Asymptote C

Average Error: 53.6% → 99.9%

Time: 10.8s

Precision: binary64

Cost: 1736.00

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{elif}\;x \leq 50000000000:\\ \;\;\;\;\frac{-1}{x + -1} + \frac{x \cdot \left(\left(x + -1\right) + \left(-1 - x\right)\right)}{\left(x + 1\right) \cdot \left(x + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

FPCore

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

↓

(FPCore (x)
 :precision binary64
 (if (<= x -2e+14)
   (/ (+ -3.0 (/ -1.0 x)) x)
   (if (<= x 50000000000.0)
     (+
      (/ -1.0 (+ x -1.0))
      (/ (* x (+ (+ x -1.0) (- -1.0 x))) (* (+ x 1.0) (+ x -1.0))))
     (/ -3.0 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 <= -2e+14) {
		tmp = (-3.0 + (-1.0 / x)) / x;
	} else if (x <= 50000000000.0) {
		tmp = (-1.0 / (x + -1.0)) + ((x * ((x + -1.0) + (-1.0 - x))) / ((x + 1.0) * (x + -1.0)));
	} else {
		tmp = -3.0 / 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 <= (-2d+14)) then
        tmp = ((-3.0d0) + ((-1.0d0) / x)) / x
    else if (x <= 50000000000.0d0) then
        tmp = ((-1.0d0) / (x + (-1.0d0))) + ((x * ((x + (-1.0d0)) + ((-1.0d0) - x))) / ((x + 1.0d0) * (x + (-1.0d0))))
    else
        tmp = (-3.0d0) / 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 <= -2e+14) {
		tmp = (-3.0 + (-1.0 / x)) / x;
	} else if (x <= 50000000000.0) {
		tmp = (-1.0 / (x + -1.0)) + ((x * ((x + -1.0) + (-1.0 - x))) / ((x + 1.0) * (x + -1.0)));
	} else {
		tmp = -3.0 / 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 <= -2e+14:
		tmp = (-3.0 + (-1.0 / x)) / x
	elif x <= 50000000000.0:
		tmp = (-1.0 / (x + -1.0)) + ((x * ((x + -1.0) + (-1.0 - x))) / ((x + 1.0) * (x + -1.0)))
	else:
		tmp = -3.0 / 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 (x <= -2e+14)
		tmp = Float64(Float64(-3.0 + Float64(-1.0 / x)) / x);
	elseif (x <= 50000000000.0)
		tmp = Float64(Float64(-1.0 / Float64(x + -1.0)) + Float64(Float64(x * Float64(Float64(x + -1.0) + Float64(-1.0 - x))) / Float64(Float64(x + 1.0) * Float64(x + -1.0))));
	else
		tmp = Float64(-3.0 / 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 <= -2e+14)
		tmp = (-3.0 + (-1.0 / x)) / x;
	elseif (x <= 50000000000.0)
		tmp = (-1.0 / (x + -1.0)) + ((x * ((x + -1.0) + (-1.0 - x))) / ((x + 1.0) * (x + -1.0)));
	else
		tmp = -3.0 / 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[x, -2e+14], N[(N[(-3.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 50000000000.0], N[(N[(-1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(x + -1.0), $MachinePrecision] + N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x + 1.0), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-3.0 / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e14

   1. Initial program 5.7

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

   2. Simplified 5.7

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

      [Start] 5.7	\[ \frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
      sub-neg [=>] 5.7	\[ \color{blue}{\frac{x}{x + 1} + \left(-\frac{x + 1}{x - 1}\right)} \]
      +-commutative [=>] 5.7	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) + \frac{x}{x + 1}} \]
      remove-double-neg [<=] 5.7	\[ \left(-\frac{x + 1}{x - 1}\right) + \color{blue}{\left(-\left(-\frac{x}{x + 1}\right)\right)} \]
      sub-neg [<=] 5.7	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) - \left(-\frac{x}{x + 1}\right)} \]
      distribute-neg-frac [=>] 5.7	\[ \color{blue}{\frac{-\left(x + 1\right)}{x - 1}} - \left(-\frac{x}{x + 1}\right) \]
      neg-sub0 [=>] 5.7	\[ \frac{\color{blue}{0 - \left(x + 1\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      +-commutative [=>] 5.7	\[ \frac{0 - \color{blue}{\left(1 + x\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      associate--r+ [=>] 5.7	\[ \frac{\color{blue}{\left(0 - 1\right) - x}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 5.7	\[ \frac{\color{blue}{-1} - x}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      sub-neg [=>] 5.7	\[ \frac{-1 - x}{\color{blue}{x + \left(-1\right)}} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 5.7	\[ \frac{-1 - x}{x + \color{blue}{-1}} - \left(-\frac{x}{x + 1}\right) \]
      /-rgt-identity [<=] 5.7	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{-\frac{x}{x + 1}}{1}} \]
      neg-mul-1 [=>] 5.7	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{-1 \cdot \frac{x}{x + 1}}}{1} \]
      metadata-eval [<=] 5.7	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\left(-1\right)} \cdot \frac{x}{x + 1}}{1} \]
      *-commutative [=>] 5.7	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\frac{x}{x + 1} \cdot \left(-1\right)}}{1} \]
      associate-/l* [=>] 5.7	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{\frac{x}{x + 1}}{\frac{1}{-1}}} \]
      metadata-eval [=>] 5.7	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\frac{1}{\color{blue}{-1}}} \]
      metadata-eval [=>] 5.7	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      metadata-eval [<=] 5.7	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      associate-/l/ [=>] 5.7	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{x}{\left(-1\right) \cdot \left(x + 1\right)}} \]
      metadata-eval [=>] 5.7	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-1} \cdot \left(x + 1\right)} \]
      neg-mul-1 [<=] 5.7	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-\left(x + 1\right)}} \]

   3. Taylor expanded in x around inf 99.5

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

   4. Simplified 100.0

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

      [Start] 99.5	\[ -\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right) \]
      neg-sub0 [=>] 99.5	\[ \color{blue}{0 - \left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right)} \]
      +-commutative [=>] 99.5	\[ 0 - \color{blue}{\left(3 \cdot \frac{1}{x} + \frac{1}{{x}^{2}}\right)} \]
      associate--r+ [=>] 99.5	\[ \color{blue}{\left(0 - 3 \cdot \frac{1}{x}\right) - \frac{1}{{x}^{2}}} \]
      neg-sub0 [<=] 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	\[ \frac{-3}{x} - \color{blue}{\frac{\frac{1}{x}}{x}} \]

   5. Applied egg-rr 100.0

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

   if -2e14 < x < 5e10

   1. Initial program 98.6

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

   2. Simplified 98.6

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

      [Start] 98.6	\[ \frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
      sub-neg [=>] 98.6	\[ \color{blue}{\frac{x}{x + 1} + \left(-\frac{x + 1}{x - 1}\right)} \]
      +-commutative [=>] 98.6	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) + \frac{x}{x + 1}} \]
      remove-double-neg [<=] 98.6	\[ \left(-\frac{x + 1}{x - 1}\right) + \color{blue}{\left(-\left(-\frac{x}{x + 1}\right)\right)} \]
      sub-neg [<=] 98.6	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) - \left(-\frac{x}{x + 1}\right)} \]
      distribute-neg-frac [=>] 98.6	\[ \color{blue}{\frac{-\left(x + 1\right)}{x - 1}} - \left(-\frac{x}{x + 1}\right) \]
      neg-sub0 [=>] 98.6	\[ \frac{\color{blue}{0 - \left(x + 1\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      +-commutative [=>] 98.6	\[ \frac{0 - \color{blue}{\left(1 + x\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      associate--r+ [=>] 98.6	\[ \frac{\color{blue}{\left(0 - 1\right) - x}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 98.6	\[ \frac{\color{blue}{-1} - x}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      sub-neg [=>] 98.6	\[ \frac{-1 - x}{\color{blue}{x + \left(-1\right)}} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 98.6	\[ \frac{-1 - x}{x + \color{blue}{-1}} - \left(-\frac{x}{x + 1}\right) \]
      /-rgt-identity [<=] 98.6	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{-\frac{x}{x + 1}}{1}} \]
      neg-mul-1 [=>] 98.6	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{-1 \cdot \frac{x}{x + 1}}}{1} \]
      metadata-eval [<=] 98.6	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\left(-1\right)} \cdot \frac{x}{x + 1}}{1} \]
      *-commutative [=>] 98.6	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\frac{x}{x + 1} \cdot \left(-1\right)}}{1} \]
      associate-/l* [=>] 98.6	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{\frac{x}{x + 1}}{\frac{1}{-1}}} \]
      metadata-eval [=>] 98.6	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\frac{1}{\color{blue}{-1}}} \]
      metadata-eval [=>] 98.6	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      metadata-eval [<=] 98.6	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      associate-/l/ [=>] 98.6	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{x}{\left(-1\right) \cdot \left(x + 1\right)}} \]
      metadata-eval [=>] 98.6	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-1} \cdot \left(x + 1\right)} \]
      neg-mul-1 [<=] 98.6	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-\left(x + 1\right)}} \]

   3. Applied egg-rr 98.6

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

   4. Applied egg-rr 98.7

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

   5. Simplified 99.9

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

      [Start] 98.7	\[ \frac{-1}{-1 + x} + \frac{\left(-x\right) \cdot \left(x + 1\right) - \left(x + -1\right) \cdot \left(-x\right)}{\left(x + -1\right) \cdot \left(x + 1\right)} \]
      *-commutative [=>] 98.7	\[ \frac{-1}{-1 + x} + \frac{\color{blue}{\left(x + 1\right) \cdot \left(-x\right)} - \left(x + -1\right) \cdot \left(-x\right)}{\left(x + -1\right) \cdot \left(x + 1\right)} \]
      distribute-rgt-out-- [=>] 99.9	\[ \frac{-1}{-1 + x} + \frac{\color{blue}{\left(-x\right) \cdot \left(\left(x + 1\right) - \left(x + -1\right)\right)}}{\left(x + -1\right) \cdot \left(x + 1\right)} \]

   if 5e10 < x

   1. Initial program 6.1

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

   2. Simplified 6.1

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

      [Start] 6.1	\[ \frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
      sub-neg [=>] 6.1	\[ \color{blue}{\frac{x}{x + 1} + \left(-\frac{x + 1}{x - 1}\right)} \]
      +-commutative [=>] 6.1	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) + \frac{x}{x + 1}} \]
      remove-double-neg [<=] 6.1	\[ \left(-\frac{x + 1}{x - 1}\right) + \color{blue}{\left(-\left(-\frac{x}{x + 1}\right)\right)} \]
      sub-neg [<=] 6.1	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) - \left(-\frac{x}{x + 1}\right)} \]
      distribute-neg-frac [=>] 6.1	\[ \color{blue}{\frac{-\left(x + 1\right)}{x - 1}} - \left(-\frac{x}{x + 1}\right) \]
      neg-sub0 [=>] 6.1	\[ \frac{\color{blue}{0 - \left(x + 1\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      +-commutative [=>] 6.1	\[ \frac{0 - \color{blue}{\left(1 + x\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      associate--r+ [=>] 6.1	\[ \frac{\color{blue}{\left(0 - 1\right) - x}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 6.1	\[ \frac{\color{blue}{-1} - x}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      sub-neg [=>] 6.1	\[ \frac{-1 - x}{\color{blue}{x + \left(-1\right)}} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 6.1	\[ \frac{-1 - x}{x + \color{blue}{-1}} - \left(-\frac{x}{x + 1}\right) \]
      /-rgt-identity [<=] 6.1	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{-\frac{x}{x + 1}}{1}} \]
      neg-mul-1 [=>] 6.1	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{-1 \cdot \frac{x}{x + 1}}}{1} \]
      metadata-eval [<=] 6.1	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\left(-1\right)} \cdot \frac{x}{x + 1}}{1} \]
      *-commutative [=>] 6.1	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\frac{x}{x + 1} \cdot \left(-1\right)}}{1} \]
      associate-/l* [=>] 6.1	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{\frac{x}{x + 1}}{\frac{1}{-1}}} \]
      metadata-eval [=>] 6.1	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\frac{1}{\color{blue}{-1}}} \]
      metadata-eval [=>] 6.1	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      metadata-eval [<=] 6.1	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      associate-/l/ [=>] 6.1	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{x}{\left(-1\right) \cdot \left(x + 1\right)}} \]
      metadata-eval [=>] 6.1	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-1} \cdot \left(x + 1\right)} \]
      neg-mul-1 [<=] 6.1	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-\left(x + 1\right)}} \]

   3. Taylor expanded in x around inf 99.8

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

4. Final simplification 99.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+14}:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{elif}\;x \leq 50000000000:\\ \;\;\;\;\frac{-1}{x + -1} + \frac{x \cdot \left(\left(x + -1\right) + \left(-1 - x\right)\right)}{\left(x + 1\right) \cdot \left(x + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

Alternatives

Alternative 1
Error	100.0%
Cost	1224.00

\[\begin{array}{l} \mathbf{if}\;x \leq -1000000000000:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{\left(x + -1\right) \cdot \left(-1 - x\right)} \cdot \left(1 + x \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

Alternative 2
Error	99.6%
Cost	1096.00

\[\begin{array}{l} \mathbf{if}\;x \leq -480000:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{elif}\;x \leq 150000000:\\ \;\;\;\;\frac{x}{x + 1} + \frac{-1 - x}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

Alternative 3
Error	100.0%
Cost	1096.00

\[\begin{array}{l} \mathbf{if}\;x \leq -5000000000:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{elif}\;x \leq 10^{+15}:\\ \;\;\;\;\frac{-1 + x \cdot -3}{\left(x + 1\right) \cdot \left(x + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x}\\ \end{array} \]

Alternative 4
Error	99.1%
Cost	969.00

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.88\right):\\ \;\;\;\;\frac{-3 + \frac{2}{x}}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + x \cdot 3\right) \cdot \left(1 + x \cdot x\right)\\ \end{array} \]

Alternative 5
Error	99.0%
Cost	841.00

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.16\right):\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{x + -1} + x \cdot 2\\ \end{array} \]

Alternative 6
Error	99.0%
Cost	841.00

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3 + \frac{2}{x}}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{x + -1} + x \cdot 2\\ \end{array} \]

Alternative 7
Error	98.8%
Cost	713.00

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) + x \cdot 2\\ \end{array} \]

Alternative 8
Error	98.2%
Cost	712.00

\[\begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\left(x + 1\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x + -1}\\ \end{array} \]

Alternative 9
Error	98.2%
Cost	584.00

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

Alternative 10
Error	98.2%
Cost	584.00

\[\begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;1 + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{x + -1}\\ \end{array} \]

Alternative 11
Error	97.6%
Cost	456.00

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

Alternative 12
Error	49.8%
Cost	64.00

\[1 \]

Reproduce

herbie shell --seed 2023093 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))