Asymptote C

Average Error: 29.2 → 0.3

Time: 8.7s

Precision: binary64

Cost: 14532

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-1 - x}{x + -1}\right)\right) - \frac{x}{-1 - x}\\ \end{array} \]

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))) 5e-10)
   (/ (+ -3.0 (/ -1.0 x)) x)
   (- (log1p (expm1 (/ (- -1.0 x) (+ x -1.0)))) (/ x (- -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))) <= 5e-10) {
		tmp = (-3.0 + (-1.0 / x)) / x;
	} else {
		tmp = log1p(expm1(((-1.0 - x) / (x + -1.0)))) - (x / (-1.0 - x));
	}
	return tmp;
}

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))) <= 5e-10) {
		tmp = (-3.0 + (-1.0 / x)) / x;
	} else {
		tmp = Math.log1p(Math.expm1(((-1.0 - x) / (x + -1.0)))) - (x / (-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))) <= 5e-10:
		tmp = (-3.0 + (-1.0 / x)) / x
	else:
		tmp = math.log1p(math.expm1(((-1.0 - x) / (x + -1.0)))) - (x / (-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))) <= 5e-10)
		tmp = Float64(Float64(-3.0 + Float64(-1.0 / x)) / x);
	else
		tmp = Float64(log1p(expm1(Float64(Float64(-1.0 - x) / Float64(x + -1.0)))) - Float64(x / Float64(-1.0 - x)));
	end
	return 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], 5e-10], N[(N[(-3.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[Log[1 + N[(Exp[N[(N[(-1.0 - x), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision] - N[(x / 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))) < 5.00000000000000031e-10

   1. Initial program 59.3

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

   2. Simplified 59.3

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

      [Start] 59.3	\[ \frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
      sub-neg [=>] 59.3	\[ \color{blue}{\frac{x}{x + 1} + \left(-\frac{x + 1}{x - 1}\right)} \]
      +-commutative [=>] 59.3	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) + \frac{x}{x + 1}} \]
      remove-double-neg [<=] 59.3	\[ \left(-\frac{x + 1}{x - 1}\right) + \color{blue}{\left(-\left(-\frac{x}{x + 1}\right)\right)} \]
      sub-neg [<=] 59.3	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) - \left(-\frac{x}{x + 1}\right)} \]
      distribute-neg-frac [=>] 59.3	\[ \color{blue}{\frac{-\left(x + 1\right)}{x - 1}} - \left(-\frac{x}{x + 1}\right) \]
      neg-sub0 [=>] 59.3	\[ \frac{\color{blue}{0 - \left(x + 1\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      +-commutative [=>] 59.3	\[ \frac{0 - \color{blue}{\left(1 + x\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      associate--r+ [=>] 59.3	\[ \frac{\color{blue}{\left(0 - 1\right) - x}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 59.3	\[ \frac{\color{blue}{-1} - x}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      sub-neg [=>] 59.3	\[ \frac{-1 - x}{\color{blue}{x + \left(-1\right)}} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 59.3	\[ \frac{-1 - x}{x + \color{blue}{-1}} - \left(-\frac{x}{x + 1}\right) \]
      /-rgt-identity [<=] 59.3	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{-\frac{x}{x + 1}}{1}} \]
      neg-mul-1 [=>] 59.3	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{-1 \cdot \frac{x}{x + 1}}}{1} \]
      metadata-eval [<=] 59.3	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\left(-1\right)} \cdot \frac{x}{x + 1}}{1} \]
      *-commutative [=>] 59.3	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\frac{x}{x + 1} \cdot \left(-1\right)}}{1} \]
      associate-/l* [=>] 59.3	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{\frac{x}{x + 1}}{\frac{1}{-1}}} \]
      metadata-eval [=>] 59.3	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\frac{1}{\color{blue}{-1}}} \]
      metadata-eval [=>] 59.3	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      metadata-eval [<=] 59.3	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      associate-/l/ [=>] 59.3	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{x}{\left(-1\right) \cdot \left(x + 1\right)}} \]
      metadata-eval [=>] 59.3	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-1} \cdot \left(x + 1\right)} \]
      neg-mul-1 [<=] 59.3	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-\left(x + 1\right)}} \]

   3. Taylor expanded in x around inf 0.7

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

   4. Simplified 0.4

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

      [Start] 0.7	\[ -\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right) \]
      distribute-neg-in [=>] 0.7	\[ \color{blue}{\left(-\frac{1}{{x}^{2}}\right) + \left(-3 \cdot \frac{1}{x}\right)} \]
      unpow2 [=>] 0.7	\[ \left(-\frac{1}{\color{blue}{x \cdot x}}\right) + \left(-3 \cdot \frac{1}{x}\right) \]
      distribute-neg-frac [=>] 0.7	\[ \color{blue}{\frac{-1}{x \cdot x}} + \left(-3 \cdot \frac{1}{x}\right) \]
      metadata-eval [=>] 0.7	\[ \frac{\color{blue}{-1}}{x \cdot x} + \left(-3 \cdot \frac{1}{x}\right) \]
      associate-*r/ [=>] 0.4	\[ \frac{-1}{x \cdot x} + \left(-\color{blue}{\frac{3 \cdot 1}{x}}\right) \]
      metadata-eval [=>] 0.4	\[ \frac{-1}{x \cdot x} + \left(-\frac{\color{blue}{3}}{x}\right) \]
      distribute-neg-frac [=>] 0.4	\[ \frac{-1}{x \cdot x} + \color{blue}{\frac{-3}{x}} \]
      metadata-eval [=>] 0.4	\[ \frac{-1}{x \cdot x} + \frac{\color{blue}{-3}}{x} \]

   5. Applied egg-rr 43.4

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

   6. Simplified 0.4

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

      [Start] 43.4	\[ \frac{x + \left(x \cdot x\right) \cdot 3}{-{x}^{3}} \]
      *-commutative [=>] 43.4	\[ \frac{x + \color{blue}{3 \cdot \left(x \cdot x\right)}}{-{x}^{3}} \]
      metadata-eval [<=] 43.4	\[ \frac{x + \color{blue}{\left(--3\right)} \cdot \left(x \cdot x\right)}{-{x}^{3}} \]
      distribute-lft-neg-in [<=] 43.4	\[ \frac{x + \color{blue}{\left(--3 \cdot \left(x \cdot x\right)\right)}}{-{x}^{3}} \]
      distribute-rgt-neg-out [<=] 43.4	\[ \frac{x + \color{blue}{-3 \cdot \left(-x \cdot x\right)}}{-{x}^{3}} \]
      distribute-rgt-neg-out [<=] 43.4	\[ \frac{x + -3 \cdot \color{blue}{\left(x \cdot \left(-x\right)\right)}}{-{x}^{3}} \]
      *-lft-identity [<=] 43.4	\[ \frac{\color{blue}{1 \cdot x} + -3 \cdot \left(x \cdot \left(-x\right)\right)}{-{x}^{3}} \]
      metadata-eval [<=] 43.4	\[ \frac{\color{blue}{\left(-1 \cdot -1\right)} \cdot x + -3 \cdot \left(x \cdot \left(-x\right)\right)}{-{x}^{3}} \]
      associate-*r* [<=] 43.4	\[ \frac{\color{blue}{-1 \cdot \left(-1 \cdot x\right)} + -3 \cdot \left(x \cdot \left(-x\right)\right)}{-{x}^{3}} \]
      neg-mul-1 [<=] 43.4	\[ \frac{-1 \cdot \color{blue}{\left(-x\right)} + -3 \cdot \left(x \cdot \left(-x\right)\right)}{-{x}^{3}} \]
      associate-*r* [=>] 43.4	\[ \frac{-1 \cdot \left(-x\right) + \color{blue}{\left(-3 \cdot x\right) \cdot \left(-x\right)}}{-{x}^{3}} \]
      *-commutative [<=] 43.4	\[ \frac{-1 \cdot \left(-x\right) + \color{blue}{\left(x \cdot -3\right)} \cdot \left(-x\right)}{-{x}^{3}} \]
      distribute-rgt-out [=>] 43.4	\[ \frac{\color{blue}{\left(-x\right) \cdot \left(-1 + x \cdot -3\right)}}{-{x}^{3}} \]
      +-commutative [<=] 43.4	\[ \frac{\left(-x\right) \cdot \color{blue}{\left(x \cdot -3 + -1\right)}}{-{x}^{3}} \]
      distribute-lft-neg-in [<=] 43.4	\[ \frac{\color{blue}{-x \cdot \left(x \cdot -3 + -1\right)}}{-{x}^{3}} \]
      distribute-neg-frac [<=] 43.4	\[ \color{blue}{-\frac{x \cdot \left(x \cdot -3 + -1\right)}{-{x}^{3}}} \]
      cube-neg [<=] 43.4	\[ -\frac{x \cdot \left(x \cdot -3 + -1\right)}{\color{blue}{{\left(-x\right)}^{3}}} \]
      unpow3 [=>] 43.5	\[ -\frac{x \cdot \left(x \cdot -3 + -1\right)}{\color{blue}{\left(\left(-x\right) \cdot \left(-x\right)\right) \cdot \left(-x\right)}} \]
      associate-/r* [=>] 32.9	\[ -\color{blue}{\frac{\frac{x \cdot \left(x \cdot -3 + -1\right)}{\left(-x\right) \cdot \left(-x\right)}}{-x}} \]

   7. Taylor expanded in x around 0 0.7

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

   8. Simplified 0.4

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

      [Start] 0.7	\[ -\left(\frac{1}{{x}^{2}} + 3 \cdot \frac{1}{x}\right) \]
      unpow2 [=>] 0.7	\[ -\left(\frac{1}{\color{blue}{x \cdot x}} + 3 \cdot \frac{1}{x}\right) \]
      associate-/r* [=>] 0.7	\[ -\left(\color{blue}{\frac{\frac{1}{x}}{x}} + 3 \cdot \frac{1}{x}\right) \]
      metadata-eval [<=] 0.7	\[ -\left(\frac{\frac{\color{blue}{-1 \cdot -1}}{x}}{x} + 3 \cdot \frac{1}{x}\right) \]
      associate-*r/ [<=] 0.7	\[ -\left(\frac{\color{blue}{-1 \cdot \frac{-1}{x}}}{x} + 3 \cdot \frac{1}{x}\right) \]
      associate-*l/ [<=] 0.7	\[ -\left(\color{blue}{\frac{-1}{x} \cdot \frac{-1}{x}} + 3 \cdot \frac{1}{x}\right) \]
      associate-*r/ [=>] 0.4	\[ -\left(\frac{-1}{x} \cdot \frac{-1}{x} + \color{blue}{\frac{3 \cdot 1}{x}}\right) \]
      metadata-eval [=>] 0.4	\[ -\left(\frac{-1}{x} \cdot \frac{-1}{x} + \frac{\color{blue}{3}}{x}\right) \]
      metadata-eval [<=] 0.4	\[ -\left(\frac{-1}{x} \cdot \frac{-1}{x} + \frac{\color{blue}{-3 \cdot -1}}{x}\right) \]
      associate-*r/ [<=] 0.7	\[ -\left(\frac{-1}{x} \cdot \frac{-1}{x} + \color{blue}{-3 \cdot \frac{-1}{x}}\right) \]
      distribute-rgt-in [<=] 0.7	\[ -\color{blue}{\frac{-1}{x} \cdot \left(\frac{-1}{x} + -3\right)} \]
      +-commutative [<=] 0.7	\[ -\frac{-1}{x} \cdot \color{blue}{\left(-3 + \frac{-1}{x}\right)} \]
      associate-*l/ [=>] 0.4	\[ -\color{blue}{\frac{-1 \cdot \left(-3 + \frac{-1}{x}\right)}{x}} \]
      distribute-lft-in [=>] 0.4	\[ -\frac{\color{blue}{-1 \cdot -3 + -1 \cdot \frac{-1}{x}}}{x} \]
      metadata-eval [=>] 0.4	\[ -\frac{\color{blue}{3} + -1 \cdot \frac{-1}{x}}{x} \]
      associate-*r/ [=>] 0.4	\[ -\frac{3 + \color{blue}{\frac{-1 \cdot -1}{x}}}{x} \]
      metadata-eval [=>] 0.4	\[ -\frac{3 + \frac{\color{blue}{1}}{x}}{x} \]

   if 5.00000000000000031e-10 < (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

   1. Initial program 0.2

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

   2. Simplified 0.2

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

      [Start] 0.2	\[ \frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
      sub-neg [=>] 0.2	\[ \color{blue}{\frac{x}{x + 1} + \left(-\frac{x + 1}{x - 1}\right)} \]
      +-commutative [=>] 0.2	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) + \frac{x}{x + 1}} \]
      remove-double-neg [<=] 0.2	\[ \left(-\frac{x + 1}{x - 1}\right) + \color{blue}{\left(-\left(-\frac{x}{x + 1}\right)\right)} \]
      sub-neg [<=] 0.2	\[ \color{blue}{\left(-\frac{x + 1}{x - 1}\right) - \left(-\frac{x}{x + 1}\right)} \]
      distribute-neg-frac [=>] 0.2	\[ \color{blue}{\frac{-\left(x + 1\right)}{x - 1}} - \left(-\frac{x}{x + 1}\right) \]
      neg-sub0 [=>] 0.2	\[ \frac{\color{blue}{0 - \left(x + 1\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      +-commutative [=>] 0.2	\[ \frac{0 - \color{blue}{\left(1 + x\right)}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      associate--r+ [=>] 0.2	\[ \frac{\color{blue}{\left(0 - 1\right) - x}}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 0.2	\[ \frac{\color{blue}{-1} - x}{x - 1} - \left(-\frac{x}{x + 1}\right) \]
      sub-neg [=>] 0.2	\[ \frac{-1 - x}{\color{blue}{x + \left(-1\right)}} - \left(-\frac{x}{x + 1}\right) \]
      metadata-eval [=>] 0.2	\[ \frac{-1 - x}{x + \color{blue}{-1}} - \left(-\frac{x}{x + 1}\right) \]
      /-rgt-identity [<=] 0.2	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{-\frac{x}{x + 1}}{1}} \]
      neg-mul-1 [=>] 0.2	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{-1 \cdot \frac{x}{x + 1}}}{1} \]
      metadata-eval [<=] 0.2	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\left(-1\right)} \cdot \frac{x}{x + 1}}{1} \]
      *-commutative [=>] 0.2	\[ \frac{-1 - x}{x + -1} - \frac{\color{blue}{\frac{x}{x + 1} \cdot \left(-1\right)}}{1} \]
      associate-/l* [=>] 0.2	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{\frac{x}{x + 1}}{\frac{1}{-1}}} \]
      metadata-eval [=>] 0.2	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\frac{1}{\color{blue}{-1}}} \]
      metadata-eval [=>] 0.2	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      metadata-eval [<=] 0.2	\[ \frac{-1 - x}{x + -1} - \frac{\frac{x}{x + 1}}{\color{blue}{-1}} \]
      associate-/l/ [=>] 0.2	\[ \frac{-1 - x}{x + -1} - \color{blue}{\frac{x}{\left(-1\right) \cdot \left(x + 1\right)}} \]
      metadata-eval [=>] 0.2	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-1} \cdot \left(x + 1\right)} \]
      neg-mul-1 [<=] 0.2	\[ \frac{-1 - x}{x + -1} - \frac{x}{\color{blue}{-\left(x + 1\right)}} \]

   3. Applied egg-rr 0.2

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-1 - x}{-1 + x}\right)\right)} - \frac{x}{-1 - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-1 - x}{x + -1}\right)\right) - \frac{x}{-1 - x}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.3
Cost	1860

\[\begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - x\right) \cdot \frac{-1}{1 - x} - \frac{x}{-1 - x}\\ \end{array} \]

Alternative 2
Error	0.3
Cost	1732

\[\begin{array}{l} t_0 := \frac{x}{x + 1} - \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{-3 + \frac{-1}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.7
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 4
Error	1.0
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 5
Error	1.4
Cost	456

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

Alternative 6
Error	31.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023073 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))