Data.Approximate.Numerics:blog from approximate-0.2.2.1

Percentage Accurate: 99.7% → 99.7%

Time: 9.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))

C

double code(double x) {
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * sqrt(x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (6.0d0 * (x - 1.0d0)) / ((x + 1.0d0) + (4.0d0 * sqrt(x)))
end function

Java

public static double code(double x) {
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * Math.sqrt(x)));
}

Python

def code(x):
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * math.sqrt(x)))

Julia

function code(x)
	return Float64(Float64(6.0 * Float64(x - 1.0)) / Float64(Float64(x + 1.0) + Float64(4.0 * sqrt(x))))
end

MATLAB

function tmp = code(x)
	tmp = (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * sqrt(x)));
end

Wolfram

code[x_] := N[(N[(6.0 * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x + 1.0), $MachinePrecision] + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))

C

double code(double x) {
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * sqrt(x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (6.0d0 * (x - 1.0d0)) / ((x + 1.0d0) + (4.0d0 * sqrt(x)))
end function

Java

public static double code(double x) {
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * Math.sqrt(x)));
}

Python

def code(x):
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * math.sqrt(x)))

Julia

function code(x)
	return Float64(Float64(6.0 * Float64(x - 1.0)) / Float64(Float64(x + 1.0) + Float64(4.0 * sqrt(x))))
end

MATLAB

function tmp = code(x)
	tmp = (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * sqrt(x)));
end

Wolfram

code[x_] := N[(N[(6.0 * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x + 1.0), $MachinePrecision] + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{6 \cdot x - 6}{1 + \left(x + 4 \cdot \sqrt{x}\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (- (* 6.0 x) 6.0) (+ 1.0 (+ x (* 4.0 (sqrt x))))))

C

double code(double x) {
	return ((6.0 * x) - 6.0) / (1.0 + (x + (4.0 * sqrt(x))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((6.0d0 * x) - 6.0d0) / (1.0d0 + (x + (4.0d0 * sqrt(x))))
end function

Java

public static double code(double x) {
	return ((6.0 * x) - 6.0) / (1.0 + (x + (4.0 * Math.sqrt(x))));
}

Python

def code(x):
	return ((6.0 * x) - 6.0) / (1.0 + (x + (4.0 * math.sqrt(x))))

Julia

function code(x)
	return Float64(Float64(Float64(6.0 * x) - 6.0) / Float64(1.0 + Float64(x + Float64(4.0 * sqrt(x)))))
end

MATLAB

function tmp = code(x)
	tmp = ((6.0 * x) - 6.0) / (1.0 + (x + (4.0 * sqrt(x))));
end

Wolfram

code[x_] := N[(N[(N[(6.0 * x), $MachinePrecision] - 6.0), $MachinePrecision] / N[(1.0 + N[(x + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 99.5%

   \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + \left(x + 4 \cdot \sqrt{x}\right)}} \]

4. Taylor expanded in x around 0 99.5%

   \[\leadsto \frac{\color{blue}{6 \cdot x - 6}}{1 + \left(x + 4 \cdot \sqrt{x}\right)} \]

5. Final simplification 99.5%

   \[\leadsto \frac{6 \cdot x - 6}{1 + \left(x + 4 \cdot \sqrt{x}\right)} \]
6. Add Preprocessing

Alternative 2: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 4:\\ \;\;\;\;\frac{6 \cdot \left(x + -1\right)}{1 + t\_0}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{x + t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 4.0 (sqrt x))))
   (if (<= x 4.0) (/ (* 6.0 (+ x -1.0)) (+ 1.0 t_0)) (* 6.0 (/ x (+ x t_0))))))

C

double code(double x) {
	double t_0 = 4.0 * sqrt(x);
	double tmp;
	if (x <= 4.0) {
		tmp = (6.0 * (x + -1.0)) / (1.0 + t_0);
	} else {
		tmp = 6.0 * (x / (x + t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.0d0 * sqrt(x)
    if (x <= 4.0d0) then
        tmp = (6.0d0 * (x + (-1.0d0))) / (1.0d0 + t_0)
    else
        tmp = 6.0d0 * (x / (x + t_0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = 4.0 * Math.sqrt(x);
	double tmp;
	if (x <= 4.0) {
		tmp = (6.0 * (x + -1.0)) / (1.0 + t_0);
	} else {
		tmp = 6.0 * (x / (x + t_0));
	}
	return tmp;
}

Python

def code(x):
	t_0 = 4.0 * math.sqrt(x)
	tmp = 0
	if x <= 4.0:
		tmp = (6.0 * (x + -1.0)) / (1.0 + t_0)
	else:
		tmp = 6.0 * (x / (x + t_0))
	return tmp

Julia

function code(x)
	t_0 = Float64(4.0 * sqrt(x))
	tmp = 0.0
	if (x <= 4.0)
		tmp = Float64(Float64(6.0 * Float64(x + -1.0)) / Float64(1.0 + t_0));
	else
		tmp = Float64(6.0 * Float64(x / Float64(x + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = 4.0 * sqrt(x);
	tmp = 0.0;
	if (x <= 4.0)
		tmp = (6.0 * (x + -1.0)) / (1.0 + t_0);
	else
		tmp = 6.0 * (x / (x + t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4.0], N[(N[(6.0 * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x / N[(x + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 4

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + 4 \cdot \sqrt{x}}} \]

   if 4 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-1 \cdot \left(x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)}} \]

      2. distribute-rgt-neg-in 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]

      3. associate-*r* 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot {\left(\sqrt{-1}\right)}^{2}} - \left(1 + \frac{1}{x}\right)\right)\right)} \]

      4. fma-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, {\left(\sqrt{-1}\right)}^{2}, -\left(1 + \frac{1}{x}\right)\right)}\right)} \]

      5. unpow2 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{\sqrt{-1} \cdot \sqrt{-1}}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      6. rem-square-sqrt 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{-1}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      7. fma-undefine 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\left(\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)}\right)} \]

      8. *-commutative 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(\sqrt{\frac{1}{x}} \cdot 4\right)} \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      9. associate-*l* 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\sqrt{\frac{1}{x}} \cdot \left(4 \cdot -1\right)} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      10. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot \color{blue}{-4} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      11. distribute-neg-in 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(\left(-1\right) + \left(-\frac{1}{x}\right)\right)}\right)\right)} \]

      12. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(\color{blue}{-1} + \left(-\frac{1}{x}\right)\right)\right)\right)} \]

      13. sub-neg 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(-1 - \frac{1}{x}\right)}\right)\right)} \]

   5. Simplified 98.9%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(-1 - \frac{1}{x}\right)\right)\right)}} \]

   6. Taylor expanded in x around inf 96.6%

      \[\leadsto \color{blue}{\frac{6}{1 - -4 \cdot \sqrt{\frac{1}{x}}}} \]

   7. Taylor expanded in x around 0 96.6%

      \[\leadsto \frac{6}{\color{blue}{\frac{x - -4 \cdot \sqrt{x}}{x}}} \]
   8. Step-by-step derivation

      1. div-inv 96.6%

         \[\leadsto \color{blue}{6 \cdot \frac{1}{\frac{x - -4 \cdot \sqrt{x}}{x}}} \]

      2. clear-num 96.6%

         \[\leadsto 6 \cdot \color{blue}{\frac{x}{x - -4 \cdot \sqrt{x}}} \]

      3. cancel-sign-sub-inv 96.6%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{x + \left(--4\right) \cdot \sqrt{x}}} \]

      4. metadata-eval 96.6%

         \[\leadsto 6 \cdot \frac{x}{x + \color{blue}{4} \cdot \sqrt{x}} \]

   9. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{x + 4 \cdot \sqrt{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4:\\ \;\;\;\;\frac{6 \cdot \left(x + -1\right)}{1 + 4 \cdot \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{x + 4 \cdot \sqrt{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 4:\\ \;\;\;\;\frac{6 \cdot x - 6}{1 + t\_0}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{x + t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 4.0 (sqrt x))))
   (if (<= x 4.0) (/ (- (* 6.0 x) 6.0) (+ 1.0 t_0)) (* 6.0 (/ x (+ x t_0))))))

C

double code(double x) {
	double t_0 = 4.0 * sqrt(x);
	double tmp;
	if (x <= 4.0) {
		tmp = ((6.0 * x) - 6.0) / (1.0 + t_0);
	} else {
		tmp = 6.0 * (x / (x + t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.0d0 * sqrt(x)
    if (x <= 4.0d0) then
        tmp = ((6.0d0 * x) - 6.0d0) / (1.0d0 + t_0)
    else
        tmp = 6.0d0 * (x / (x + t_0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = 4.0 * Math.sqrt(x);
	double tmp;
	if (x <= 4.0) {
		tmp = ((6.0 * x) - 6.0) / (1.0 + t_0);
	} else {
		tmp = 6.0 * (x / (x + t_0));
	}
	return tmp;
}

Python

def code(x):
	t_0 = 4.0 * math.sqrt(x)
	tmp = 0
	if x <= 4.0:
		tmp = ((6.0 * x) - 6.0) / (1.0 + t_0)
	else:
		tmp = 6.0 * (x / (x + t_0))
	return tmp

Julia

function code(x)
	t_0 = Float64(4.0 * sqrt(x))
	tmp = 0.0
	if (x <= 4.0)
		tmp = Float64(Float64(Float64(6.0 * x) - 6.0) / Float64(1.0 + t_0));
	else
		tmp = Float64(6.0 * Float64(x / Float64(x + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = 4.0 * sqrt(x);
	tmp = 0.0;
	if (x <= 4.0)
		tmp = ((6.0 * x) - 6.0) / (1.0 + t_0);
	else
		tmp = 6.0 * (x / (x + t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4.0], N[(N[(N[(6.0 * x), $MachinePrecision] - 6.0), $MachinePrecision] / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x / N[(x + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 4

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + 4 \cdot \sqrt{x}}} \]

   4. Taylor expanded in x around 0 98.2%

      \[\leadsto \frac{\color{blue}{6 \cdot x - 6}}{1 + 4 \cdot \sqrt{x}} \]

   if 4 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-1 \cdot \left(x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)}} \]

      2. distribute-rgt-neg-in 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]

      3. associate-*r* 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot {\left(\sqrt{-1}\right)}^{2}} - \left(1 + \frac{1}{x}\right)\right)\right)} \]

      4. fma-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, {\left(\sqrt{-1}\right)}^{2}, -\left(1 + \frac{1}{x}\right)\right)}\right)} \]

      5. unpow2 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{\sqrt{-1} \cdot \sqrt{-1}}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      6. rem-square-sqrt 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{-1}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      7. fma-undefine 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\left(\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)}\right)} \]

      8. *-commutative 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(\sqrt{\frac{1}{x}} \cdot 4\right)} \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      9. associate-*l* 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\sqrt{\frac{1}{x}} \cdot \left(4 \cdot -1\right)} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      10. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot \color{blue}{-4} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      11. distribute-neg-in 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(\left(-1\right) + \left(-\frac{1}{x}\right)\right)}\right)\right)} \]

      12. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(\color{blue}{-1} + \left(-\frac{1}{x}\right)\right)\right)\right)} \]

      13. sub-neg 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(-1 - \frac{1}{x}\right)}\right)\right)} \]

   5. Simplified 98.9%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(-1 - \frac{1}{x}\right)\right)\right)}} \]

   6. Taylor expanded in x around inf 96.6%

      \[\leadsto \color{blue}{\frac{6}{1 - -4 \cdot \sqrt{\frac{1}{x}}}} \]

   7. Taylor expanded in x around 0 96.6%

      \[\leadsto \frac{6}{\color{blue}{\frac{x - -4 \cdot \sqrt{x}}{x}}} \]
   8. Step-by-step derivation

      1. div-inv 96.6%

         \[\leadsto \color{blue}{6 \cdot \frac{1}{\frac{x - -4 \cdot \sqrt{x}}{x}}} \]

      2. clear-num 96.6%

         \[\leadsto 6 \cdot \color{blue}{\frac{x}{x - -4 \cdot \sqrt{x}}} \]

      3. cancel-sign-sub-inv 96.6%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{x + \left(--4\right) \cdot \sqrt{x}}} \]

      4. metadata-eval 96.6%

         \[\leadsto 6 \cdot \frac{x}{x + \color{blue}{4} \cdot \sqrt{x}} \]

   9. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{x + 4 \cdot \sqrt{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4:\\ \;\;\;\;\frac{6 \cdot x - 6}{1 + 4 \cdot \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{x + 4 \cdot \sqrt{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4 \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{-6}{1 + t\_0}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{x + t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 4.0 (sqrt x))))
   (if (<= x 1.0) (/ -6.0 (+ 1.0 t_0)) (* 6.0 (/ x (+ x t_0))))))

C

double code(double x) {
	double t_0 = 4.0 * sqrt(x);
	double tmp;
	if (x <= 1.0) {
		tmp = -6.0 / (1.0 + t_0);
	} else {
		tmp = 6.0 * (x / (x + t_0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 4.0d0 * sqrt(x)
    if (x <= 1.0d0) then
        tmp = (-6.0d0) / (1.0d0 + t_0)
    else
        tmp = 6.0d0 * (x / (x + t_0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = 4.0 * Math.sqrt(x);
	double tmp;
	if (x <= 1.0) {
		tmp = -6.0 / (1.0 + t_0);
	} else {
		tmp = 6.0 * (x / (x + t_0));
	}
	return tmp;
}

Python

def code(x):
	t_0 = 4.0 * math.sqrt(x)
	tmp = 0
	if x <= 1.0:
		tmp = -6.0 / (1.0 + t_0)
	else:
		tmp = 6.0 * (x / (x + t_0))
	return tmp

Julia

function code(x)
	t_0 = Float64(4.0 * sqrt(x))
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(-6.0 / Float64(1.0 + t_0));
	else
		tmp = Float64(6.0 * Float64(x / Float64(x + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = 4.0 * sqrt(x);
	tmp = 0.0;
	if (x <= 1.0)
		tmp = -6.0 / (1.0 + t_0);
	else
		tmp = 6.0 * (x / (x + t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.0], N[(-6.0 / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x / N[(x + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.1%

      \[\leadsto \color{blue}{\frac{-6}{1 + 4 \cdot \sqrt{x}}} \]

   if 1 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-1 \cdot \left(x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)}} \]

      2. distribute-rgt-neg-in 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]

      3. associate-*r* 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot {\left(\sqrt{-1}\right)}^{2}} - \left(1 + \frac{1}{x}\right)\right)\right)} \]

      4. fma-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, {\left(\sqrt{-1}\right)}^{2}, -\left(1 + \frac{1}{x}\right)\right)}\right)} \]

      5. unpow2 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{\sqrt{-1} \cdot \sqrt{-1}}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      6. rem-square-sqrt 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{-1}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      7. fma-undefine 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\left(\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)}\right)} \]

      8. *-commutative 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(\sqrt{\frac{1}{x}} \cdot 4\right)} \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      9. associate-*l* 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\sqrt{\frac{1}{x}} \cdot \left(4 \cdot -1\right)} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      10. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot \color{blue}{-4} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      11. distribute-neg-in 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(\left(-1\right) + \left(-\frac{1}{x}\right)\right)}\right)\right)} \]

      12. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(\color{blue}{-1} + \left(-\frac{1}{x}\right)\right)\right)\right)} \]

      13. sub-neg 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(-1 - \frac{1}{x}\right)}\right)\right)} \]

   5. Simplified 98.9%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(-1 - \frac{1}{x}\right)\right)\right)}} \]

   6. Taylor expanded in x around inf 96.6%

      \[\leadsto \color{blue}{\frac{6}{1 - -4 \cdot \sqrt{\frac{1}{x}}}} \]

   7. Taylor expanded in x around 0 96.6%

      \[\leadsto \frac{6}{\color{blue}{\frac{x - -4 \cdot \sqrt{x}}{x}}} \]
   8. Step-by-step derivation

      1. div-inv 96.6%

         \[\leadsto \color{blue}{6 \cdot \frac{1}{\frac{x - -4 \cdot \sqrt{x}}{x}}} \]

      2. clear-num 96.6%

         \[\leadsto 6 \cdot \color{blue}{\frac{x}{x - -4 \cdot \sqrt{x}}} \]

      3. cancel-sign-sub-inv 96.6%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{x + \left(--4\right) \cdot \sqrt{x}}} \]

      4. metadata-eval 96.6%

         \[\leadsto 6 \cdot \frac{x}{x + \color{blue}{4} \cdot \sqrt{x}} \]

   9. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{x + 4 \cdot \sqrt{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{-6}{1 + 4 \cdot \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{x + 4 \cdot \sqrt{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + 4 \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{-6}{1 + t\_0}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (+ x (* 4.0 (sqrt x)))))
   (if (<= x 1.0) (/ -6.0 (+ 1.0 t_0)) (* 6.0 (/ x t_0)))))

C

double code(double x) {
	double t_0 = x + (4.0 * sqrt(x));
	double tmp;
	if (x <= 1.0) {
		tmp = -6.0 / (1.0 + t_0);
	} else {
		tmp = 6.0 * (x / t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (4.0d0 * sqrt(x))
    if (x <= 1.0d0) then
        tmp = (-6.0d0) / (1.0d0 + t_0)
    else
        tmp = 6.0d0 * (x / t_0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x + (4.0 * Math.sqrt(x));
	double tmp;
	if (x <= 1.0) {
		tmp = -6.0 / (1.0 + t_0);
	} else {
		tmp = 6.0 * (x / t_0);
	}
	return tmp;
}

Python

def code(x):
	t_0 = x + (4.0 * math.sqrt(x))
	tmp = 0
	if x <= 1.0:
		tmp = -6.0 / (1.0 + t_0)
	else:
		tmp = 6.0 * (x / t_0)
	return tmp

Julia

function code(x)
	t_0 = Float64(x + Float64(4.0 * sqrt(x)))
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(-6.0 / Float64(1.0 + t_0));
	else
		tmp = Float64(6.0 * Float64(x / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x + (4.0 * sqrt(x));
	tmp = 0.0;
	if (x <= 1.0)
		tmp = -6.0 / (1.0 + t_0);
	else
		tmp = 6.0 * (x / t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.0], N[(-6.0 / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + \left(x + 4 \cdot \sqrt{x}\right)}} \]

   4. Taylor expanded in x around 0 98.1%

      \[\leadsto \frac{\color{blue}{-6}}{1 + \left(x + 4 \cdot \sqrt{x}\right)} \]

   if 1 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-1 \cdot \left(x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)}} \]

      2. distribute-rgt-neg-in 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]

      3. associate-*r* 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot {\left(\sqrt{-1}\right)}^{2}} - \left(1 + \frac{1}{x}\right)\right)\right)} \]

      4. fma-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, {\left(\sqrt{-1}\right)}^{2}, -\left(1 + \frac{1}{x}\right)\right)}\right)} \]

      5. unpow2 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{\sqrt{-1} \cdot \sqrt{-1}}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      6. rem-square-sqrt 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{-1}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      7. fma-undefine 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\left(\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)}\right)} \]

      8. *-commutative 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(\sqrt{\frac{1}{x}} \cdot 4\right)} \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      9. associate-*l* 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\sqrt{\frac{1}{x}} \cdot \left(4 \cdot -1\right)} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      10. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot \color{blue}{-4} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      11. distribute-neg-in 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(\left(-1\right) + \left(-\frac{1}{x}\right)\right)}\right)\right)} \]

      12. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(\color{blue}{-1} + \left(-\frac{1}{x}\right)\right)\right)\right)} \]

      13. sub-neg 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(-1 - \frac{1}{x}\right)}\right)\right)} \]

   5. Simplified 98.9%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(-1 - \frac{1}{x}\right)\right)\right)}} \]

   6. Taylor expanded in x around inf 96.6%

      \[\leadsto \color{blue}{\frac{6}{1 - -4 \cdot \sqrt{\frac{1}{x}}}} \]

   7. Taylor expanded in x around 0 96.6%

      \[\leadsto \frac{6}{\color{blue}{\frac{x - -4 \cdot \sqrt{x}}{x}}} \]
   8. Step-by-step derivation

      1. div-inv 96.6%

         \[\leadsto \color{blue}{6 \cdot \frac{1}{\frac{x - -4 \cdot \sqrt{x}}{x}}} \]

      2. clear-num 96.6%

         \[\leadsto 6 \cdot \color{blue}{\frac{x}{x - -4 \cdot \sqrt{x}}} \]

      3. cancel-sign-sub-inv 96.6%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{x + \left(--4\right) \cdot \sqrt{x}}} \]

      4. metadata-eval 96.6%

         \[\leadsto 6 \cdot \frac{x}{x + \color{blue}{4} \cdot \sqrt{x}} \]

   9. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{x + 4 \cdot \sqrt{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{-6}{1 + \left(x + 4 \cdot \sqrt{x}\right)}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{x}{x + 4 \cdot \sqrt{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{6 \cdot \left(x + -1\right)}{1 + \left(x + 4 \cdot \sqrt{x}\right)} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (* 6.0 (+ x -1.0)) (+ 1.0 (+ x (* 4.0 (sqrt x))))))

C

double code(double x) {
	return (6.0 * (x + -1.0)) / (1.0 + (x + (4.0 * sqrt(x))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (6.0d0 * (x + (-1.0d0))) / (1.0d0 + (x + (4.0d0 * sqrt(x))))
end function

Java

public static double code(double x) {
	return (6.0 * (x + -1.0)) / (1.0 + (x + (4.0 * Math.sqrt(x))));
}

Python

def code(x):
	return (6.0 * (x + -1.0)) / (1.0 + (x + (4.0 * math.sqrt(x))))

Julia

function code(x)
	return Float64(Float64(6.0 * Float64(x + -1.0)) / Float64(1.0 + Float64(x + Float64(4.0 * sqrt(x)))))
end

MATLAB

function tmp = code(x)
	tmp = (6.0 * (x + -1.0)) / (1.0 + (x + (4.0 * sqrt(x))));
end

Wolfram

code[x_] := N[(N[(6.0 * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(x + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 99.5%

   \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + \left(x + 4 \cdot \sqrt{x}\right)}} \]

4. Final simplification 99.5%

   \[\leadsto \frac{6 \cdot \left(x + -1\right)}{1 + \left(x + 4 \cdot \sqrt{x}\right)} \]
5. Add Preprocessing

Alternative 7: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.26:\\ \;\;\;\;\frac{-6}{1 + 4 \cdot \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-6}{\frac{4}{\sqrt{x}} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 0.26)
   (/ -6.0 (+ 1.0 (* 4.0 (sqrt x))))
   (/ -6.0 (+ (/ 4.0 (sqrt x)) -1.0))))

C

double code(double x) {
	double tmp;
	if (x <= 0.26) {
		tmp = -6.0 / (1.0 + (4.0 * sqrt(x)));
	} else {
		tmp = -6.0 / ((4.0 / sqrt(x)) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.26d0) then
        tmp = (-6.0d0) / (1.0d0 + (4.0d0 * sqrt(x)))
    else
        tmp = (-6.0d0) / ((4.0d0 / sqrt(x)) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.26) {
		tmp = -6.0 / (1.0 + (4.0 * Math.sqrt(x)));
	} else {
		tmp = -6.0 / ((4.0 / Math.sqrt(x)) + -1.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.26:
		tmp = -6.0 / (1.0 + (4.0 * math.sqrt(x)))
	else:
		tmp = -6.0 / ((4.0 / math.sqrt(x)) + -1.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.26)
		tmp = Float64(-6.0 / Float64(1.0 + Float64(4.0 * sqrt(x))));
	else
		tmp = Float64(-6.0 / Float64(Float64(4.0 / sqrt(x)) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.26)
		tmp = -6.0 / (1.0 + (4.0 * sqrt(x)));
	else
		tmp = -6.0 / ((4.0 / sqrt(x)) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.26], N[(-6.0 / N[(1.0 + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 / N[(N[(4.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.26000000000000001

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.6%

      \[\leadsto \color{blue}{\frac{-6}{1 + 4 \cdot \sqrt{x}}} \]

   if 0.26000000000000001 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-1 \cdot \left(x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)}} \]

      2. distribute-rgt-neg-in 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]

      3. associate-*r* 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot {\left(\sqrt{-1}\right)}^{2}} - \left(1 + \frac{1}{x}\right)\right)\right)} \]

      4. fma-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, {\left(\sqrt{-1}\right)}^{2}, -\left(1 + \frac{1}{x}\right)\right)}\right)} \]

      5. unpow2 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{\sqrt{-1} \cdot \sqrt{-1}}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      6. rem-square-sqrt 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{-1}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      7. fma-undefine 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\left(\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)}\right)} \]

      8. *-commutative 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(\sqrt{\frac{1}{x}} \cdot 4\right)} \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      9. associate-*l* 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\sqrt{\frac{1}{x}} \cdot \left(4 \cdot -1\right)} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      10. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot \color{blue}{-4} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      11. distribute-neg-in 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(\left(-1\right) + \left(-\frac{1}{x}\right)\right)}\right)\right)} \]

      12. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(\color{blue}{-1} + \left(-\frac{1}{x}\right)\right)\right)\right)} \]

      13. sub-neg 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(-1 - \frac{1}{x}\right)}\right)\right)} \]

   5. Simplified 98.9%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(-1 - \frac{1}{x}\right)\right)\right)}} \]

   6. Taylor expanded in x around inf 95.8%

      \[\leadsto \color{blue}{\frac{6}{1 - -4 \cdot \sqrt{\frac{1}{x}}}} \]
   7. Step-by-step derivation

      1. frac-2neg 95.8%

         \[\leadsto \color{blue}{\frac{-6}{-\left(1 - -4 \cdot \sqrt{\frac{1}{x}}\right)}} \]

      2. metadata-eval 95.8%

         \[\leadsto \frac{\color{blue}{-6}}{-\left(1 - -4 \cdot \sqrt{\frac{1}{x}}\right)} \]

      3. div-inv 95.8%

         \[\leadsto \color{blue}{-6 \cdot \frac{1}{-\left(1 - -4 \cdot \sqrt{\frac{1}{x}}\right)}} \]

      4. cancel-sign-sub-inv 95.8%

         \[\leadsto -6 \cdot \frac{1}{-\color{blue}{\left(1 + \left(--4\right) \cdot \sqrt{\frac{1}{x}}\right)}} \]

      5. metadata-eval 95.8%

         \[\leadsto -6 \cdot \frac{1}{-\left(1 + \color{blue}{4} \cdot \sqrt{\frac{1}{x}}\right)} \]

      6. +-commutative 95.8%

         \[\leadsto -6 \cdot \frac{1}{-\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}} + 1\right)}} \]

      7. distribute-neg-in 95.8%

         \[\leadsto -6 \cdot \frac{1}{\color{blue}{\left(-4 \cdot \sqrt{\frac{1}{x}}\right) + \left(-1\right)}} \]

   8. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{-6 \cdot \frac{1}{\frac{4}{\sqrt{x}} + -1}} \]
   9. Step-by-step derivation

      1. associate-*r/ 92.3%

         \[\leadsto \color{blue}{\frac{-6 \cdot 1}{\frac{4}{\sqrt{x}} + -1}} \]

      2. metadata-eval 92.3%

         \[\leadsto \frac{\color{blue}{-6}}{\frac{4}{\sqrt{x}} + -1} \]

      3. +-commutative 92.3%

         \[\leadsto \frac{-6}{\color{blue}{-1 + \frac{4}{\sqrt{x}}}} \]

   10. Simplified 92.3%

       \[\leadsto \color{blue}{\frac{-6}{-1 + \frac{4}{\sqrt{x}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.26:\\ \;\;\;\;\frac{-6}{1 + 4 \cdot \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-6}{\frac{4}{\sqrt{x}} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{-6}{1 + 4 \cdot \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{6}{1 + \frac{4}{\sqrt{x}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.0)
   (/ -6.0 (+ 1.0 (* 4.0 (sqrt x))))
   (/ 6.0 (+ 1.0 (/ 4.0 (sqrt x))))))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = -6.0 / (1.0 + (4.0 * sqrt(x)));
	} else {
		tmp = 6.0 / (1.0 + (4.0 / sqrt(x)));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = (-6.0d0) / (1.0d0 + (4.0d0 * sqrt(x)))
    else
        tmp = 6.0d0 / (1.0d0 + (4.0d0 / sqrt(x)))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = -6.0 / (1.0 + (4.0 * Math.sqrt(x)));
	} else {
		tmp = 6.0 / (1.0 + (4.0 / Math.sqrt(x)));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = -6.0 / (1.0 + (4.0 * math.sqrt(x)))
	else:
		tmp = 6.0 / (1.0 + (4.0 / math.sqrt(x)))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(-6.0 / Float64(1.0 + Float64(4.0 * sqrt(x))));
	else
		tmp = Float64(6.0 / Float64(1.0 + Float64(4.0 / sqrt(x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = -6.0 / (1.0 + (4.0 * sqrt(x)));
	else
		tmp = 6.0 / (1.0 + (4.0 / sqrt(x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], N[(-6.0 / N[(1.0 + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 / N[(1.0 + N[(4.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.1%

      \[\leadsto \color{blue}{\frac{-6}{1 + 4 \cdot \sqrt{x}}} \]

   if 1 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-1 \cdot \left(x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)}} \]

      2. distribute-rgt-neg-in 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]

      3. associate-*r* 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot {\left(\sqrt{-1}\right)}^{2}} - \left(1 + \frac{1}{x}\right)\right)\right)} \]

      4. fma-neg 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, {\left(\sqrt{-1}\right)}^{2}, -\left(1 + \frac{1}{x}\right)\right)}\right)} \]

      5. unpow2 0.0%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{\sqrt{-1} \cdot \sqrt{-1}}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      6. rem-square-sqrt 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{-1}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

      7. fma-undefine 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\left(\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)}\right)} \]

      8. *-commutative 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(\sqrt{\frac{1}{x}} \cdot 4\right)} \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      9. associate-*l* 98.9%

         \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\sqrt{\frac{1}{x}} \cdot \left(4 \cdot -1\right)} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      10. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot \color{blue}{-4} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

      11. distribute-neg-in 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(\left(-1\right) + \left(-\frac{1}{x}\right)\right)}\right)\right)} \]

      12. metadata-eval 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(\color{blue}{-1} + \left(-\frac{1}{x}\right)\right)\right)\right)} \]

      13. sub-neg 98.9%

          \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(-1 - \frac{1}{x}\right)}\right)\right)} \]

   5. Simplified 98.9%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(-1 - \frac{1}{x}\right)\right)\right)}} \]

   6. Taylor expanded in x around inf 96.6%

      \[\leadsto \color{blue}{\frac{6}{1 - -4 \cdot \sqrt{\frac{1}{x}}}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 96.6%

         \[\leadsto \frac{6}{\color{blue}{1 + \left(--4\right) \cdot \sqrt{\frac{1}{x}}}} \]

      2. metadata-eval 96.6%

         \[\leadsto \frac{6}{1 + \color{blue}{4} \cdot \sqrt{\frac{1}{x}}} \]

      3. +-commutative 96.6%

         \[\leadsto \frac{6}{\color{blue}{4 \cdot \sqrt{\frac{1}{x}} + 1}} \]

      4. sqrt-div 96.6%

         \[\leadsto \frac{6}{4 \cdot \color{blue}{\frac{\sqrt{1}}{\sqrt{x}}} + 1} \]

      5. metadata-eval 96.6%

         \[\leadsto \frac{6}{4 \cdot \frac{\color{blue}{1}}{\sqrt{x}} + 1} \]

      6. un-div-inv 96.6%

         \[\leadsto \frac{6}{\color{blue}{\frac{4}{\sqrt{x}}} + 1} \]

   8. Applied egg-rr 96.6%

      \[\leadsto \frac{6}{\color{blue}{\frac{4}{\sqrt{x}} + 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\frac{-6}{1 + 4 \cdot \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{6}{1 + \frac{4}{\sqrt{x}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 7.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\sqrt{\frac{1}{x}} \cdot -1.5\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.0) (* (sqrt (/ 1.0 x)) -1.5) (* (sqrt x) 1.5)))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = sqrt((1.0 / x)) * -1.5;
	} else {
		tmp = sqrt(x) * 1.5;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = sqrt((1.0d0 / x)) * (-1.5d0)
    else
        tmp = sqrt(x) * 1.5d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = Math.sqrt((1.0 / x)) * -1.5;
	} else {
		tmp = Math.sqrt(x) * 1.5;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = math.sqrt((1.0 / x)) * -1.5
	else:
		tmp = math.sqrt(x) * 1.5
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(sqrt(Float64(1.0 / x)) * -1.5);
	else
		tmp = Float64(sqrt(x) * 1.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = sqrt((1.0 / x)) * -1.5;
	else
		tmp = sqrt(x) * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], N[(N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision] * -1.5), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * 1.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.1%

      \[\leadsto \color{blue}{\frac{-6}{1 + 4 \cdot \sqrt{x}}} \]

   4. Taylor expanded in x around inf 6.9%

      \[\leadsto \color{blue}{-1.5 \cdot \sqrt{\frac{1}{x}}} \]
   5. Step-by-step derivation

      1. *-commutative 6.9%

         \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot -1.5} \]

   6. Simplified 6.9%

      \[\leadsto \color{blue}{\sqrt{\frac{1}{x}} \cdot -1.5} \]

   if 1 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 7.2%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + 4 \cdot \sqrt{x}}} \]

   4. Taylor expanded in x around inf 7.2%

      \[\leadsto \color{blue}{1.5 \cdot \sqrt{x}} \]
   5. Step-by-step derivation

      1. *-commutative 7.2%

         \[\leadsto \color{blue}{\sqrt{x} \cdot 1.5} \]

   6. Simplified 7.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot 1.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 7.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\sqrt{\frac{1}{x}} \cdot -1.5\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 6.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\sqrt{x} \cdot -1.5\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 2.25}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.0) (* (sqrt x) -1.5) (sqrt (* x 2.25))))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = sqrt(x) * -1.5;
	} else {
		tmp = sqrt((x * 2.25));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = sqrt(x) * (-1.5d0)
    else
        tmp = sqrt((x * 2.25d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = Math.sqrt(x) * -1.5;
	} else {
		tmp = Math.sqrt((x * 2.25));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = math.sqrt(x) * -1.5
	else:
		tmp = math.sqrt((x * 2.25))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(sqrt(x) * -1.5);
	else
		tmp = sqrt(Float64(x * 2.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = sqrt(x) * -1.5;
	else
		tmp = sqrt((x * 2.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], N[(N[Sqrt[x], $MachinePrecision] * -1.5), $MachinePrecision], N[Sqrt[N[(x * 2.25), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + 4 \cdot \sqrt{x}}} \]

   4. Taylor expanded in x around -inf 6.9%

      \[\leadsto \color{blue}{-1.5 \cdot \sqrt{x}} \]
   5. Step-by-step derivation

      1. *-commutative 6.9%

         \[\leadsto \color{blue}{\sqrt{x} \cdot -1.5} \]

   6. Simplified 6.9%

      \[\leadsto \color{blue}{\sqrt{x} \cdot -1.5} \]

   if 1 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 7.2%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + 4 \cdot \sqrt{x}}} \]

   4. Taylor expanded in x around -inf 1.3%

      \[\leadsto \color{blue}{-1.5 \cdot \sqrt{x}} \]
   5. Step-by-step derivation

      1. *-commutative 1.3%

         \[\leadsto \color{blue}{\sqrt{x} \cdot -1.5} \]

   6. Simplified 1.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot -1.5} \]
   7. Step-by-step derivation

      1. pow1 1.3%

         \[\leadsto \color{blue}{{\left(\sqrt{x} \cdot -1.5\right)}^{1}} \]

      2. add-sqr-sqrt 0.0%

         \[\leadsto {\color{blue}{\left(\sqrt{\sqrt{x} \cdot -1.5} \cdot \sqrt{\sqrt{x} \cdot -1.5}\right)}}^{1} \]

      3. sqrt-unprod 7.2%

         \[\leadsto {\color{blue}{\left(\sqrt{\left(\sqrt{x} \cdot -1.5\right) \cdot \left(\sqrt{x} \cdot -1.5\right)}\right)}}^{1} \]

      4. swap-sqr 7.2%

         \[\leadsto {\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-1.5 \cdot -1.5\right)}}\right)}^{1} \]

      5. add-sqr-sqrt 7.2%

         \[\leadsto {\left(\sqrt{\color{blue}{x} \cdot \left(-1.5 \cdot -1.5\right)}\right)}^{1} \]

      6. metadata-eval 7.2%

         \[\leadsto {\left(\sqrt{x \cdot \color{blue}{2.25}}\right)}^{1} \]

   8. Applied egg-rr 7.2%

      \[\leadsto \color{blue}{{\left(\sqrt{x \cdot 2.25}\right)}^{1}} \]
   9. Step-by-step derivation

      1. unpow1 7.2%

         \[\leadsto \color{blue}{\sqrt{x \cdot 2.25}} \]

   10. Simplified 7.2%

       \[\leadsto \color{blue}{\sqrt{x \cdot 2.25}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 7.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\sqrt{x} \cdot -1.5\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 2.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 6.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\sqrt{x} \cdot -1.5\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot 1.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.0) (* (sqrt x) -1.5) (* (sqrt x) 1.5)))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = sqrt(x) * -1.5;
	} else {
		tmp = sqrt(x) * 1.5;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = sqrt(x) * (-1.5d0)
    else
        tmp = sqrt(x) * 1.5d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = Math.sqrt(x) * -1.5;
	} else {
		tmp = Math.sqrt(x) * 1.5;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = math.sqrt(x) * -1.5
	else:
		tmp = math.sqrt(x) * 1.5
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(sqrt(x) * -1.5);
	else
		tmp = Float64(sqrt(x) * 1.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = sqrt(x) * -1.5;
	else
		tmp = sqrt(x) * 1.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], N[(N[Sqrt[x], $MachinePrecision] * -1.5), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * 1.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 100.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + 4 \cdot \sqrt{x}}} \]

   4. Taylor expanded in x around -inf 6.9%

      \[\leadsto \color{blue}{-1.5 \cdot \sqrt{x}} \]
   5. Step-by-step derivation

      1. *-commutative 6.9%

         \[\leadsto \color{blue}{\sqrt{x} \cdot -1.5} \]

   6. Simplified 6.9%

      \[\leadsto \color{blue}{\sqrt{x} \cdot -1.5} \]

   if 1 < x

   1. Initial program 98.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 7.2%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + 4 \cdot \sqrt{x}}} \]

   4. Taylor expanded in x around inf 7.2%

      \[\leadsto \color{blue}{1.5 \cdot \sqrt{x}} \]
   5. Step-by-step derivation

      1. *-commutative 7.2%

         \[\leadsto \color{blue}{\sqrt{x} \cdot 1.5} \]

   6. Simplified 7.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot 1.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 7.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;\sqrt{x} \cdot -1.5\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot 1.5\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{-6}{\frac{4}{\sqrt{x}} + -1} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ -6.0 (+ (/ 4.0 (sqrt x)) -1.0)))

C

double code(double x) {
	return -6.0 / ((4.0 / sqrt(x)) + -1.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (-6.0d0) / ((4.0d0 / sqrt(x)) + (-1.0d0))
end function

Java

public static double code(double x) {
	return -6.0 / ((4.0 / Math.sqrt(x)) + -1.0);
}

Python

def code(x):
	return -6.0 / ((4.0 / math.sqrt(x)) + -1.0)

Julia

function code(x)
	return Float64(-6.0 / Float64(Float64(4.0 / sqrt(x)) + -1.0))
end

MATLAB

function tmp = code(x)
	tmp = -6.0 / ((4.0 / sqrt(x)) + -1.0);
end

Wolfram

code[x_] := N[(-6.0 / N[(N[(4.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
2. Add Preprocessing

3. Taylor expanded in x around -inf 0.0%

   \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-1 \cdot \left(x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]
4. Step-by-step derivation

   1. mul-1-neg 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{-x \cdot \left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)}} \]

   2. distribute-rgt-neg-in 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(4 \cdot \left(\sqrt{\frac{1}{x}} \cdot {\left(\sqrt{-1}\right)}^{2}\right) - \left(1 + \frac{1}{x}\right)\right)\right)}} \]

   3. associate-*r* 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot {\left(\sqrt{-1}\right)}^{2}} - \left(1 + \frac{1}{x}\right)\right)\right)} \]

   4. fma-neg 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, {\left(\sqrt{-1}\right)}^{2}, -\left(1 + \frac{1}{x}\right)\right)}\right)} \]

   5. unpow2 0.0%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{\sqrt{-1} \cdot \sqrt{-1}}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

   6. rem-square-sqrt 99.4%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\mathsf{fma}\left(4 \cdot \sqrt{\frac{1}{x}}, \color{blue}{-1}, -\left(1 + \frac{1}{x}\right)\right)\right)} \]

   7. fma-undefine 99.4%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\color{blue}{\left(\left(4 \cdot \sqrt{\frac{1}{x}}\right) \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)}\right)} \]

   8. *-commutative 99.4%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\left(\sqrt{\frac{1}{x}} \cdot 4\right)} \cdot -1 + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

   9. associate-*l* 99.4%

      \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\color{blue}{\sqrt{\frac{1}{x}} \cdot \left(4 \cdot -1\right)} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

   10. metadata-eval 99.4%

       \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot \color{blue}{-4} + \left(-\left(1 + \frac{1}{x}\right)\right)\right)\right)} \]

   11. distribute-neg-in 99.4%

       \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(\left(-1\right) + \left(-\frac{1}{x}\right)\right)}\right)\right)} \]

   12. metadata-eval 99.4%

       \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(\color{blue}{-1} + \left(-\frac{1}{x}\right)\right)\right)\right)} \]

   13. sub-neg 99.4%

       \[\leadsto \frac{6 \cdot \left(x - 1\right)}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \color{blue}{\left(-1 - \frac{1}{x}\right)}\right)\right)} \]

5. Simplified 99.4%

   \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{x \cdot \left(-\left(\sqrt{\frac{1}{x}} \cdot -4 + \left(-1 - \frac{1}{x}\right)\right)\right)}} \]

6. Taylor expanded in x around inf 44.8%

   \[\leadsto \color{blue}{\frac{6}{1 - -4 \cdot \sqrt{\frac{1}{x}}}} \]
7. Step-by-step derivation

   1. frac-2neg 44.8%

      \[\leadsto \color{blue}{\frac{-6}{-\left(1 - -4 \cdot \sqrt{\frac{1}{x}}\right)}} \]

   2. metadata-eval 44.8%

      \[\leadsto \frac{\color{blue}{-6}}{-\left(1 - -4 \cdot \sqrt{\frac{1}{x}}\right)} \]

   3. div-inv 44.8%

      \[\leadsto \color{blue}{-6 \cdot \frac{1}{-\left(1 - -4 \cdot \sqrt{\frac{1}{x}}\right)}} \]

   4. cancel-sign-sub-inv 44.8%

      \[\leadsto -6 \cdot \frac{1}{-\color{blue}{\left(1 + \left(--4\right) \cdot \sqrt{\frac{1}{x}}\right)}} \]

   5. metadata-eval 44.8%

      \[\leadsto -6 \cdot \frac{1}{-\left(1 + \color{blue}{4} \cdot \sqrt{\frac{1}{x}}\right)} \]

   6. +-commutative 44.8%

      \[\leadsto -6 \cdot \frac{1}{-\color{blue}{\left(4 \cdot \sqrt{\frac{1}{x}} + 1\right)}} \]

   7. distribute-neg-in 44.8%

      \[\leadsto -6 \cdot \frac{1}{\color{blue}{\left(-4 \cdot \sqrt{\frac{1}{x}}\right) + \left(-1\right)}} \]

8. Applied egg-rr 45.9%

   \[\leadsto \color{blue}{-6 \cdot \frac{1}{\frac{4}{\sqrt{x}} + -1}} \]
9. Step-by-step derivation

   1. associate-*r/ 45.9%

      \[\leadsto \color{blue}{\frac{-6 \cdot 1}{\frac{4}{\sqrt{x}} + -1}} \]

   2. metadata-eval 45.9%

      \[\leadsto \frac{\color{blue}{-6}}{\frac{4}{\sqrt{x}} + -1} \]

   3. +-commutative 45.9%

      \[\leadsto \frac{-6}{\color{blue}{-1 + \frac{4}{\sqrt{x}}}} \]

10. Simplified 45.9%

    \[\leadsto \color{blue}{\frac{-6}{-1 + \frac{4}{\sqrt{x}}}} \]

11. Final simplification 45.9%

    \[\leadsto \frac{-6}{\frac{4}{\sqrt{x}} + -1} \]
12. Add Preprocessing

Alternative 13: 4.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{x \cdot 2.25} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (sqrt (* x 2.25)))

C

double code(double x) {
	return sqrt((x * 2.25));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((x * 2.25d0))
end function

Java

public static double code(double x) {
	return Math.sqrt((x * 2.25));
}

Python

def code(x):
	return math.sqrt((x * 2.25))

Julia

function code(x)
	return sqrt(Float64(x * 2.25))
end

MATLAB

function tmp = code(x)
	tmp = sqrt((x * 2.25));
end

Wolfram

code[x_] := N[Sqrt[N[(x * 2.25), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 56.9%

   \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 + 4 \cdot \sqrt{x}}} \]

4. Taylor expanded in x around -inf 4.4%

   \[\leadsto \color{blue}{-1.5 \cdot \sqrt{x}} \]
5. Step-by-step derivation

   1. *-commutative 4.4%

      \[\leadsto \color{blue}{\sqrt{x} \cdot -1.5} \]

6. Simplified 4.4%

   \[\leadsto \color{blue}{\sqrt{x} \cdot -1.5} \]
7. Step-by-step derivation

   1. pow1 4.4%

      \[\leadsto \color{blue}{{\left(\sqrt{x} \cdot -1.5\right)}^{1}} \]

   2. add-sqr-sqrt 0.0%

      \[\leadsto {\color{blue}{\left(\sqrt{\sqrt{x} \cdot -1.5} \cdot \sqrt{\sqrt{x} \cdot -1.5}\right)}}^{1} \]

   3. sqrt-unprod 4.3%

      \[\leadsto {\color{blue}{\left(\sqrt{\left(\sqrt{x} \cdot -1.5\right) \cdot \left(\sqrt{x} \cdot -1.5\right)}\right)}}^{1} \]

   4. swap-sqr 4.3%

      \[\leadsto {\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-1.5 \cdot -1.5\right)}}\right)}^{1} \]

   5. add-sqr-sqrt 4.3%

      \[\leadsto {\left(\sqrt{\color{blue}{x} \cdot \left(-1.5 \cdot -1.5\right)}\right)}^{1} \]

   6. metadata-eval 4.3%

      \[\leadsto {\left(\sqrt{x \cdot \color{blue}{2.25}}\right)}^{1} \]

8. Applied egg-rr 4.3%

   \[\leadsto \color{blue}{{\left(\sqrt{x \cdot 2.25}\right)}^{1}} \]
9. Step-by-step derivation

   1. unpow1 4.3%

      \[\leadsto \color{blue}{\sqrt{x \cdot 2.25}} \]

10. Simplified 4.3%

    \[\leadsto \color{blue}{\sqrt{x \cdot 2.25}} \]

11. Final simplification 4.3%

    \[\leadsto \sqrt{x \cdot 2.25} \]
12. Add Preprocessing

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))))

C

double code(double x) {
	return 6.0 / (((x + 1.0) + (4.0 * sqrt(x))) / (x - 1.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 6.0d0 / (((x + 1.0d0) + (4.0d0 * sqrt(x))) / (x - 1.0d0))
end function

Java

public static double code(double x) {
	return 6.0 / (((x + 1.0) + (4.0 * Math.sqrt(x))) / (x - 1.0));
}

Python

def code(x):
	return 6.0 / (((x + 1.0) + (4.0 * math.sqrt(x))) / (x - 1.0))

Julia

function code(x)
	return Float64(6.0 / Float64(Float64(Float64(x + 1.0) + Float64(4.0 * sqrt(x))) / Float64(x - 1.0)))
end

MATLAB

function tmp = code(x)
	tmp = 6.0 / (((x + 1.0) + (4.0 * sqrt(x))) / (x - 1.0));
end

Wolfram

code[x_] := N[(6.0 / N[(N[(N[(x + 1.0), $MachinePrecision] + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024096 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"
  :precision binary64

  :alt
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))