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

Percentage Accurate: 99.4% → 99.4%

Time: 9.4s

Alternatives: 11

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

\[\begin{array}{l} \\ \sqrt{x} \cdot \mathsf{fma}\left(3, y + -1, \frac{0.3333333333333333}{x}\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (sqrt x) (fma 3.0 (+ y -1.0) (/ 0.3333333333333333 x))))

C

double code(double x, double y) {
	return sqrt(x) * fma(3.0, (y + -1.0), (0.3333333333333333 / x));
}

Julia

function code(x, y)
	return Float64(sqrt(x) * fma(3.0, Float64(y + -1.0), Float64(0.3333333333333333 / x)))
end

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
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. +-commutative 99.4%

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

   4. associate--l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. sub-neg 99.4%

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

   9. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in x around 0 99.4%

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

   1. fma-def 99.4%

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

   2. sub-neg 99.4%

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

   3. metadata-eval 99.4%

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

   4. associate-*r/ 99.4%

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

   5. metadata-eval 99.4%

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

7. Simplified 99.4%

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

8. Final simplification 99.4%

   \[\leadsto \sqrt{x} \cdot \mathsf{fma}\left(3, y + -1, \frac{0.3333333333333333}{x}\right) \]
9. Add Preprocessing

Alternative 2: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ t_1 := 3 \cdot \left(\sqrt{x} \cdot y\right)\\ t_2 := \sqrt{x} \cdot -3\\ t_3 := \sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{if}\;x \leq 5 \cdot 10^{-105}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-96}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+221}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+239}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x)))
        (t_1 (* 3.0 (* (sqrt x) y)))
        (t_2 (* (sqrt x) -3.0))
        (t_3 (* (sqrt x) (* 3.0 y))))
   (if (<= x 5e-105)
     t_0
     (if (<= x 1.75e-96)
       t_3
       (if (<= x 9.6e-40)
         t_0
         (if (<= x 1.65e+70)
           t_1
           (if (<= x 5e+135)
             t_2
             (if (<= x 2.6e+221) t_3 (if (<= x 6.6e+239) t_2 t_1)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double t_1 = 3.0 * (sqrt(x) * y);
	double t_2 = sqrt(x) * -3.0;
	double t_3 = sqrt(x) * (3.0 * y);
	double tmp;
	if (x <= 5e-105) {
		tmp = t_0;
	} else if (x <= 1.75e-96) {
		tmp = t_3;
	} else if (x <= 9.6e-40) {
		tmp = t_0;
	} else if (x <= 1.65e+70) {
		tmp = t_1;
	} else if (x <= 5e+135) {
		tmp = t_2;
	} else if (x <= 2.6e+221) {
		tmp = t_3;
	} else if (x <= 6.6e+239) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    t_1 = 3.0d0 * (sqrt(x) * y)
    t_2 = sqrt(x) * (-3.0d0)
    t_3 = sqrt(x) * (3.0d0 * y)
    if (x <= 5d-105) then
        tmp = t_0
    else if (x <= 1.75d-96) then
        tmp = t_3
    else if (x <= 9.6d-40) then
        tmp = t_0
    else if (x <= 1.65d+70) then
        tmp = t_1
    else if (x <= 5d+135) then
        tmp = t_2
    else if (x <= 2.6d+221) then
        tmp = t_3
    else if (x <= 6.6d+239) then
        tmp = t_2
    else
        tmp = t_1
    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 = 3.0 * (Math.sqrt(x) * y);
	double t_2 = Math.sqrt(x) * -3.0;
	double t_3 = Math.sqrt(x) * (3.0 * y);
	double tmp;
	if (x <= 5e-105) {
		tmp = t_0;
	} else if (x <= 1.75e-96) {
		tmp = t_3;
	} else if (x <= 9.6e-40) {
		tmp = t_0;
	} else if (x <= 1.65e+70) {
		tmp = t_1;
	} else if (x <= 5e+135) {
		tmp = t_2;
	} else if (x <= 2.6e+221) {
		tmp = t_3;
	} else if (x <= 6.6e+239) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	t_1 = 3.0 * (math.sqrt(x) * y)
	t_2 = math.sqrt(x) * -3.0
	t_3 = math.sqrt(x) * (3.0 * y)
	tmp = 0
	if x <= 5e-105:
		tmp = t_0
	elif x <= 1.75e-96:
		tmp = t_3
	elif x <= 9.6e-40:
		tmp = t_0
	elif x <= 1.65e+70:
		tmp = t_1
	elif x <= 5e+135:
		tmp = t_2
	elif x <= 2.6e+221:
		tmp = t_3
	elif x <= 6.6e+239:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	t_1 = Float64(3.0 * Float64(sqrt(x) * y))
	t_2 = Float64(sqrt(x) * -3.0)
	t_3 = Float64(sqrt(x) * Float64(3.0 * y))
	tmp = 0.0
	if (x <= 5e-105)
		tmp = t_0;
	elseif (x <= 1.75e-96)
		tmp = t_3;
	elseif (x <= 9.6e-40)
		tmp = t_0;
	elseif (x <= 1.65e+70)
		tmp = t_1;
	elseif (x <= 5e+135)
		tmp = t_2;
	elseif (x <= 2.6e+221)
		tmp = t_3;
	elseif (x <= 6.6e+239)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	t_1 = 3.0 * (sqrt(x) * y);
	t_2 = sqrt(x) * -3.0;
	t_3 = sqrt(x) * (3.0 * y);
	tmp = 0.0;
	if (x <= 5e-105)
		tmp = t_0;
	elseif (x <= 1.75e-96)
		tmp = t_3;
	elseif (x <= 9.6e-40)
		tmp = t_0;
	elseif (x <= 1.65e+70)
		tmp = t_1;
	elseif (x <= 5e+135)
		tmp = t_2;
	elseif (x <= 2.6e+221)
		tmp = t_3;
	elseif (x <= 6.6e+239)
		tmp = t_2;
	else
		tmp = t_1;
	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[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 5e-105], t$95$0, If[LessEqual[x, 1.75e-96], t$95$3, If[LessEqual[x, 9.6e-40], t$95$0, If[LessEqual[x, 1.65e+70], t$95$1, If[LessEqual[x, 5e+135], t$95$2, If[LessEqual[x, 2.6e+221], t$95$3, If[LessEqual[x, 6.6e+239], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 4.99999999999999963e-105 or 1.7499999999999999e-96 < x < 9.59999999999999965e-40

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      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. +-commutative 99.2%

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

      4. associate--l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. sub-neg 99.2%

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

      9. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 85.2%

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

   if 4.99999999999999963e-105 < x < 1.7499999999999999e-96 or 5.00000000000000029e135 < x < 2.60000000000000004e221

   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* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-*l* 73.0%

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

      3. *-commutative 73.0%

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

   7. Simplified 73.0%

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

   if 9.59999999999999965e-40 < x < 1.65000000000000008e70 or 6.5999999999999997e239 < 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* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 65.3%

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

   if 1.65000000000000008e70 < x < 5.00000000000000029e135 or 2.60000000000000004e221 < x < 6.5999999999999997e239

   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. +-commutative 99.4%

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

      4. associate--l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. sub-neg 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 99.4%

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

   6. Taylor expanded in y around 0 70.2%

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

      1. *-commutative 70.2%

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

   8. Simplified 70.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-105}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-96}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-40}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+70}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+135}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+221}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+239}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{if}\;x \leq 5 \cdot 10^{-105}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-96}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x))))
   (if (<= x 5e-105)
     t_0
     (if (<= x 1.75e-96)
       (* (sqrt x) (* 3.0 y))
       (if (<= x 2.35e-39) t_0 (* (sqrt x) (* 3.0 (+ y -1.0))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (x <= 5e-105) {
		tmp = t_0;
	} else if (x <= 1.75e-96) {
		tmp = sqrt(x) * (3.0 * y);
	} else if (x <= 2.35e-39) {
		tmp = t_0;
	} else {
		tmp = sqrt(x) * (3.0 * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    if (x <= 5d-105) then
        tmp = t_0
    else if (x <= 1.75d-96) then
        tmp = sqrt(x) * (3.0d0 * y)
    else if (x <= 2.35d-39) then
        tmp = t_0
    else
        tmp = sqrt(x) * (3.0d0 * (y + (-1.0d0)))
    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 tmp;
	if (x <= 5e-105) {
		tmp = t_0;
	} else if (x <= 1.75e-96) {
		tmp = Math.sqrt(x) * (3.0 * y);
	} else if (x <= 2.35e-39) {
		tmp = t_0;
	} else {
		tmp = Math.sqrt(x) * (3.0 * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	tmp = 0
	if x <= 5e-105:
		tmp = t_0
	elif x <= 1.75e-96:
		tmp = math.sqrt(x) * (3.0 * y)
	elif x <= 2.35e-39:
		tmp = t_0
	else:
		tmp = math.sqrt(x) * (3.0 * (y + -1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	tmp = 0.0
	if (x <= 5e-105)
		tmp = t_0;
	elseif (x <= 1.75e-96)
		tmp = Float64(sqrt(x) * Float64(3.0 * y));
	elseif (x <= 2.35e-39)
		tmp = t_0;
	else
		tmp = Float64(sqrt(x) * Float64(3.0 * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	tmp = 0.0;
	if (x <= 5e-105)
		tmp = t_0;
	elseif (x <= 1.75e-96)
		tmp = sqrt(x) * (3.0 * y);
	elseif (x <= 2.35e-39)
		tmp = t_0;
	else
		tmp = sqrt(x) * (3.0 * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 5e-105], t$95$0, If[LessEqual[x, 1.75e-96], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e-39], t$95$0, N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 4.99999999999999963e-105 or 1.7499999999999999e-96 < x < 2.3500000000000001e-39

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      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. +-commutative 99.2%

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

      4. associate--l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. sub-neg 99.2%

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

      9. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 85.2%

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

   if 4.99999999999999963e-105 < x < 1.7499999999999999e-96

   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* 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-/r* 99.7%

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

      7. metadata-eval 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*l* 90.4%

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

      3. *-commutative 90.4%

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

   7. Simplified 90.4%

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

   if 2.3500000000000001e-39 < x

   1. Initial program 99.5%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. 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. +-commutative 99.5%

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

      4. associate--l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. sub-neg 99.5%

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

      9. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-105}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-96}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-105}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(-1 + \frac{0.1111111111111111}{x}\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-96}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-38}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 5e-105)
   (* 3.0 (* (sqrt x) (+ -1.0 (/ 0.1111111111111111 x))))
   (if (<= x 1.75e-96)
     (* (sqrt x) (* 3.0 y))
     (if (<= x 1.08e-38)
       (* (sqrt x) (/ 0.3333333333333333 x))
       (* (sqrt x) (* 3.0 (+ y -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 5e-105) {
		tmp = 3.0 * (sqrt(x) * (-1.0 + (0.1111111111111111 / x)));
	} else if (x <= 1.75e-96) {
		tmp = sqrt(x) * (3.0 * y);
	} else if (x <= 1.08e-38) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else {
		tmp = sqrt(x) * (3.0 * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 5d-105) then
        tmp = 3.0d0 * (sqrt(x) * ((-1.0d0) + (0.1111111111111111d0 / x)))
    else if (x <= 1.75d-96) then
        tmp = sqrt(x) * (3.0d0 * y)
    else if (x <= 1.08d-38) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else
        tmp = sqrt(x) * (3.0d0 * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 5e-105) {
		tmp = 3.0 * (Math.sqrt(x) * (-1.0 + (0.1111111111111111 / x)));
	} else if (x <= 1.75e-96) {
		tmp = Math.sqrt(x) * (3.0 * y);
	} else if (x <= 1.08e-38) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else {
		tmp = Math.sqrt(x) * (3.0 * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 5e-105:
		tmp = 3.0 * (math.sqrt(x) * (-1.0 + (0.1111111111111111 / x)))
	elif x <= 1.75e-96:
		tmp = math.sqrt(x) * (3.0 * y)
	elif x <= 1.08e-38:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	else:
		tmp = math.sqrt(x) * (3.0 * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 5e-105)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(-1.0 + Float64(0.1111111111111111 / x))));
	elseif (x <= 1.75e-96)
		tmp = Float64(sqrt(x) * Float64(3.0 * y));
	elseif (x <= 1.08e-38)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	else
		tmp = Float64(sqrt(x) * Float64(3.0 * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 5e-105)
		tmp = 3.0 * (sqrt(x) * (-1.0 + (0.1111111111111111 / x)));
	elseif (x <= 1.75e-96)
		tmp = sqrt(x) * (3.0 * y);
	elseif (x <= 1.08e-38)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	else
		tmp = sqrt(x) * (3.0 * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 5e-105], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(-1.0 + N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-96], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e-38], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 4.99999999999999963e-105

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-*l* 99.1%

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

      3. +-commutative 99.1%

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

      4. associate--l+ 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/r* 99.1%

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

      7. metadata-eval 99.1%

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

      8. sub-neg 99.1%

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

      9. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. sub-neg 83.6%

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

      2. associate-*r/ 83.8%

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

      3. metadata-eval 83.8%

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

      4. metadata-eval 83.8%

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

   7. Simplified 83.8%

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

   if 4.99999999999999963e-105 < x < 1.7499999999999999e-96

   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* 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-/r* 99.7%

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

      7. metadata-eval 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*l* 90.4%

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

      3. *-commutative 90.4%

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

   7. Simplified 90.4%

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

   if 1.7499999999999999e-96 < x < 1.08e-38

   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* 99.5%

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

      3. +-commutative 99.5%

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

      4. associate--l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. sub-neg 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 91.1%

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

   if 1.08e-38 < x

   1. Initial program 99.5%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. 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. +-commutative 99.5%

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

      4. associate--l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. sub-neg 99.5%

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

      9. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-105}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(-1 + \frac{0.1111111111111111}{x}\right)\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-96}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-38}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(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 <= -1.0) 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 <= -1.0) || !(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 <= -1.0) || ~((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, -1.0], 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 < -1 or 1 < y

   1. Initial program 99.4%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. 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. +-commutative 99.4%

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

      4. associate--l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. sub-neg 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 69.9%

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

   if -1 < 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. +-commutative 99.4%

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

      4. associate--l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. sub-neg 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 44.3%

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

   6. Taylor expanded in y around 0 42.8%

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

      1. *-commutative 42.8%

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

   8. Simplified 42.8%

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

4. Final simplification 57.5%

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

Alternative 6: 61.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if 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* 99.5%

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

      3. +-commutative 99.5%

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

      4. associate--l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. sub-neg 99.5%

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

      9. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 68.7%

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

   if -1 < 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. +-commutative 99.4%

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

      4. associate--l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. sub-neg 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 44.3%

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

   6. Taylor expanded in y around 0 42.8%

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

      1. *-commutative 42.8%

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

   8. Simplified 42.8%

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

   if 1 < y

   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. +-commutative 99.2%

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

      4. associate--l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. sub-neg 99.2%

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

      9. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*l* 71.3%

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

      3. *-commutative 71.3%

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

   7. Simplified 71.3%

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

4. Final simplification 57.5%

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

Alternative 7: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + 3 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6.5e-7)
   (* (sqrt x) (+ (/ 0.3333333333333333 x) (* 3.0 y)))
   (* (sqrt x) (* 3.0 (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6.5e-7) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + (3.0 * y));
	} else {
		tmp = sqrt(x) * (3.0 * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6.5d-7) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (3.0d0 * y))
    else
        tmp = sqrt(x) * (3.0d0 * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6.5e-7) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + (3.0 * y));
	} else {
		tmp = Math.sqrt(x) * (3.0 * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6.5e-7:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + (3.0 * y))
	else:
		tmp = math.sqrt(x) * (3.0 * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6.5e-7)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + Float64(3.0 * y)));
	else
		tmp = Float64(sqrt(x) * Float64(3.0 * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6.5e-7)
		tmp = sqrt(x) * ((0.3333333333333333 / x) + (3.0 * y));
	else
		tmp = sqrt(x) * (3.0 * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6.5e-7], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.50000000000000024e-7

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      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. +-commutative 99.2%

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

      4. associate--l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. sub-neg 99.2%

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

      9. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. distribute-lft-in 99.2%

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

      2. div-inv 99.2%

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

      3. associate-*r* 99.2%

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

      4. metadata-eval 99.2%

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

      5. div-inv 99.2%

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

      6. +-commutative 99.2%

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

      7. distribute-rgt-in 99.2%

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

      8. metadata-eval 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in y around inf 98.8%

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

   if 6.50000000000000024e-7 < 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* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. sub-neg 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + 3 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-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. +-commutative 99.4%

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

   4. associate--l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. sub-neg 99.4%

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

   9. metadata-eval 99.4%

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

3. Simplified 99.4%

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

   1. clear-num 99.3%

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

   2. div-inv 99.4%

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

   3. metadata-eval 99.4%

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

   4. frac-2neg 99.4%

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

   5. metadata-eval 99.4%

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

   6. div-inv 99.4%

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

   7. distribute-rgt-neg-in 99.4%

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

   8. metadata-eval 99.4%

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

6. Applied egg-rr 99.4%

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

7. Final simplification 99.4%

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

Alternative 9: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-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. +-commutative 99.4%

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

   4. associate--l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. sub-neg 99.4%

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

   9. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

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

Alternative 10: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-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. +-commutative 99.4%

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

   4. associate--l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. sub-neg 99.4%

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

   9. metadata-eval 99.4%

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

3. Simplified 99.4%

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

   1. distribute-lft-in 99.4%

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

   2. div-inv 99.4%

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

   3. associate-*r* 99.4%

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

   4. metadata-eval 99.4%

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

   5. div-inv 99.4%

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

   6. +-commutative 99.4%

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

   7. distribute-rgt-in 99.4%

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

   8. metadata-eval 99.4%

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

6. Applied egg-rr 99.4%

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

7. Final simplification 99.4%

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

Alternative 11: 26.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
2. 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. +-commutative 99.4%

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

   4. associate--l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. sub-neg 99.4%

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

   9. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in x around inf 58.6%

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

6. Taylor expanded in y around 0 21.0%

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

   1. *-commutative 21.0%

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

8. Simplified 21.0%

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

9. Final simplification 21.0%

   \[\leadsto \sqrt{x} \cdot -3 \]
10. Add Preprocessing

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024027 
(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)))