033:
		tmp = 3.0 * (math.sqrt(x) / (x * 9.0))
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6.4e-95)
		tmp = Float64(Float64((x ^ 0.5) / x) / 3.0);
	elseif (x <= 1.26e-42)
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	elseif (x <= 0.0033)
		tmp = Float64(3.0 * Float64(sqrt(x) / Float64(x * 9.0)));
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6.4e-95)
		tmp = ((x ^ 0.5) / x) / 3.0;
	elseif (x <= 1.26e-42)
		tmp = y * (sqrt(x) * 3.0);
	elseif (x <= 0.0033)
		tmp = 3.0 * (sqrt(x) / (x * 9.0));
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6.4e-95], N[(N[(N[Power[x, 0.5], $MachinePrecision] / x), $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 1.26e-42], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.0033], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 6.3999999999999994e-95

   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* 99.4%

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

      2. +-commutative 99.4%

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

      3. associate--l+ 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 81.7%

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

      1. associate-*r* 81.7%

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

      2. *-commutative 81.7%

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

      3. clear-num 81.6%

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

      4. un-div-inv 81.6%

         \[\leadsto \color{blue}{\frac{\sqrt{x} \cdot 3}{\frac{x}{0.1111111111111111}}} \]

      5. div-inv 81.8%

         \[\leadsto \frac{\sqrt{x} \cdot 3}{\color{blue}{x \cdot \frac{1}{0.1111111111111111}}} \]

      6. metadata-eval 81.8%

         \[\leadsto \frac{\sqrt{x} \cdot 3}{x \cdot \color{blue}{9}} \]

   6. Applied egg-rr 81.8%

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

      1. associate-/l* 81.9%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{\frac{x \cdot 9}{3}}} \]

      2. associate-/l* 81.6%

         \[\leadsto \frac{\sqrt{x}}{\color{blue}{\frac{x}{\frac{3}{9}}}} \]

      3. metadata-eval 81.6%

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

      4. pow1/2 81.6%

         \[\leadsto \frac{\color{blue}{{x}^{0.5}}}{\frac{x}{0.3333333333333333}} \]

      5. sqr-pow 81.5%

         \[\leadsto \frac{\color{blue}{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}}{\frac{x}{0.3333333333333333}} \]

      6. div-inv 81.6%

         \[\leadsto \frac{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}{\color{blue}{x \cdot \frac{1}{0.3333333333333333}}} \]

      7. metadata-eval 81.6%

         \[\leadsto \frac{{x}^{\left(\frac{0.5}{2}\right)} \cdot {x}^{\left(\frac{0.5}{2}\right)}}{x \cdot \color{blue}{3}} \]

      8. times-frac 81.7%

         \[\leadsto \color{blue}{\frac{{x}^{\left(\frac{0.5}{2}\right)}}{x} \cdot \frac{{x}^{\left(\frac{0.5}{2}\right)}}{3}} \]

      9. metadata-eval 81.7%

         \[\leadsto \frac{{x}^{\color{blue}{0.25}}}{x} \cdot \frac{{x}^{\left(\frac{0.5}{2}\right)}}{3} \]

      10. metadata-eval 81.7%

          \[\leadsto \frac{{x}^{0.25}}{x} \cdot \frac{{x}^{\color{blue}{0.25}}}{3} \]

   8. Applied egg-rr 81.7%

      \[\leadsto \color{blue}{\frac{{x}^{0.25}}{x} \cdot \frac{{x}^{0.25}}{3}} \]
   9. Step-by-step derivation

      1. associate-*r/ 81.7%

         \[\leadsto \color{blue}{\frac{\frac{{x}^{0.25}}{x} \cdot {x}^{0.25}}{3}} \]

      2. associate-*l/ 81.7%

         \[\leadsto \frac{\color{blue}{\frac{{x}^{0.25} \cdot {x}^{0.25}}{x}}}{3} \]

      3. pow-sqr 81.9%

         \[\leadsto \frac{\frac{\color{blue}{{x}^{\left(2 \cdot 0.25\right)}}}{x}}{3} \]

      4. metadata-eval 81.9%

         \[\leadsto \frac{\frac{{x}^{\color{blue}{0.5}}}{x}}{3} \]

   10. Simplified 81.9%

       \[\leadsto \color{blue}{\frac{\frac{{x}^{0.5}}{x}}{3}} \]

   if 6.3999999999999994e-95 < x < 1.26e-42

   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* 99.0%

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

      2. +-commutative 99.0%

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

      3. associate--l+ 99.0%

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

      4. *-commutative 99.0%

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

      5. associate-/r* 99.2%

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

      6. metadata-eval 99.2%

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

      7. sub-neg 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 99.1%

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

      1. distribute-lft-out 99.2%

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

      2. associate-*r/ 99.2%

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

      3. metadata-eval 99.2%

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

      4. sub-neg 99.2%

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

      5. metadata-eval 99.2%

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

      6. +-commutative 99.2%

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

      7. distribute-lft-out 99.2%

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

      8. associate-+r+ 99.2%

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

      9. +-commutative 99.2%

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

      10. associate-*r* 99.4%

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

      11. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in y around inf 62.7%

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

   if 1.26e-42 < x < 0.0033

   1. Initial program 98.9%

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

      1. associate-*l* 98.9%

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

      2. +-commutative 98.9%

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

      3. associate--l+ 98.9%

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

      4. *-commutative 98.9%

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

      5. associate-/r* 98.8%

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

      6. metadata-eval 98.8%

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

      7. sub-neg 98.8%

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

      8. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

      1. clear-num 98.8%

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

      2. div-inv 98.9%

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

      3. metadata-eval 98.9%

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

      4. +-commutative 98.9%

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

      5. associate-+r+ 98.9%

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

      6. metadata-eval 98.9%

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

      7. sub-neg 98.9%

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

      8. +-commutative 98.9%

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

      9. flip-+ 98.9%

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

      10. clear-num 98.9%

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

      11. un-div-inv 98.8%

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

      12. clear-num 98.9%

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

      13. flip-+ 98.9%

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

   5. Applied egg-rr 99.0%

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

   6. Taylor expanded in x around 0 68.7%

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

      1. *-commutative 68.7%

         \[\leadsto 3 \cdot \frac{\sqrt{x}}{\color{blue}{x \cdot 9}} \]

   8. Simplified 68.7%

      \[\leadsto 3 \cdot \frac{\sqrt{x}}{\color{blue}{x \cdot 9}} \]

   if 0.0033 < 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. 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. +-commutative 99.5%

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

      3. associate--l+ 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-/r* 99.5%

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

      6. metadata-eval 99.5%

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

      7. sub-neg 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 98.5%

      \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \color{blue}{\left(y - 1\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.4 \cdot 10^{-95}:\\ \;\;\;\;\frac{\frac{{x}^{0.5}}{x}}{3}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.0033:\\ \;\;\;\;3 \cdot \frac{\sqrt{x}}{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 8: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -42:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 85000000000000:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{1}{x \cdot 3}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -42.0)
   (* 3.0 (* (sqrt x) (+ y -1.0)))
   (if (<= y 85000000000000.0)
     (* (sqrt x) (+ -3.0 (/ 1.0 (* x 3.0))))
     (* y (* (sqrt x) 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -42.0) {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	} else if (y <= 85000000000000.0) {
		tmp = sqrt(x) * (-3.0 + (1.0 / (x * 3.0)));
	} else {
		tmp = y * (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 <= (-42.0d0)) then
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    else if (y <= 85000000000000.0d0) then
        tmp = sqrt(x) * ((-3.0d0) + (1.0d0 / (x * 3.0d0)))
    else
        tmp = y * (sqrt(x) * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -42.0) {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	} else if (y <= 85000000000000.0) {
		tmp = Math.sqrt(x) * (-3.0 + (1.0 / (x * 3.0)));
	} else {
		tmp = y * (Math.sqrt(x) * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -42.0:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	elif y <= 85000000000000.0:
		tmp = math.sqrt(x) * (-3.0 + (1.0 / (x * 3.0)))
	else:
		tmp = y * (math.sqrt(x) * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -42.0)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	elseif (y <= 85000000000000.0)
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(1.0 / Float64(x * 3.0))));
	else
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -42.0)
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	elseif (y <= 85000000000000.0)
		tmp = sqrt(x) * (-3.0 + (1.0 / (x * 3.0)));
	else
		tmp = y * (sqrt(x) * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -42.0], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 85000000000000.0], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(1.0 / N[(x * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -42

   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%

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

      2. +-commutative 99.4%

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

      3. associate--l+ 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-/r* 99.4%

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

      6. metadata-eval 99.4%

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

      7. sub-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 77.5%

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

   if -42 < y < 8.5e13

   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. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. distribute-lft-in 99.4%

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

      6. metadata-eval 99.4%

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

      7. metadata-eval 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. fma-def 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 98.7%

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

      1. associate-*r/ 98.7%

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

      2. metadata-eval 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

   6. Simplified 98.7%

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

      1. clear-num 98.6%

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

      2. inv-pow 98.6%

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

      3. sqr-pow 98.4%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{{\left(\frac{x}{0.3333333333333333}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{x}{0.3333333333333333}\right)}^{\left(\frac{-1}{2}\right)}} + -3\right) \]

      4. div-inv 98.5%

         \[\leadsto \sqrt{x} \cdot \left({\color{blue}{\left(x \cdot \frac{1}{0.3333333333333333}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{x}{0.3333333333333333}\right)}^{\left(\frac{-1}{2}\right)} + -3\right) \]

      5. metadata-eval 98.5%

         \[\leadsto \sqrt{x} \cdot \left({\left(x \cdot \color{blue}{3}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{x}{0.3333333333333333}\right)}^{\left(\frac{-1}{2}\right)} + -3\right) \]

      6. metadata-eval 98.5%

         \[\leadsto \sqrt{x} \cdot \left({\left(x \cdot 3\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{x}{0.3333333333333333}\right)}^{\left(\frac{-1}{2}\right)} + -3\right) \]

      7. div-inv 98.5%

         \[\leadsto \sqrt{x} \cdot \left({\left(x \cdot 3\right)}^{-0.5} \cdot {\color{blue}{\left(x \cdot \frac{1}{0.3333333333333333}\right)}}^{\left(\frac{-1}{2}\right)} + -3\right) \]

      8. metadata-eval 98.5%

         \[\leadsto \sqrt{x} \cdot \left({\left(x \cdot 3\right)}^{-0.5} \cdot {\left(x \cdot \color{blue}{3}\right)}^{\left(\frac{-1}{2}\right)} + -3\right) \]

      9. metadata-eval 98.5%

         \[\leadsto \sqrt{x} \cdot \left({\left(x \cdot 3\right)}^{-0.5} \cdot {\left(x \cdot 3\right)}^{\color{blue}{-0.5}} + -3\right) \]

   8. Applied egg-rr 98.5%

      \[\leadsto \sqrt{x} \cdot \left(\color{blue}{{\left(x \cdot 3\right)}^{-0.5} \cdot {\left(x \cdot 3\right)}^{-0.5}} + -3\right) \]
   9. Step-by-step derivation

      1. pow-sqr 98.7%

         \[\leadsto \sqrt{x} \cdot \left(\color{blue}{{\left(x \cdot 3\right)}^{\left(2 \cdot -0.5\right)}} + -3\right) \]

      2. metadata-eval 98.7%

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

      3. unpow-1 98.7%

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

   10. Simplified 98.7%

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

   if 8.5e13 < y

   1. Initial program 99.7%

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

      1. associate-*l* 99.3%

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

      2. +-commutative 99.3%

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

      3. associate--l+ 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 99.1%

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

      1. distribute-lft-out 99.2%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

      6. +-commutative 99.3%

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

      7. distribute-lft-out 99.3%

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

      8. associate-+r+ 99.3%

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

      9. +-commutative 99.3%

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

      10. associate-*r* 99.7%

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

      11. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 80.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -42:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 85000000000000:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{1}{x \cdot 3}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \]

Alternative 9: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2900:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 82000000000000:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2900.0)
   (* 3.0 (* (sqrt x) (+ y -1.0)))
   (if (<= y 82000000000000.0)
     (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))
     (* y (* (sqrt x) 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2900.0) {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	} else if (y <= 82000000000000.0) {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = y * (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 <= (-2900.0d0)) then
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    else if (y <= 82000000000000.0d0) then
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    else
        tmp = y * (sqrt(x) * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2900.0) {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	} else if (y <= 82000000000000.0) {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = y * (Math.sqrt(x) * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2900.0:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	elif y <= 82000000000000.0:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	else:
		tmp = y * (math.sqrt(x) * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2900.0)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	elseif (y <= 82000000000000.0)
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	else
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2900.0)
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	elseif (y <= 82000000000000.0)
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	else
		tmp = y * (sqrt(x) * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2900.0], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 82000000000000.0], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2900

   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%

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

      2. +-commutative 99.4%

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

      3. associate--l+ 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-/r* 99.4%

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

      6. metadata-eval 99.4%

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

      7. sub-neg 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 77.5%

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

   if -2900 < y < 8.2e13

   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. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. distribute-lft-in 99.4%

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

      6. metadata-eval 99.4%

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

      7. metadata-eval 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. fma-def 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 98.7%

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

      1. associate-*r/ 98.7%

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

      2. metadata-eval 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

   6. Simplified 98.7%

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

   if 8.2e13 < y

   1. Initial program 99.7%

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

      1. associate-*l* 99.3%

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

      2. +-commutative 99.3%

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

      3. associate--l+ 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. sub-neg 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 99.1%

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

      1. distribute-lft-out 99.2%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

      6. +-commutative 99.3%

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

      7. distribute-lft-out 99.3%

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

      8. associate-+r+ 99.3%

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

      9. +-commutative 99.3%

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

      10. associate-*r* 99.7%

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

      11. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 80.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2900:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;y \leq 82000000000000:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \]

Alternative 10: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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* 99.4%

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

   2. +-commutative 99.4%

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

   3. associate--l+ 99.4%

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

   4. *-commutative 99.4%

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

   5. associate-/r* 99.4%

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

   6. metadata-eval 99.4%

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

   7. sub-neg 99.4%

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

   8. metadata-eval 99.4%

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

3. Simplified 99.4%

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

4. Final simplification 99.4%

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

Alternative 11: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. *-commutative 99.5%

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

   2. associate-*l* 99.4%

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

   3. associate--l+ 99.4%

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

   4. distribute-lft-in 99.4%

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

   5. fma-def 99.4%

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

   6. sub-neg 99.4%

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

   7. +-commutative 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. metadata-eval 99.4%

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

   10. metadata-eval 99.4%

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

   11. *-commutative 99.4%

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

   12. associate-/r* 99.4%

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

   13. associate-*r/ 99.5%

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

   14. metadata-eval 99.5%

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

   15. metadata-eval 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \mathsf{fma}\left(3, y, -3 + \frac{0.3333333333333333}{x}\right)} \]
4. Step-by-step derivation

   1. fma-udef 99.5%

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

   2. +-commutative 99.5%

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

   3. +-commutative 99.5%

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

5. Applied egg-rr 99.5%

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

6. Final simplification 99.5%

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

Alternative 12: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-53} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.8e-53) (not (<= y 1.0)))
   (* 3.0 (* (sqrt x) y))
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.8e-53) || !(y <= 1.0)) {
		tmp = 3.0 * (sqrt(x) * y);
	} else {
		tmp = sqrt(x) * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-3.8d-53)) .or. (.not. (y <= 1.0d0))) then
        tmp = 3.0d0 * (sqrt(x) * y)
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.8e-53) || !(y <= 1.0)) {
		tmp = 3.0 * (Math.sqrt(x) * y);
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.8e-53) or not (y <= 1.0):
		tmp = 3.0 * (math.sqrt(x) * y)
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.8e-53) || !(y <= 1.0))
		tmp = Float64(3.0 * Float64(sqrt(x) * y));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.8e-53) || ~((y <= 1.0)))
		tmp = 3.0 * (sqrt(x) * y);
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.8e-53], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999998e-53 or 1 < y

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l* 99.5%

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

      3. sub-neg 99.5%

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

      4. +-commutative 99.5%

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

      5. distribute-lft-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. fma-def 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 70.2%

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

   if -3.7999999999999998e-53 < y < 1

   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. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. distribute-lft-in 99.4%

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

      6. metadata-eval 99.4%

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

      7. metadata-eval 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. fma-def 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 99.4%

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

      1. associate-*r/ 99.4%

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

      2. metadata-eval 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x around inf 50.6%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-53} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 13: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-53} \lor \neg \left(y \leq 0.98\right):\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.8e-53) (not (<= y 0.98)))
   (* (sqrt x) (* 3.0 y))
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.8e-53) || !(y <= 0.98)) {
		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 <= (-3.8d-53)) .or. (.not. (y <= 0.98d0))) 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 <= -3.8e-53) || !(y <= 0.98)) {
		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 <= -3.8e-53) or not (y <= 0.98):
		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 <= -3.8e-53) || !(y <= 0.98))
		tmp = Float64(sqrt(x) * Float64(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 <= -3.8e-53) || ~((y <= 0.98)))
		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, -3.8e-53], N[Not[LessEqual[y, 0.98]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999998e-53 or 0.97999999999999998 < 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. *-commutative 99.5%

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

      2. associate-*l* 99.5%

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

      3. sub-neg 99.5%

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

      4. +-commutative 99.5%

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

      5. distribute-lft-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. fma-def 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 70.2%

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

      1. associate-*r* 70.4%

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

      2. *-commutative 70.4%

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

      3. associate-*r* 70.4%

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

   6. Simplified 70.4%

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

   if -3.7999999999999998e-53 < y < 0.97999999999999998

   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. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. sub-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. distribute-lft-in 99.4%

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

      6. metadata-eval 99.4%

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

      7. metadata-eval 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. fma-def 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 99.4%

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

      1. associate-*r/ 99.4%

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

      2. metadata-eval 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x around inf 50.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-53} \lor \neg \left(y \leq 0.98\right):\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 14: 25.4% 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 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l* 99.4%

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

   3. sub-neg 99.4%

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

   4. +-commutative 99.4%

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

   5. distribute-lft-in 99.4%

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

   6. metadata-eval 99.4%

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

   7. metadata-eval 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. fma-def 99.4%

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

   10. *-commutative 99.4%

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

   11. associate-/r* 99.5%

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

   12. associate-*r/ 99.5%

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

   13. metadata-eval 99.5%

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

   14. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in y around 0 64.9%

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

   1. associate-*r/ 64.9%

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

   2. metadata-eval 64.9%

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

   3. sub-neg 64.9%

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

   4. metadata-eval 64.9%

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

6. Simplified 64.9%

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

7. Taylor expanded in x around inf 26.8%

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

8. Final simplification 26.8%

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

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 2023297 
(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)))