Asymptote C

Average Accuracy: 53.4% → 99.9%

Time: 11.8s

Precision: binary64

Cost: 13892

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -2100:\\ \;\;\;\;\frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{x + 3}{{x}^{3}}\right)\\ \mathbf{elif}\;x \leq 440000:\\ \;\;\;\;\frac{x}{x + 1} - \frac{x + 1}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x} - \frac{\frac{1}{x}}{x}\\ \end{array} \]

FPCore

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

↓

(FPCore (x)
 :precision binary64
 (if (<= x -2100.0)
   (- (/ -1.0 (pow x 4.0)) (+ (/ 3.0 x) (/ (+ x 3.0) (pow x 3.0))))
   (if (<= x 440000.0)
     (- (/ x (+ x 1.0)) (/ (+ x 1.0) (+ x -1.0)))
     (- (/ -3.0 x) (/ (/ 1.0 x) 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 <= -2100.0) {
		tmp = (-1.0 / pow(x, 4.0)) - ((3.0 / x) + ((x + 3.0) / pow(x, 3.0)));
	} else if (x <= 440000.0) {
		tmp = (x / (x + 1.0)) - ((x + 1.0) / (x + -1.0));
	} else {
		tmp = (-3.0 / x) - ((1.0 / x) / 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 <= (-2100.0d0)) then
        tmp = ((-1.0d0) / (x ** 4.0d0)) - ((3.0d0 / x) + ((x + 3.0d0) / (x ** 3.0d0)))
    else if (x <= 440000.0d0) then
        tmp = (x / (x + 1.0d0)) - ((x + 1.0d0) / (x + (-1.0d0)))
    else
        tmp = ((-3.0d0) / x) - ((1.0d0 / x) / 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 <= -2100.0) {
		tmp = (-1.0 / Math.pow(x, 4.0)) - ((3.0 / x) + ((x + 3.0) / Math.pow(x, 3.0)));
	} else if (x <= 440000.0) {
		tmp = (x / (x + 1.0)) - ((x + 1.0) / (x + -1.0));
	} else {
		tmp = (-3.0 / x) - ((1.0 / x) / 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 <= -2100.0:
		tmp = (-1.0 / math.pow(x, 4.0)) - ((3.0 / x) + ((x + 3.0) / math.pow(x, 3.0)))
	elif x <= 440000.0:
		tmp = (x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))
	else:
		tmp = (-3.0 / x) - ((1.0 / x) / 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 (x <= -2100.0)
		tmp = Float64(Float64(-1.0 / (x ^ 4.0)) - Float64(Float64(3.0 / x) + Float64(Float64(x + 3.0) / (x ^ 3.0))));
	elseif (x <= 440000.0)
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x + -1.0)));
	else
		tmp = Float64(Float64(-3.0 / x) - Float64(Float64(1.0 / x) / 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 <= -2100.0)
		tmp = (-1.0 / (x ^ 4.0)) - ((3.0 / x) + ((x + 3.0) / (x ^ 3.0)));
	elseif (x <= 440000.0)
		tmp = (x / (x + 1.0)) - ((x + 1.0) / (x + -1.0));
	else
		tmp = (-3.0 / x) - ((1.0 / x) / 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[x, -2100.0], N[(N[(-1.0 / N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision] - N[(N[(3.0 / x), $MachinePrecision] + N[(N[(x + 3.0), $MachinePrecision] / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 440000.0], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-3.0 / x), $MachinePrecision] - N[(N[(1.0 / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2100

   1. Initial program 7.9%

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

   2. Applied egg-rr 5.9%

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

      [Start] 7.9	\[ \frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
      sub-neg [=>] 7.9	\[ \color{blue}{\frac{x}{x + 1} + \left(-\frac{x + 1}{x - 1}\right)} \]
      +-commutative [=>] 7.9	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) + \frac{x}{x + 1}} \]
      div-inv [=>] 7.7	\[ \left(-\color{blue}{\left(x + 1\right) \cdot \frac{1}{x - 1}}\right) + \frac{x}{x + 1} \]
      distribute-rgt-neg-in [=>] 7.7	\[ \color{blue}{\left(x + 1\right) \cdot \left(-\frac{1}{x - 1}\right)} + \frac{x}{x + 1} \]
      fma-def [=>] 5.9	\[ \color{blue}{\mathsf{fma}\left(x + 1, -\frac{1}{x - 1}, \frac{x}{x + 1}\right)} \]
      sub-neg [=>] 5.9	\[ \mathsf{fma}\left(x + 1, -\frac{1}{\color{blue}{x + \left(-1\right)}}, \frac{x}{x + 1}\right) \]
      metadata-eval [=>] 5.9	\[ \mathsf{fma}\left(x + 1, -\frac{1}{x + \color{blue}{-1}}, \frac{x}{x + 1}\right) \]

   3. Taylor expanded in x around inf 99.3%

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

   4. Simplified 100.0%

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

      [Start] 99.3	\[ -\left(\frac{1}{{x}^{4}} + \left(\frac{1}{{x}^{2}} + \left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right)\right)\right) \]
      distribute-neg-in [=>] 99.3	\[ \color{blue}{\left(-\frac{1}{{x}^{4}}\right) + \left(-\left(\frac{1}{{x}^{2}} + \left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right)\right)\right)} \]
      unsub-neg [=>] 99.3	\[ \color{blue}{\left(-\frac{1}{{x}^{4}}\right) - \left(\frac{1}{{x}^{2}} + \left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right)\right)} \]
      +-commutative [=>] 99.3	\[ \left(-\frac{1}{{x}^{4}}\right) - \color{blue}{\left(\left(3 \cdot \frac{1}{{x}^{3}} + 3 \cdot \frac{1}{x}\right) + \frac{1}{{x}^{2}}\right)} \]
      +-commutative [=>] 99.3	\[ \left(-\frac{1}{{x}^{4}}\right) - \left(\color{blue}{\left(3 \cdot \frac{1}{x} + 3 \cdot \frac{1}{{x}^{3}}\right)} + \frac{1}{{x}^{2}}\right) \]
      associate-+l+ [=>] 99.3	\[ \left(-\frac{1}{{x}^{4}}\right) - \color{blue}{\left(3 \cdot \frac{1}{x} + \left(3 \cdot \frac{1}{{x}^{3}} + \frac{1}{{x}^{2}}\right)\right)} \]
      distribute-neg-frac [=>] 99.3	\[ \color{blue}{\frac{-1}{{x}^{4}}} - \left(3 \cdot \frac{1}{x} + \left(3 \cdot \frac{1}{{x}^{3}} + \frac{1}{{x}^{2}}\right)\right) \]
      metadata-eval [=>] 99.3	\[ \frac{\color{blue}{-1}}{{x}^{4}} - \left(3 \cdot \frac{1}{x} + \left(3 \cdot \frac{1}{{x}^{3}} + \frac{1}{{x}^{2}}\right)\right) \]
      associate-*r/ [=>] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\color{blue}{\frac{3 \cdot 1}{x}} + \left(3 \cdot \frac{1}{{x}^{3}} + \frac{1}{{x}^{2}}\right)\right) \]
      metadata-eval [=>] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\frac{\color{blue}{3}}{x} + \left(3 \cdot \frac{1}{{x}^{3}} + \frac{1}{{x}^{2}}\right)\right) \]
      +-commutative [=>] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \color{blue}{\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{{x}^{3}}\right)}\right) \]
      unpow2 [=>] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\frac{1}{\color{blue}{x \cdot x}} + 3 \cdot \frac{1}{{x}^{3}}\right)\right) \]
      associate-*r/ [=>] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\frac{1}{x \cdot x} + \color{blue}{\frac{3 \cdot 1}{{x}^{3}}}\right)\right) \]
      metadata-eval [=>] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\frac{1}{x \cdot x} + \frac{\color{blue}{3}}{{x}^{3}}\right)\right) \]

   5. Applied egg-rr 26.8%

      \[\leadsto \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \color{blue}{\left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right) \cdot \frac{1}{{x}^{5}}}\right) \]
      Proof

      [Start] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\frac{1}{x \cdot x} + \frac{3}{{x}^{3}}\right)\right) \]
      frac-add [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \color{blue}{\frac{1 \cdot {x}^{3} + \left(x \cdot x\right) \cdot 3}{\left(x \cdot x\right) \cdot {x}^{3}}}\right) \]
      div-inv [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \color{blue}{\left(1 \cdot {x}^{3} + \left(x \cdot x\right) \cdot 3\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot {x}^{3}}}\right) \]
      *-un-lft-identity [<=] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\color{blue}{{x}^{3}} + \left(x \cdot x\right) \cdot 3\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot {x}^{3}}\right) \]
      unpow3 [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\color{blue}{\left(x \cdot x\right) \cdot x} + \left(x \cdot x\right) \cdot 3\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot {x}^{3}}\right) \]
      distribute-lft-out [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \color{blue}{\left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right)} \cdot \frac{1}{\left(x \cdot x\right) \cdot {x}^{3}}\right) \]
      pow2 [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right) \cdot \frac{1}{\color{blue}{{x}^{2}} \cdot {x}^{3}}\right) \]
      metadata-eval [<=] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right) \cdot \frac{1}{{x}^{\color{blue}{\left(\sqrt{4}\right)}} \cdot {x}^{3}}\right) \]
      pow-prod-up [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right) \cdot \frac{1}{\color{blue}{{x}^{\left(\sqrt{4} + 3\right)}}}\right) \]
      metadata-eval [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right) \cdot \frac{1}{{x}^{\left(\color{blue}{2} + 3\right)}}\right) \]
      metadata-eval [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right) \cdot \frac{1}{{x}^{\color{blue}{5}}}\right) \]

   6. Simplified 100.0%

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

      [Start] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right) \cdot \frac{1}{{x}^{5}}\right) \]
      associate-*r/ [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \color{blue}{\frac{\left(\left(x \cdot x\right) \cdot \left(x + 3\right)\right) \cdot 1}{{x}^{5}}}\right) \]
      *-rgt-identity [=>] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\color{blue}{\left(x \cdot x\right) \cdot \left(x + 3\right)}}{{x}^{5}}\right) \]
      metadata-eval [<=] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\left(x \cdot x\right) \cdot \left(x + 3\right)}{{x}^{\color{blue}{\left(4 + 1\right)}}}\right) \]
      pow-plus [<=] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\left(x \cdot x\right) \cdot \left(x + 3\right)}{\color{blue}{{x}^{4} \cdot x}}\right) \]
      metadata-eval [<=] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\left(x \cdot x\right) \cdot \left(x + 3\right)}{{x}^{\color{blue}{\left(3 + 1\right)}} \cdot x}\right) \]
      pow-plus [<=] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\left(x \cdot x\right) \cdot \left(x + 3\right)}{\color{blue}{\left({x}^{3} \cdot x\right)} \cdot x}\right) \]
      associate-*r* [<=] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\left(x \cdot x\right) \cdot \left(x + 3\right)}{\color{blue}{{x}^{3} \cdot \left(x \cdot x\right)}}\right) \]
      associate-/l/ [<=] 26.8	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \color{blue}{\frac{\frac{\left(x \cdot x\right) \cdot \left(x + 3\right)}{x \cdot x}}{{x}^{3}}}\right) \]
      associate-/l* [=>] 39.3	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\color{blue}{\frac{x \cdot x}{\frac{x \cdot x}{x + 3}}}}{{x}^{3}}\right) \]
      associate-/r/ [=>] 39.3	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\color{blue}{\frac{x \cdot x}{x \cdot x} \cdot \left(x + 3\right)}}{{x}^{3}}\right) \]
      *-inverses [=>] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\color{blue}{1} \cdot \left(x + 3\right)}{{x}^{3}}\right) \]
      *-lft-identity [=>] 100.0	\[ \frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{\color{blue}{x + 3}}{{x}^{3}}\right) \]

   if -2100 < x < 4.4e5

   1. Initial program 100.0%

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

   if 4.4e5 < x

   1. Initial program 7.0%

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

   2. Taylor expanded in x around inf 99.5%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{-3}{x} - \frac{\frac{1}{x}}{x}} \]
      Proof

      [Start] 99.5	\[ -\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right) \]
      +-commutative [=>] 99.5	\[ -\color{blue}{\left(3 \cdot \frac{1}{x} + \frac{1}{{x}^{2}}\right)} \]
      distribute-neg-in [=>] 99.5	\[ \color{blue}{\left(-3 \cdot \frac{1}{x}\right) + \left(-\frac{1}{{x}^{2}}\right)} \]
      sub-neg [<=] 99.5	\[ \color{blue}{\left(-3 \cdot \frac{1}{x}\right) - \frac{1}{{x}^{2}}} \]
      associate-*r/ [=>] 100.0	\[ \left(-\color{blue}{\frac{3 \cdot 1}{x}}\right) - \frac{1}{{x}^{2}} \]
      metadata-eval [=>] 100.0	\[ \left(-\frac{\color{blue}{3}}{x}\right) - \frac{1}{{x}^{2}} \]
      distribute-neg-frac [=>] 100.0	\[ \color{blue}{\frac{-3}{x}} - \frac{1}{{x}^{2}} \]
      metadata-eval [=>] 100.0	\[ \frac{\color{blue}{-3}}{x} - \frac{1}{{x}^{2}} \]
      unpow2 [=>] 100.0	\[ \frac{-3}{x} - \frac{1}{\color{blue}{x \cdot x}} \]
      associate-/r* [=>] 100.0	\[ \frac{-3}{x} - \color{blue}{\frac{\frac{1}{x}}{x}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2100:\\ \;\;\;\;\frac{-1}{{x}^{4}} - \left(\frac{3}{x} + \frac{x + 3}{{x}^{3}}\right)\\ \mathbf{elif}\;x \leq 440000:\\ \;\;\;\;\frac{x}{x + 1} - \frac{x + 1}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x} - \frac{\frac{1}{x}}{x}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.8%
Cost	13897

\[\begin{array}{l} \mathbf{if}\;x \leq -350000 \lor \neg \left(x \leq 380000\right):\\ \;\;\;\;\frac{-3}{x} - \frac{\frac{1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{x + 1}, x, \frac{\mathsf{fma}\left(-1, x, -1\right)}{x + -1}\right)\\ \end{array} \]

Alternative 2
Accuracy	99.8%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;x \leq -290000 \lor \neg \left(x \leq 440000\right):\\ \;\;\;\;\frac{-3}{x} - \frac{\frac{1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{x + 1}{x + -1}\\ \end{array} \]

Alternative 3
Accuracy	99.0%
Cost	841

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

Alternative 4
Accuracy	99.0%
Cost	841

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

Alternative 5
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 6
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 7
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 8
Accuracy	50.0%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023157 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))