Asymptote C

Percentage Accurate: 54.0% → 99.8%

Time: 6.0s

Precision: binary64

Cost: 2244

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 0.0001:\\ \;\;\;\;\frac{\frac{-3 + \frac{-1}{x}}{x}}{x \cdot x} + \left(\frac{-1}{x \cdot x} - \frac{3}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x}}{1 + \frac{-1}{x}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x)
 :precision binary64
 (if (<= (- (/ x (+ x 1.0)) (/ (+ x 1.0) (+ x -1.0))) 0.0001)
   (+ (/ (/ (+ -3.0 (/ -1.0 x)) x) (* x x)) (- (/ -1.0 (* x x)) (/ 3.0 x)))
   (/ (- (/ (+ x -1.0) (+ x 1.0)) (/ (+ x 1.0) x)) (+ 1.0 (/ -1.0 x)))))

C

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

↓

double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 0.0001) {
		tmp = (((-3.0 + (-1.0 / x)) / x) / (x * x)) + ((-1.0 / (x * x)) - (3.0 / x));
	} else {
		tmp = (((x + -1.0) / (x + 1.0)) - ((x + 1.0) / x)) / (1.0 + (-1.0 / x));
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x / (x + 1.0d0)) - ((x + 1.0d0) / (x + (-1.0d0)))) <= 0.0001d0) then
        tmp = ((((-3.0d0) + ((-1.0d0) / x)) / x) / (x * x)) + (((-1.0d0) / (x * x)) - (3.0d0 / x))
    else
        tmp = (((x + (-1.0d0)) / (x + 1.0d0)) - ((x + 1.0d0) / x)) / (1.0d0 + ((-1.0d0) / x))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 0.0001) {
		tmp = (((-3.0 + (-1.0 / x)) / x) / (x * x)) + ((-1.0 / (x * x)) - (3.0 / x));
	} else {
		tmp = (((x + -1.0) / (x + 1.0)) - ((x + 1.0) / x)) / (1.0 + (-1.0 / x));
	}
	return tmp;
}

Python

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

↓

def code(x):
	tmp = 0
	if ((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 0.0001:
		tmp = (((-3.0 + (-1.0 / x)) / x) / (x * x)) + ((-1.0 / (x * x)) - (3.0 / x))
	else:
		tmp = (((x + -1.0) / (x + 1.0)) - ((x + 1.0) / x)) / (1.0 + (-1.0 / x))
	return tmp

Julia

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

↓

function code(x)
	tmp = 0.0
	if (Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x + -1.0))) <= 0.0001)
		tmp = Float64(Float64(Float64(Float64(-3.0 + Float64(-1.0 / x)) / x) / Float64(x * x)) + Float64(Float64(-1.0 / Float64(x * x)) - Float64(3.0 / x)));
	else
		tmp = Float64(Float64(Float64(Float64(x + -1.0) / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / x)) / Float64(1.0 + Float64(-1.0 / x)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 0.0001)
		tmp = (((-3.0 + (-1.0 / x)) / x) / (x * x)) + ((-1.0 / (x * x)) - (3.0 / x));
	else
		tmp = (((x + -1.0) / (x + 1.0)) - ((x + 1.0) / x)) / (1.0 + (-1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_] := If[LessEqual[N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0001], N[(N[(N[(N[(-3.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(3.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + -1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) < 1.00000000000000005e-4

   1. Initial program 7.4%

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

   2. Applied egg-rr 7.4%

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

      [Start] 7.4%	\[ \frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
      clear-num [=>] 7.4%	\[ \color{blue}{\frac{1}{\frac{x + 1}{x}}} - \frac{x + 1}{x - 1} \]
      clear-num [=>] 7.4%	\[ \frac{1}{\frac{x + 1}{x}} - \color{blue}{\frac{1}{\frac{x - 1}{x + 1}}} \]
      frac-sub [=>] 7.4%	\[ \color{blue}{\frac{1 \cdot \frac{x - 1}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x - 1}{x + 1}}} \]
      *-un-lft-identity [<=] 7.4%	\[ \frac{\color{blue}{\frac{x - 1}{x + 1}} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x - 1}{x + 1}} \]
      sub-neg [=>] 7.4%	\[ \frac{\frac{\color{blue}{x + \left(-1\right)}}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x - 1}{x + 1}} \]
      metadata-eval [=>] 7.4%	\[ \frac{\frac{x + \color{blue}{-1}}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x - 1}{x + 1}} \]
      sub-neg [=>] 7.4%	\[ \frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{\color{blue}{x + \left(-1\right)}}{x + 1}} \]
      metadata-eval [=>] 7.4%	\[ \frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x + \color{blue}{-1}}{x + 1}} \]

   3. Taylor expanded in x around 0 7.4%

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

   4. Taylor expanded in x around inf 99.6%

      \[\leadsto \color{blue}{-\left(\frac{1}{{x}^{4}} + \left(\frac{1}{{x}^{2}} + \left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right)\right)\right)} \]

   5. Simplified 100.0%

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

      [Start] 99.6%	\[ -\left(\frac{1}{{x}^{4}} + \left(\frac{1}{{x}^{2}} + \left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right)\right)\right) \]
      distribute-neg-in [=>] 99.6%	\[ \color{blue}{\left(-\frac{1}{{x}^{4}}\right) + \left(-\left(\frac{1}{{x}^{2}} + \left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right)\right)\right)} \]
      distribute-neg-frac [=>] 99.6%	\[ \color{blue}{\frac{-1}{{x}^{4}}} + \left(-\left(\frac{1}{{x}^{2}} + \left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right)\right)\right) \]
      metadata-eval [=>] 99.6%	\[ \frac{\color{blue}{-1}}{{x}^{4}} + \left(-\left(\frac{1}{{x}^{2}} + \left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right)\right)\right) \]
      associate-+r+ [=>] 99.6%	\[ \frac{-1}{{x}^{4}} + \left(-\color{blue}{\left(\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{{x}^{3}}\right) + 3 \cdot \frac{1}{x}\right)}\right) \]
      +-commutative [<=] 99.6%	\[ \frac{-1}{{x}^{4}} + \left(-\color{blue}{\left(3 \cdot \frac{1}{x} + \left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{{x}^{3}}\right)\right)}\right) \]
      associate-+r+ [=>] 99.6%	\[ \frac{-1}{{x}^{4}} + \left(-\color{blue}{\left(\left(3 \cdot \frac{1}{x} + \frac{1}{{x}^{2}}\right) + 3 \cdot \frac{1}{{x}^{3}}\right)}\right) \]
      +-commutative [<=] 99.6%	\[ \frac{-1}{{x}^{4}} + \left(-\left(\color{blue}{\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)} + 3 \cdot \frac{1}{{x}^{3}}\right)\right) \]
      associate-*r/ [=>] 99.6%	\[ \frac{-1}{{x}^{4}} + \left(-\left(\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right) + \color{blue}{\frac{3 \cdot 1}{{x}^{3}}}\right)\right) \]
      metadata-eval [=>] 99.6%	\[ \frac{-1}{{x}^{4}} + \left(-\left(\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right) + \frac{\color{blue}{3}}{{x}^{3}}\right)\right) \]
      +-commutative [<=] 99.6%	\[ \frac{-1}{{x}^{4}} + \left(-\color{blue}{\left(\frac{3}{{x}^{3}} + \left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)\right)}\right) \]
      distribute-neg-in [=>] 99.6%	\[ \frac{-1}{{x}^{4}} + \color{blue}{\left(\left(-\frac{3}{{x}^{3}}\right) + \left(-\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)\right)\right)} \]

   6. Taylor expanded in x around 0 99.6%

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

   7. Simplified 100.0%

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

      [Start] 99.6%	\[ \frac{\frac{-3 + \frac{-1}{x}}{x}}{x \cdot x} + \left(-\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)\right) \]
      unpow2 [=>] 99.6%	\[ \frac{\frac{-3 + \frac{-1}{x}}{x}}{x \cdot x} + \left(-\left(\frac{1}{\color{blue}{x \cdot x}} + 3 \cdot \frac{1}{x}\right)\right) \]
      associate-*r/ [=>] 100.0%	\[ \frac{\frac{-3 + \frac{-1}{x}}{x}}{x \cdot x} + \left(-\left(\frac{1}{x \cdot x} + \color{blue}{\frac{3 \cdot 1}{x}}\right)\right) \]
      metadata-eval [=>] 100.0%	\[ \frac{\frac{-3 + \frac{-1}{x}}{x}}{x \cdot x} + \left(-\left(\frac{1}{x \cdot x} + \frac{\color{blue}{3}}{x}\right)\right) \]

   if 1.00000000000000005e-4 < (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

   1. Initial program 99.9%

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

   2. Applied egg-rr 99.9%

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

      [Start] 99.9%	\[ \frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
      clear-num [=>] 99.9%	\[ \color{blue}{\frac{1}{\frac{x + 1}{x}}} - \frac{x + 1}{x - 1} \]
      clear-num [=>] 99.9%	\[ \frac{1}{\frac{x + 1}{x}} - \color{blue}{\frac{1}{\frac{x - 1}{x + 1}}} \]
      frac-sub [=>] 99.9%	\[ \color{blue}{\frac{1 \cdot \frac{x - 1}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x - 1}{x + 1}}} \]
      *-un-lft-identity [<=] 99.9%	\[ \frac{\color{blue}{\frac{x - 1}{x + 1}} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x - 1}{x + 1}} \]
      sub-neg [=>] 99.9%	\[ \frac{\frac{\color{blue}{x + \left(-1\right)}}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x - 1}{x + 1}} \]
      metadata-eval [=>] 99.9%	\[ \frac{\frac{x + \color{blue}{-1}}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x - 1}{x + 1}} \]
      sub-neg [=>] 99.9%	\[ \frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{\color{blue}{x + \left(-1\right)}}{x + 1}} \]
      metadata-eval [=>] 99.9%	\[ \frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x} \cdot 1}{\frac{x + 1}{x} \cdot \frac{x + \color{blue}{-1}}{x + 1}} \]

   3. Taylor expanded in x around 0 100.0%

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

   4. Applied egg-rr 100.0%

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

      [Start] 100.0%	\[ \frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x} \cdot 1}{1 - \frac{1}{x}} \]
      div-sub [=>] 100.0%	\[ \color{blue}{\frac{\frac{x + -1}{x + 1}}{1 - \frac{1}{x}} - \frac{\frac{x + 1}{x} \cdot 1}{1 - \frac{1}{x}}} \]
      +-commutative [=>] 100.0%	\[ \frac{\frac{\color{blue}{-1 + x}}{x + 1}}{1 - \frac{1}{x}} - \frac{\frac{x + 1}{x} \cdot 1}{1 - \frac{1}{x}} \]
      *-rgt-identity [=>] 100.0%	\[ \frac{\frac{-1 + x}{x + 1}}{1 - \frac{1}{x}} - \frac{\color{blue}{\frac{x + 1}{x}}}{1 - \frac{1}{x}} \]

   5. Simplified 100.0%

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

      [Start] 100.0%	\[ \frac{\frac{-1 + x}{x + 1}}{1 - \frac{1}{x}} - \frac{\frac{x + 1}{x}}{1 - \frac{1}{x}} \]
      div-sub [<=] 100.0%	\[ \color{blue}{\frac{\frac{-1 + x}{x + 1} - \frac{x + 1}{x}}{1 - \frac{1}{x}}} \]
      +-commutative [=>] 100.0%	\[ \frac{\frac{\color{blue}{x + -1}}{x + 1} - \frac{x + 1}{x}}{1 - \frac{1}{x}} \]
      sub-neg [=>] 100.0%	\[ \frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x}}{\color{blue}{1 + \left(-\frac{1}{x}\right)}} \]
      distribute-neg-frac [=>] 100.0%	\[ \frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x}}{1 + \color{blue}{\frac{-1}{x}}} \]
      metadata-eval [=>] 100.0%	\[ \frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x}}{1 + \frac{\color{blue}{-1}}{x}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 0.0001:\\ \;\;\;\;\frac{\frac{-3 + \frac{-1}{x}}{x}}{x \cdot x} + \left(\frac{-1}{x \cdot x} - \frac{3}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x}}{1 + \frac{-1}{x}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.8%
Cost	2244

\[\begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 0.0001:\\ \;\;\;\;\frac{\frac{-3 + \frac{-1}{x}}{x}}{x \cdot x} + \left(\frac{-1}{x \cdot x} - \frac{3}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x}}{1 + \frac{-1}{x}}\\ \end{array} \]

Alternative 2
Accuracy	99.8%
Cost	2116

\[\begin{array}{l} t_0 := \frac{x}{x + 1}\\ t_1 := \frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{if}\;t_0 - \frac{x + 1}{x + -1} \leq 0.0001:\\ \;\;\;\;t_1 + \frac{t_1}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{1}{x + -1} \cdot \left(-1 - x\right)\\ \end{array} \]

Alternative 3
Accuracy	99.8%
Cost	2116

\[\begin{array}{l} t_0 := \frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 0.0001:\\ \;\;\;\;t_0 + \frac{t_0}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + -1}{x + 1} - \frac{x + 1}{x}}{1 + \frac{-1}{x}}\\ \end{array} \]

Alternative 4
Accuracy	99.7%
Cost	1860

\[\begin{array}{l} t_0 := \frac{x}{x + 1} - \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 \leq 0.0001:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x} + \frac{\frac{-3}{x}}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Accuracy	99.7%
Cost	1860

\[\begin{array}{l} t_0 := \frac{x}{x + 1}\\ \mathbf{if}\;t_0 - \frac{x + 1}{x + -1} \leq 0.0001:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x} + \frac{\frac{-3}{x}}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{1}{x + -1} \cdot \left(-1 - x\right)\\ \end{array} \]

Alternative 6
Accuracy	99.4%
Cost	1732

\[\begin{array}{l} t_0 := \frac{x}{x + 1} - \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Accuracy	99.0%
Cost	713

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

Alternative 8
Accuracy	98.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;1 + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

Alternative 9
Accuracy	98.0%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

Alternative 10
Accuracy	50.6%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023165 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))