Asymptote B

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1 + x}{x}\\ \frac{t_0 + \left(x + -1\right)}{t_0 \cdot \left(x + -1\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ (+ 1.0 x) x))) (/ (+ t_0 (+ x -1.0)) (* t_0 (+ x -1.0)))))

C

double code(double x) {
	double t_0 = (1.0 + x) / x;
	return (t_0 + (x + -1.0)) / (t_0 * (x + -1.0));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = (1.0d0 + x) / x
    code = (t_0 + (x + (-1.0d0))) / (t_0 * (x + (-1.0d0)))
end function

Java

public static double code(double x) {
	double t_0 = (1.0 + x) / x;
	return (t_0 + (x + -1.0)) / (t_0 * (x + -1.0));
}

Python

def code(x):
	t_0 = (1.0 + x) / x
	return (t_0 + (x + -1.0)) / (t_0 * (x + -1.0))

Julia

function code(x)
	t_0 = Float64(Float64(1.0 + x) / x)
	return Float64(Float64(t_0 + Float64(x + -1.0)) / Float64(t_0 * Float64(x + -1.0)))
end

MATLAB

function tmp = code(x)
	t_0 = (1.0 + x) / x;
	tmp = (t_0 + (x + -1.0)) / (t_0 * (x + -1.0));
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{1}{x - 1} + \frac{x}{x + 1} \]
2. Step-by-step derivation

   1. clear-num 100.0%

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

   2. frac-add 100.0%

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

   3. *-un-lft-identity 100.0%

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

   4. +-commutative 100.0%

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

   5. *-commutative 100.0%

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

   6. *-un-lft-identity 100.0%

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

   7. sub-neg 100.0%

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

   8. metadata-eval 100.0%

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

   9. sub-neg 100.0%

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

   10. metadata-eval 100.0%

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

   11. +-commutative 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	tmp = 0
	if x <= -1.0:
		tmp = 1.0
	elif x <= 1.0:
		tmp = -1.0
	else:
		tmp = 1.0 + (2.0 / (x * x))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 100.0%

      \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

   2. Taylor expanded in x around inf 100.0%

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

   if -1 < x < 1

   1. Initial program 100.0%

      \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

   2. Taylor expanded in x around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. metadata-eval 98.6%

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

      3. neg-mul-1 98.6%

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

      4. +-commutative 98.6%

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

      5. unsub-neg 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in x around 0 98.6%

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

   if 1 < x

   1. Initial program 100.0%

      \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

   2. Taylor expanded in x around inf 99.1%

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

      1. associate-*r/ 99.1%

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

      2. metadata-eval 99.1%

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

      3. unpow2 99.1%

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

   4. Simplified 99.1%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{x \cdot x}\\ \end{array} \]

Alternative 3: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45:\\ \;\;\;\;x + \frac{1}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.0)
   1.0
   (if (<= x 1.45) (+ x (/ 1.0 (+ x -1.0))) (+ 1.0 (/ 2.0 (* x x))))))

C

double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = 1.0;
	} else if (x <= 1.45) {
		tmp = x + (1.0 / (x + -1.0));
	} else {
		tmp = 1.0 + (2.0 / (x * x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = 1.0d0
    else if (x <= 1.45d0) then
        tmp = x + (1.0d0 / (x + (-1.0d0)))
    else
        tmp = 1.0d0 + (2.0d0 / (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = 1.0;
	} else if (x <= 1.45) {
		tmp = x + (1.0 / (x + -1.0));
	} else {
		tmp = 1.0 + (2.0 / (x * x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.0:
		tmp = 1.0
	elif x <= 1.45:
		tmp = x + (1.0 / (x + -1.0))
	else:
		tmp = 1.0 + (2.0 / (x * x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = 1.0;
	elseif (x <= 1.45)
		tmp = Float64(x + Float64(1.0 / Float64(x + -1.0)));
	else
		tmp = Float64(1.0 + Float64(2.0 / Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = 1.0;
	elseif (x <= 1.45)
		tmp = x + (1.0 / (x + -1.0));
	else
		tmp = 1.0 + (2.0 / (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.0], 1.0, If[LessEqual[x, 1.45], N[(x + N[(1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(2.0 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 100.0%

      \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

   2. Taylor expanded in x around inf 100.0%

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

   if -1 < x < 1.44999999999999996

   1. Initial program 100.0%

      \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

   2. Taylor expanded in x around 0 98.7%

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

   if 1.44999999999999996 < x

   1. Initial program 100.0%

      \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

   2. Taylor expanded in x around inf 99.1%

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

      1. associate-*r/ 99.1%

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

      2. metadata-eval 99.1%

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

      3. unpow2 99.1%

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

   4. Simplified 99.1%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45:\\ \;\;\;\;x + \frac{1}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{x \cdot x}\\ \end{array} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

2. Final simplification 100.0%

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

Alternative 5: 99.1% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = 1.0;
	} else if (x <= 1.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.0:
		tmp = 1.0
	elif x <= 1.0:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = 1.0;
	elseif (x <= 1.0)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_] := If[LessEqual[x, -1.0], 1.0, If[LessEqual[x, 1.0], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 100.0%

      \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

   2. Taylor expanded in x around inf 99.1%

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

   if -1 < x < 1

   1. Initial program 100.0%

      \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

   2. Taylor expanded in x around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. metadata-eval 98.6%

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

      3. neg-mul-1 98.6%

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

      4. +-commutative 98.6%

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

      5. unsub-neg 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in x around 0 98.6%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 50.5% accurate, 11.0× 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 100.0%

   \[\frac{1}{x - 1} + \frac{x}{x + 1} \]

2. Taylor expanded in x around 0 49.4%

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

   1. sub-neg 49.4%

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

   2. metadata-eval 49.4%

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

   3. neg-mul-1 49.4%

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

   4. +-commutative 49.4%

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

   5. unsub-neg 49.4%

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

4. Simplified 49.4%

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

5. Taylor expanded in x around 0 48.6%

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

6. Final simplification 48.6%

   \[\leadsto -1 \]

Reproduce

herbie shell --seed 2023178 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))