3frac (problem 3.3.3)

Percentage Accurate: 85.6% → 99.6%

Time: 8.5s

Alternatives: 5

Speedup: 1.4×

Specification

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: 85.6% 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: 99.6% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.1%

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

3. Simplified 83.1%

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

   1. frac-2neg 83.1%

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

   2. frac-2neg 83.1%

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

   3. metadata-eval 83.1%

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

   4. frac-sub 54.8%

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

   5. metadata-eval 54.8%

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

   6. +-commutative 54.8%

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

   7. distribute-neg-in 54.8%

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

   8. metadata-eval 54.8%

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

   9. sub-neg 54.8%

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

   10. +-commutative 54.8%

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

   11. distribute-neg-in 54.8%

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

   12. metadata-eval 54.8%

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

   13. sub-neg 54.8%

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

5. Applied egg-rr 54.8%

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

   1. cancel-sign-sub 54.8%

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

   2. *-commutative 54.8%

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

   3. neg-mul-1 54.8%

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

   4. unsub-neg 54.8%

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

   5. sub-neg 54.8%

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

   6. distribute-lft-in 54.9%

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

   7. sqr-neg 54.9%

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

   8. unpow2 54.9%

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

   9. *-rgt-identity 54.9%

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

   10. +-commutative 54.9%

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

   11. sub-neg 54.9%

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

   12. unpow2 54.9%

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

7. Simplified 54.9%

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

   1. frac-sub 53.9%

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

   2. *-un-lft-identity 53.9%

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

9. Applied egg-rr 53.9%

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

10. Taylor expanded in x around 0 99.7%

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

11. Final simplification 99.7%

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

Alternative 2: 84.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;-1 + \left(1 - \frac{-2}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0)))
   (+ -1.0 (- 1.0 (/ -2.0 x)))
   (- (/ (- 2.0) x) x)))

C

double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = -1.0 + (1.0 - (-2.0 / x));
	} else {
		tmp = (-2.0 / x) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (-1.0d0) + (1.0d0 - ((-2.0d0) / x))
    else
        tmp = (-2.0d0 / x) - x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = -1.0 + (1.0 - (-2.0 / x));
	} else {
		tmp = (-2.0 / x) - x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = -1.0 + (1.0 - (-2.0 / x))
	else:
		tmp = (-2.0 / x) - x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(-1.0 + Float64(1.0 - Float64(-2.0 / x)));
	else
		tmp = Float64(Float64(Float64(-2.0) / x) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = -1.0 + (1.0 - (-2.0 / x));
	else
		tmp = (-2.0 / x) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(-1.0 + N[(1.0 - N[(-2.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-2.0) / x), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 68.8%

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

   3. Simplified 68.8%

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

   4. Taylor expanded in x around 0 3.5%

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

   5. Taylor expanded in x around 0 67.7%

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

      1. associate--r- 67.7%

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

      2. frac-2neg 67.7%

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

      3. metadata-eval 67.7%

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

      4. add-sqr-sqrt 36.2%

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

      5. sqrt-unprod 67.8%

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

      6. sqr-neg 67.8%

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

      7. sqrt-prod 31.6%

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

      8. add-sqr-sqrt 68.1%

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

   7. Applied egg-rr 68.1%

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

   if -1 < x < 1

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 96.8%

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

   5. Taylor expanded in x around 0 96.8%

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

      1. mul-1-neg 96.8%

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

      2. associate-*r/ 96.8%

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

      3. metadata-eval 96.8%

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

   7. Simplified 96.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;-1 + \left(1 - \frac{-2}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{x} - x\\ \end{array} \]

Alternative 3: 84.3% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.1%

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

3. Simplified 83.1%

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

4. Taylor expanded in x around 0 46.1%

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

5. Taylor expanded in x around 0 81.0%

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

6. Final simplification 81.0%

   \[\leadsto 1 + \left(-1 - \frac{2}{x}\right) \]

Alternative 4: 52.7% 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 83.1%

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

3. Simplified 83.1%

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

4. Taylor expanded in x around 0 46.9%

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

5. Final simplification 46.9%

   \[\leadsto \frac{-2}{x} \]

Alternative 5: 3.3% 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 83.1%

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

3. Simplified 83.1%

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

4. Taylor expanded in x around 0 46.1%

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

5. Taylor expanded in x around inf 3.5%

   \[\leadsto \color{blue}{-1} \]

6. Final simplification 3.5%

   \[\leadsto -1 \]

Developer target: 99.6% 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 2023271 
(FPCore (x)
  :name "3frac (problem 3.3.3)"
  :precision binary64

  :herbie-target
  (/ 2.0 (* x (- (* x x) 1.0)))

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