3frac (problem 3.3.3)

Percentage Accurate: 68.3% → 99.5%

Time: 9.4s

Alternatives: 7

Speedup: 1.7×

Specification

\[\left|x\right| > 1\]

Math

\[\begin{array}{l} \\ \left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

C

double code(double x) {
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((1.0d0 / (x + 1.0d0)) - (2.0d0 / x)) + (1.0d0 / (x - 1.0d0))
end function

Java

public static double code(double x) {
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
}

Python

def code(x):
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0))

Julia

function code(x)
	return Float64(Float64(Float64(1.0 / Float64(x + 1.0)) - Float64(2.0 / x)) + Float64(1.0 / Float64(x - 1.0)))
end

MATLAB

function tmp = code(x)
	tmp = ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
end

Wolfram

code[x_] := N[(N[(N[(1.0 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

C

double code(double x) {
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((1.0d0 / (x + 1.0d0)) - (2.0d0 / x)) + (1.0d0 / (x - 1.0d0))
end function

Java

public static double code(double x) {
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
}

Python

def code(x):
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0))

Julia

function code(x)
	return Float64(Float64(Float64(1.0 / Float64(x + 1.0)) - Float64(2.0 / x)) + Float64(1.0 / Float64(x - 1.0)))
end

MATLAB

function tmp = code(x)
	tmp = ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
end

Wolfram

code[x_] := N[(N[(N[(1.0 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(2, {x}^{-2}, 2\right) \cdot {x}^{-3} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (fma 2.0 (pow x -2.0) 2.0) (pow x -3.0)))

C

double code(double x) {
	return fma(2.0, pow(x, -2.0), 2.0) * pow(x, -3.0);
}

Julia

function code(x)
	return Float64(fma(2.0, (x ^ -2.0), 2.0) * (x ^ -3.0))
end

Wolfram

code[x_] := N[(N[(2.0 * N[Power[x, -2.0], $MachinePrecision] + 2.0), $MachinePrecision] * N[Power[x, -3.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.8%

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

3. Taylor expanded in x around inf 98.6%

   \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{{x}^{2}}}{{x}^{3}}} \]
4. Step-by-step derivation

   1. associate-*r/ 98.6%

      \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{{x}^{2}}}}{{x}^{3}} \]

   2. metadata-eval 98.6%

      \[\leadsto \frac{2 + \frac{\color{blue}{2}}{{x}^{2}}}{{x}^{3}} \]

5. Simplified 98.6%

   \[\leadsto \color{blue}{\frac{2 + \frac{2}{{x}^{2}}}{{x}^{3}}} \]
6. Step-by-step derivation

   1. div-inv 98.6%

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

   2. +-commutative 98.6%

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

   3. div-inv 98.6%

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

   4. fma-define 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, \frac{1}{{x}^{2}}, 2\right)} \cdot \frac{1}{{x}^{3}} \]

   5. pow-flip 98.6%

      \[\leadsto \mathsf{fma}\left(2, \color{blue}{{x}^{\left(-2\right)}}, 2\right) \cdot \frac{1}{{x}^{3}} \]

   6. metadata-eval 98.6%

      \[\leadsto \mathsf{fma}\left(2, {x}^{\color{blue}{-2}}, 2\right) \cdot \frac{1}{{x}^{3}} \]

   7. pow-flip 99.5%

      \[\leadsto \mathsf{fma}\left(2, {x}^{-2}, 2\right) \cdot \color{blue}{{x}^{\left(-3\right)}} \]

   8. metadata-eval 99.5%

      \[\leadsto \mathsf{fma}\left(2, {x}^{-2}, 2\right) \cdot {x}^{\color{blue}{-3}} \]

7. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2, {x}^{-2}, 2\right) \cdot {x}^{-3}} \]
8. Add Preprocessing

Alternative 2: 99.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2 + \frac{2}{{x}^{2}}}{{x}^{2}}}{x} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (/ (+ 2.0 (/ 2.0 (pow x 2.0))) (pow x 2.0)) x))

C

double code(double x) {
	return ((2.0 + (2.0 / pow(x, 2.0))) / pow(x, 2.0)) / x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((2.0d0 + (2.0d0 / (x ** 2.0d0))) / (x ** 2.0d0)) / x
end function

Java

public static double code(double x) {
	return ((2.0 + (2.0 / Math.pow(x, 2.0))) / Math.pow(x, 2.0)) / x;
}

Python

def code(x):
	return ((2.0 + (2.0 / math.pow(x, 2.0))) / math.pow(x, 2.0)) / x

Julia

function code(x)
	return Float64(Float64(Float64(2.0 + Float64(2.0 / (x ^ 2.0))) / (x ^ 2.0)) / x)
end

MATLAB

function tmp = code(x)
	tmp = ((2.0 + (2.0 / (x ^ 2.0))) / (x ^ 2.0)) / x;
end

Wolfram

code[x_] := N[(N[(N[(2.0 + N[(2.0 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]

Derivation

1. Initial program 73.8%

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

3. Taylor expanded in x around inf 98.6%

   \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{{x}^{2}}}{{x}^{3}}} \]
4. Step-by-step derivation

   1. associate-*r/ 98.6%

      \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{{x}^{2}}}}{{x}^{3}} \]

   2. metadata-eval 98.6%

      \[\leadsto \frac{2 + \frac{\color{blue}{2}}{{x}^{2}}}{{x}^{3}} \]

5. Simplified 98.6%

   \[\leadsto \color{blue}{\frac{2 + \frac{2}{{x}^{2}}}{{x}^{3}}} \]
6. Step-by-step derivation

   1. *-un-lft-identity 98.6%

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

   2. cube-mult 98.6%

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

   3. unpow2 98.6%

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

   4. times-frac 99.4%

      \[\leadsto \color{blue}{\frac{1}{x} \cdot \frac{2 + \frac{2}{{x}^{2}}}{{x}^{2}}} \]

   5. +-commutative 99.4%

      \[\leadsto \frac{1}{x} \cdot \frac{\color{blue}{\frac{2}{{x}^{2}} + 2}}{{x}^{2}} \]

   6. div-inv 99.4%

      \[\leadsto \frac{1}{x} \cdot \frac{\color{blue}{2 \cdot \frac{1}{{x}^{2}}} + 2}{{x}^{2}} \]

   7. fma-define 99.4%

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

   8. pow-flip 99.4%

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

   9. metadata-eval 99.4%

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

7. Applied egg-rr 99.4%

   \[\leadsto \color{blue}{\frac{1}{x} \cdot \frac{\mathsf{fma}\left(2, {x}^{-2}, 2\right)}{{x}^{2}}} \]
8. Step-by-step derivation

   1. associate-*l/ 99.4%

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

   2. *-lft-identity 99.4%

      \[\leadsto \frac{\color{blue}{\frac{\mathsf{fma}\left(2, {x}^{-2}, 2\right)}{{x}^{2}}}}{x} \]

9. Simplified 99.4%

   \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(2, {x}^{-2}, 2\right)}{{x}^{2}}}{x}} \]

10. Taylor expanded in x around inf 99.4%

    \[\leadsto \frac{\color{blue}{\frac{2 + 2 \cdot \frac{1}{{x}^{2}}}{{x}^{2}}}}{x} \]
11. Step-by-step derivation

    1. associate-*r/ 99.4%

       \[\leadsto \frac{\frac{2 + \color{blue}{\frac{2 \cdot 1}{{x}^{2}}}}{{x}^{2}}}{x} \]

    2. metadata-eval 99.4%

       \[\leadsto \frac{\frac{2 + \frac{\color{blue}{2}}{{x}^{2}}}{{x}^{2}}}{x} \]

12. Simplified 99.4%

    \[\leadsto \frac{\color{blue}{\frac{2 + \frac{2}{{x}^{2}}}{{x}^{2}}}}{x} \]
13. Add Preprocessing

Alternative 3: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ 2 \cdot {x}^{-3} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 2.0 (pow x -3.0)))

C

double code(double x) {
	return 2.0 * pow(x, -3.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.0d0 * (x ** (-3.0d0))
end function

Java

public static double code(double x) {
	return 2.0 * Math.pow(x, -3.0);
}

Python

def code(x):
	return 2.0 * math.pow(x, -3.0)

Julia

function code(x)
	return Float64(2.0 * (x ^ -3.0))
end

MATLAB

function tmp = code(x)
	tmp = 2.0 * (x ^ -3.0);
end

Wolfram

code[x_] := N[(2.0 * N[Power[x, -3.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.8%

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

3. Taylor expanded in x around inf 98.1%

   \[\leadsto \color{blue}{\frac{2}{{x}^{3}}} \]
4. Step-by-step derivation

   1. div-inv 98.1%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{3}}} \]

   2. pow-flip 99.0%

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

   3. metadata-eval 99.0%

      \[\leadsto 2 \cdot {x}^{\color{blue}{-3}} \]

5. Applied egg-rr 99.0%

   \[\leadsto \color{blue}{2 \cdot {x}^{-3}} \]
6. Add Preprocessing

Alternative 4: 71.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

public static double code(double x) {
	return (1.0 / x) / (x * (x + -1.0));
}

Python

def code(x):
	return (1.0 / x) / (x * (x + -1.0))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.8%

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

3. Taylor expanded in x around inf 72.7%

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

   1. associate-*r/ 72.7%

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

   2. neg-mul-1 72.7%

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

   3. distribute-neg-in 72.7%

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

   4. metadata-eval 72.7%

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

   5. unsub-neg 72.7%

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

5. Simplified 72.7%

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

   1. +-commutative 72.7%

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

   2. frac-add 72.7%

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

   3. *-un-lft-identity 72.7%

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

   4. sub-neg 72.7%

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

   5. metadata-eval 72.7%

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

   6. sub-neg 72.7%

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

   7. neg-mul-1 72.7%

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

   8. div-inv 72.7%

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

   9. sub-neg 72.7%

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

   10. metadata-eval 72.7%

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

7. Applied egg-rr 72.7%

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

8. Taylor expanded in x around 0 76.1%

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

9. Final simplification 76.1%

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

Alternative 5: 67.0% accurate, 1.7× speedup

Math

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

FPCore

(FPCore (x) :precision binary64 (+ (/ -1.0 x) (/ 1.0 (+ x -1.0))))

C

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

Fortran

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

Java

public static double code(double x) {
	return (-1.0 / x) + (1.0 / (x + -1.0));
}

Python

def code(x):
	return (-1.0 / x) + (1.0 / (x + -1.0))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.8%

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

3. Taylor expanded in x around inf 72.4%

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

4. Final simplification 72.4%

   \[\leadsto \frac{-1}{x} + \frac{1}{x + -1} \]
5. Add Preprocessing

Alternative 6: 5.0% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \frac{-2}{x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ -2.0 x))

C

double code(double x) {
	return -2.0 / x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (-2.0d0) / x
end function

Java

public static double code(double x) {
	return -2.0 / x;
}

Python

def code(x):
	return -2.0 / x

Julia

function code(x)
	return Float64(-2.0 / x)
end

MATLAB

function tmp = code(x)
	tmp = -2.0 / x;
end

Wolfram

code[x_] := N[(-2.0 / x), $MachinePrecision]

Derivation

1. Initial program 73.8%

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

3. Taylor expanded in x around 0 5.0%

   \[\leadsto \color{blue}{\frac{-2}{x}} \]
4. Add Preprocessing

Alternative 7: 3.4% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0
end function

Java

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

1. Initial program 73.8%

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

3. Taylor expanded in x around 0 3.4%

   \[\leadsto \color{blue}{\frac{x - 2}{x}} + \frac{1}{x - 1} \]

4. Taylor expanded in x around inf 3.4%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Developer target: 99.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \frac{2}{x \cdot \left(x \cdot x - 1\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 2.0 (* x (- (* x x) 1.0))))

C

double code(double x) {
	return 2.0 / (x * ((x * x) - 1.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 2.0d0 / (x * ((x * x) - 1.0d0))
end function

Java

public static double code(double x) {
	return 2.0 / (x * ((x * x) - 1.0));
}

Python

def code(x):
	return 2.0 / (x * ((x * x) - 1.0))

Julia

function code(x)
	return Float64(2.0 / Float64(x * Float64(Float64(x * x) - 1.0)))
end

MATLAB

function tmp = code(x)
	tmp = 2.0 / (x * ((x * x) - 1.0));
end

Wolfram

code[x_] := N[(2.0 / N[(x * N[(N[(x * x), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024096 
(FPCore (x)
  :name "3frac (problem 3.3.3)"
  :precision binary64
  :pre (> (fabs x) 1.0)

  :alt
  (/ 2.0 (* x (- (* x x) 1.0)))

  (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))