Toniolo and Linder, Equation (7)

Average Error: 43.0 → 12.6

Time: 23.5s

Precision: binary64

Cost: 15176

Math

\[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}} \]

↓

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot t + \frac{t \cdot t}{x}\right)\\ t_2 := \frac{\ell \cdot \ell}{x}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{t \cdot \sqrt{2}}{\sqrt{\left(t_2 + t_1\right) + \frac{\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)}{x}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-177}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 55000000000000:\\ \;\;\;\;t \cdot \frac{\sqrt{2}}{\sqrt{t_2 + \left(t_1 + \ell \cdot \frac{\ell}{x}\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x l t)
 :precision binary64
 (/
  (* (sqrt 2.0) t)
  (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))))

↓

(FPCore (x l t)
 :precision binary64
 (let* ((t_1 (* 2.0 (+ (* t t) (/ (* t t) x)))) (t_2 (/ (* l l) x)))
   (if (<= t -2.4e+33)
     (+ (/ 0.5 (pow x 3.0)) (+ -1.0 (+ (/ 1.0 x) (/ -0.5 (* x x)))))
     (if (<= t -2.5e-301)
       (/
        (* t (sqrt 2.0))
        (sqrt (+ (+ t_2 t_1) (/ (+ (* l l) (* 2.0 (* t t))) x))))
       (if (<= t 4e-177)
         1.0
         (if (<= t 55000000000000.0)
           (* t (/ (sqrt 2.0) (sqrt (+ t_2 (+ t_1 (* l (/ l x)))))))
           1.0))))))

C

double code(double x, double l, double t) {
	return (sqrt(2.0) * t) / sqrt(((((x + 1.0) / (x - 1.0)) * ((l * l) + (2.0 * (t * t)))) - (l * l)));
}

↓

double code(double x, double l, double t) {
	double t_1 = 2.0 * ((t * t) + ((t * t) / x));
	double t_2 = (l * l) / x;
	double tmp;
	if (t <= -2.4e+33) {
		tmp = (0.5 / pow(x, 3.0)) + (-1.0 + ((1.0 / x) + (-0.5 / (x * x))));
	} else if (t <= -2.5e-301) {
		tmp = (t * sqrt(2.0)) / sqrt(((t_2 + t_1) + (((l * l) + (2.0 * (t * t))) / x)));
	} else if (t <= 4e-177) {
		tmp = 1.0;
	} else if (t <= 55000000000000.0) {
		tmp = t * (sqrt(2.0) / sqrt((t_2 + (t_1 + (l * (l / x))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, l, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: l
    real(8), intent (in) :: t
    code = (sqrt(2.0d0) * t) / sqrt(((((x + 1.0d0) / (x - 1.0d0)) * ((l * l) + (2.0d0 * (t * t)))) - (l * l)))
end function

↓

real(8) function code(x, l, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: l
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((t * t) + ((t * t) / x))
    t_2 = (l * l) / x
    if (t <= (-2.4d+33)) then
        tmp = (0.5d0 / (x ** 3.0d0)) + ((-1.0d0) + ((1.0d0 / x) + ((-0.5d0) / (x * x))))
    else if (t <= (-2.5d-301)) then
        tmp = (t * sqrt(2.0d0)) / sqrt(((t_2 + t_1) + (((l * l) + (2.0d0 * (t * t))) / x)))
    else if (t <= 4d-177) then
        tmp = 1.0d0
    else if (t <= 55000000000000.0d0) then
        tmp = t * (sqrt(2.0d0) / sqrt((t_2 + (t_1 + (l * (l / x))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double l, double t) {
	return (Math.sqrt(2.0) * t) / Math.sqrt(((((x + 1.0) / (x - 1.0)) * ((l * l) + (2.0 * (t * t)))) - (l * l)));
}

↓

public static double code(double x, double l, double t) {
	double t_1 = 2.0 * ((t * t) + ((t * t) / x));
	double t_2 = (l * l) / x;
	double tmp;
	if (t <= -2.4e+33) {
		tmp = (0.5 / Math.pow(x, 3.0)) + (-1.0 + ((1.0 / x) + (-0.5 / (x * x))));
	} else if (t <= -2.5e-301) {
		tmp = (t * Math.sqrt(2.0)) / Math.sqrt(((t_2 + t_1) + (((l * l) + (2.0 * (t * t))) / x)));
	} else if (t <= 4e-177) {
		tmp = 1.0;
	} else if (t <= 55000000000000.0) {
		tmp = t * (Math.sqrt(2.0) / Math.sqrt((t_2 + (t_1 + (l * (l / x))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, l, t):
	return (math.sqrt(2.0) * t) / math.sqrt(((((x + 1.0) / (x - 1.0)) * ((l * l) + (2.0 * (t * t)))) - (l * l)))

↓

def code(x, l, t):
	t_1 = 2.0 * ((t * t) + ((t * t) / x))
	t_2 = (l * l) / x
	tmp = 0
	if t <= -2.4e+33:
		tmp = (0.5 / math.pow(x, 3.0)) + (-1.0 + ((1.0 / x) + (-0.5 / (x * x))))
	elif t <= -2.5e-301:
		tmp = (t * math.sqrt(2.0)) / math.sqrt(((t_2 + t_1) + (((l * l) + (2.0 * (t * t))) / x)))
	elif t <= 4e-177:
		tmp = 1.0
	elif t <= 55000000000000.0:
		tmp = t * (math.sqrt(2.0) / math.sqrt((t_2 + (t_1 + (l * (l / x))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, l, t)
	return Float64(Float64(sqrt(2.0) * t) / sqrt(Float64(Float64(Float64(Float64(x + 1.0) / Float64(x - 1.0)) * Float64(Float64(l * l) + Float64(2.0 * Float64(t * t)))) - Float64(l * l))))
end

↓

function code(x, l, t)
	t_1 = Float64(2.0 * Float64(Float64(t * t) + Float64(Float64(t * t) / x)))
	t_2 = Float64(Float64(l * l) / x)
	tmp = 0.0
	if (t <= -2.4e+33)
		tmp = Float64(Float64(0.5 / (x ^ 3.0)) + Float64(-1.0 + Float64(Float64(1.0 / x) + Float64(-0.5 / Float64(x * x)))));
	elseif (t <= -2.5e-301)
		tmp = Float64(Float64(t * sqrt(2.0)) / sqrt(Float64(Float64(t_2 + t_1) + Float64(Float64(Float64(l * l) + Float64(2.0 * Float64(t * t))) / x))));
	elseif (t <= 4e-177)
		tmp = 1.0;
	elseif (t <= 55000000000000.0)
		tmp = Float64(t * Float64(sqrt(2.0) / sqrt(Float64(t_2 + Float64(t_1 + Float64(l * Float64(l / x)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp = code(x, l, t)
	tmp = (sqrt(2.0) * t) / sqrt(((((x + 1.0) / (x - 1.0)) * ((l * l) + (2.0 * (t * t)))) - (l * l)));
end

↓

function tmp_2 = code(x, l, t)
	t_1 = 2.0 * ((t * t) + ((t * t) / x));
	t_2 = (l * l) / x;
	tmp = 0.0;
	if (t <= -2.4e+33)
		tmp = (0.5 / (x ^ 3.0)) + (-1.0 + ((1.0 / x) + (-0.5 / (x * x))));
	elseif (t <= -2.5e-301)
		tmp = (t * sqrt(2.0)) / sqrt(((t_2 + t_1) + (((l * l) + (2.0 * (t * t))) / x)));
	elseif (t <= 4e-177)
		tmp = 1.0;
	elseif (t <= 55000000000000.0)
		tmp = t * (sqrt(2.0) / sqrt((t_2 + (t_1 + (l * (l / x))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, l_, t_] := N[(N[(N[Sqrt[2.0], $MachinePrecision] * t), $MachinePrecision] / N[Sqrt[N[(N[(N[(N[(x + 1.0), $MachinePrecision] / N[(x - 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(l * l), $MachinePrecision] + N[(2.0 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(l * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[x_, l_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(t * t), $MachinePrecision] + N[(N[(t * t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(l * l), $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[t, -2.4e+33], N[(N[(0.5 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(-1.0 + N[(N[(1.0 / x), $MachinePrecision] + N[(-0.5 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.5e-301], N[(N[(t * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] / N[Sqrt[N[(N[(t$95$2 + t$95$1), $MachinePrecision] + N[(N[(N[(l * l), $MachinePrecision] + N[(2.0 * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-177], 1.0, If[LessEqual[t, 55000000000000.0], N[(t * N[(N[Sqrt[2.0], $MachinePrecision] / N[Sqrt[N[(t$95$2 + N[(t$95$1 + N[(l * N[(l / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.4e33

   1. Initial program 42.8

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}} \]

   2. Simplified 42.8

      \[\leadsto \color{blue}{\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x + -1} \cdot \mathsf{fma}\left(\ell, \ell, 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}} \]
      Proof
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x (Rewrite<= metadata-eval (neg.f64 1)))) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (Rewrite<= sub-neg_binary64 (-.f64 x 1))) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))) (*.f64 l l)))): 1 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (Rewrite=> fma-neg_binary64 (fma.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (neg.f64 (neg.f64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))) (neg.f64 (*.f64 l l)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite=> remove-double-neg_binary64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (neg.f64 (*.f64 l l))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in t around -inf 4.8

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\sqrt{2} \cdot \sqrt{0.5}\right) \cdot \sqrt{\frac{x - 1}{1 + x}}\right)} \]

   4. Simplified 4.8

      \[\leadsto \color{blue}{\sqrt{2} \cdot \left(-\sqrt{0.5} \cdot \sqrt{\frac{-1 + x}{x + 1}}\right)} \]
      Proof
      (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (+.f64 -1 x) (+.f64 x 1)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 x -1)) (+.f64 x 1)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (+.f64 x (Rewrite<= metadata-eval (neg.f64 1))) (+.f64 x 1)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x 1)) (+.f64 x 1)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (-.f64 x 1) (Rewrite<= +-commutative_binary64 (+.f64 1 x))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (-.f64 x 1) (+.f64 1 x))))))): 0 points increase in error, 0 points decrease in error
      (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 (-.f64 x 1) (+.f64 1 x)))))): 5 points increase in error, 0 points decrease in error
      (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (sqrt.f64 (/.f64 (-.f64 x 1) (+.f64 1 x)))))): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 63.0

      \[\leadsto \color{blue}{0 + \sqrt{2 \cdot \left(0.5 \cdot \frac{-1 + x}{x + 1}\right)}} \]

   6. Simplified 63.0

      \[\leadsto \color{blue}{\sqrt{\frac{-1 + x}{x + 1}}} \]
      Proof
      (sqrt.f64 (/.f64 (+.f64 -1 x) (+.f64 x 1))): 0 points increase in error, 0 points decrease in error
      (sqrt.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (+.f64 -1 x) (+.f64 x 1))))): 0 points increase in error, 0 points decrease in error
      (sqrt.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 2 1/2)) (/.f64 (+.f64 -1 x) (+.f64 x 1)))): 0 points increase in error, 0 points decrease in error
      (sqrt.f64 (Rewrite<= associate-*r*_binary64 (*.f64 2 (*.f64 1/2 (/.f64 (+.f64 -1 x) (+.f64 x 1)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-lft-identity_binary64 (+.f64 0 (sqrt.f64 (*.f64 2 (*.f64 1/2 (/.f64 (+.f64 -1 x) (+.f64 x 1))))))): 0 points increase in error, 0 points decrease in error

   7. Taylor expanded in x around -inf 64.0

      \[\leadsto \color{blue}{0.5 \cdot \frac{2 \cdot \frac{1}{{\left(\sqrt{-1}\right)}^{2}} + \left(2 + \frac{1}{{\left(\sqrt{-1}\right)}^{4}}\right)}{{x}^{3}} + \left(-0.5 \cdot \frac{2 + {\left(\frac{-1}{\sqrt{-1}}\right)}^{2}}{{x}^{2}} + \left({\left(\sqrt{-1}\right)}^{2} + \frac{1}{x}\right)\right)} \]

   8. Simplified 4.2

      \[\leadsto \color{blue}{\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)} \]
      Proof
      (+.f64 (/.f64 1/2 (pow.f64 x 3)) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (Rewrite<= /-rgt-identity_binary64 (/.f64 (pow.f64 x 3) 1))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (Rewrite<= metadata-eval (+.f64 3 -2)))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (Rewrite<= metadata-eval (+.f64 2 1)) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (Rewrite<= metadata-eval (/.f64 1 1))) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (Rewrite<= metadata-eval (*.f64 -1 -1)))) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (*.f64 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))) -1))) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 256 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2)) -1))) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2))))) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (Rewrite=> pow-sqr_binary64 (pow.f64 (sqrt.f64 -1) (*.f64 2 2))))) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) (Rewrite=> metadata-eval 4)))) -2))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (Rewrite<= metadata-eval (*.f64 2 -1))))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (Rewrite<= metadata-eval (/.f64 1 -1)))))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (/.f64 1 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (/.f64 1 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2))))))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))))))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1/2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3)))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (Rewrite<= unpow2_binary64 (pow.f64 x 2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (Rewrite<= /-rgt-identity_binary64 (/.f64 (pow.f64 x 2) 1)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (Rewrite=> unpow2_binary64 (*.f64 x x)) 1))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (Rewrite<= metadata-eval (+.f64 3 -2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (Rewrite<= metadata-eval (+.f64 2 1)) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (Rewrite<= metadata-eval (/.f64 1 1))) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (Rewrite<= metadata-eval (*.f64 -1 -1)))) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (*.f64 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))) -1))) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2)) -1))) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2))))) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (Rewrite=> pow-sqr_binary64 (pow.f64 (sqrt.f64 -1) (*.f64 2 2))))) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) (Rewrite=> metadata-eval 4)))) -2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (Rewrite<= metadata-eval (*.f64 2 -1)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (Rewrite<= metadata-eval (/.f64 1 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (/.f64 1 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (/.f64 1 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (Rewrite<= associate-+r+_binary64 (+.f64 2 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (pow.f64 (sqrt.f64 -1) (Rewrite<= metadata-eval (*.f64 2 2))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (Rewrite<= pow-sqr_binary64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (sqrt.f64 -1) 2))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (*.f64 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))) (pow.f64 (sqrt.f64 -1) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (*.f64 (Rewrite=> rem-square-sqrt_binary64 -1) (pow.f64 (sqrt.f64 -1) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (*.f64 -1 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (*.f64 -1 (Rewrite=> rem-square-sqrt_binary64 -1)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (Rewrite=> metadata-eval 1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (Rewrite=> metadata-eval 1)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))))) 1))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (Rewrite=> rem-square-sqrt_binary64 -1))) 1))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (*.f64 2 (Rewrite=> metadata-eval -1)) 1))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (+.f64 (Rewrite=> metadata-eval -2) 1))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (Rewrite=> metadata-eval -1))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (Rewrite<= metadata-eval (neg.f64 1)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (Rewrite<= metadata-eval (+.f64 3 -2))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (Rewrite<= metadata-eval (+.f64 2 1)) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (Rewrite<= metadata-eval (/.f64 1 1))) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (Rewrite<= metadata-eval (*.f64 -1 -1)))) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (*.f64 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))) -1))) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2)) -1))) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2))))) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (Rewrite=> pow-sqr_binary64 (pow.f64 (sqrt.f64 -1) (*.f64 2 2))))) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) (Rewrite=> metadata-eval 4)))) -2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (Rewrite<= metadata-eval (*.f64 2 -1)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (Rewrite<= metadata-eval (/.f64 1 -1))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (/.f64 1 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (/.f64 1 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (Rewrite<= associate-+r+_binary64 (+.f64 2 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))))) (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (Rewrite=> rem-square-sqrt_binary64 -1))) (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (Rewrite=> metadata-eval -1)) (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 (Rewrite=> metadata-eval -2) (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 -2 (/.f64 1 (pow.f64 (sqrt.f64 -1) (Rewrite<= metadata-eval (*.f64 2 2))))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 -2 (/.f64 1 (Rewrite<= pow-sqr_binary64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (sqrt.f64 -1) 2))))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 -2 (/.f64 1 (*.f64 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))) (pow.f64 (sqrt.f64 -1) 2)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 -2 (/.f64 1 (*.f64 (Rewrite=> rem-square-sqrt_binary64 -1) (pow.f64 (sqrt.f64 -1) 2)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 -2 (/.f64 1 (*.f64 -1 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 -2 (/.f64 1 (*.f64 -1 (Rewrite=> rem-square-sqrt_binary64 -1)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 -2 (/.f64 1 (Rewrite=> metadata-eval 1))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (+.f64 -2 (Rewrite=> metadata-eval 1)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (Rewrite=> metadata-eval -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (Rewrite<= metadata-eval (/.f64 1 -1)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (/.f64 1 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 -1))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 1 (sqrt.f64 -1)))) (sqrt.f64 -1)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (sqrt.f64 -1)) (/.f64 1 (sqrt.f64 -1)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (+.f64 2 (Rewrite<= unpow2_binary64 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (*.f64 (Rewrite<= metadata-eval (/.f64 -1 -1)) (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (Rewrite<= associate-/r/_binary64 (/.f64 -1 (/.f64 -1 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 -1 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2))) -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (/.f64 (*.f64 -1 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2))) (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (neg.f64 (Rewrite=> times-frac_binary64 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (sqrt.f64 -1))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (Rewrite=> distribute-rgt-neg-in_binary64 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (neg.f64 (/.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2)) (sqrt.f64 -1))))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (Rewrite<= distribute-frac-neg_binary64 (/.f64 (neg.f64 (+.f64 2 (pow.f64 (/.f64 1 (sqrt.f64 -1)) 2))) (sqrt.f64 -1)))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (Rewrite=> unpow2_binary64 (*.f64 (/.f64 1 (sqrt.f64 -1)) (/.f64 1 (sqrt.f64 -1)))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 1 (/.f64 1 (sqrt.f64 -1))) (sqrt.f64 -1))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (/.f64 (Rewrite=> *-lft-identity_binary64 (/.f64 1 (sqrt.f64 -1))) (sqrt.f64 -1)))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (Rewrite<= associate-/r*_binary64 (/.f64 1 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (/.f64 1 (Rewrite=> rem-square-sqrt_binary64 -1)))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (Rewrite=> metadata-eval -1))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (Rewrite<= metadata-eval (+.f64 -2 1)))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (Rewrite<= metadata-eval (*.f64 2 -1)) 1))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (Rewrite<= metadata-eval (/.f64 1 -1))) 1))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))))) 1))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2)))) 1))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (Rewrite<= metadata-eval (/.f64 1 1))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (Rewrite<= metadata-eval (*.f64 -1 -1)))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (*.f64 (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))) -1))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2)) -1))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2))))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (Rewrite=> pow-sqr_binary64 (pow.f64 (sqrt.f64 -1) (*.f64 2 2))))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1 (pow.f64 (sqrt.f64 -1) (Rewrite=> metadata-eval 4)))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 2 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (Rewrite=> associate-+r+_binary64 (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4))) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2)))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) (Rewrite<= metadata-eval (*.f64 2 2))))) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (Rewrite<= pow-sqr_binary64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (sqrt.f64 -1) 2))))) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (*.f64 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (*.f64 (Rewrite=> rem-square-sqrt_binary64 -1) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (*.f64 -1 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))))) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (*.f64 -1 (Rewrite=> rem-square-sqrt_binary64 -1)))) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (+.f64 2 (/.f64 1 (Rewrite=> metadata-eval 1))) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (+.f64 2 (Rewrite=> metadata-eval 1)) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 (Rewrite=> metadata-eval 3) (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 3 (*.f64 2 (/.f64 1 (Rewrite=> unpow2_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1))))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 3 (*.f64 2 (/.f64 1 (Rewrite=> rem-square-sqrt_binary64 -1))))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 3 (*.f64 2 (Rewrite=> metadata-eval -1)))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (+.f64 3 (Rewrite=> metadata-eval -2))) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (neg.f64 (Rewrite=> metadata-eval 1)) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (*.f64 (/.f64 -1 (sqrt.f64 -1)) (/.f64 (Rewrite=> metadata-eval -1) (sqrt.f64 -1))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (/.f64 (*.f64 x x) (+.f64 2 (Rewrite<= unpow2_binary64 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 -1/2 (Rewrite=> associate-/l*_binary64 (/.f64 x (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) x))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 -1/2 x) (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) x)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1/2 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2))) (*.f64 x x)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (/.f64 (*.f64 -1/2 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2))) (Rewrite<= unpow2_binary64 (pow.f64 x 2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 -1 (+.f64 (/.f64 1 x) (Rewrite<= associate-*r/_binary64 (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (pow.f64 x 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 -1 (/.f64 1 x)) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (pow.f64 x 2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (/.f64 1 x) -1)) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (pow.f64 x 2))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 (+.f64 (/.f64 1 x) (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 -1) (sqrt.f64 -1)))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (pow.f64 x 2))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 (+.f64 (/.f64 1 x) (Rewrite<= unpow2_binary64 (pow.f64 (sqrt.f64 -1) 2))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (pow.f64 x 2))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) (/.f64 1 x))) (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (pow.f64 x 2))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 1/2 (/.f64 (+.f64 (*.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 2))) (+.f64 2 (/.f64 1 (pow.f64 (sqrt.f64 -1) 4)))) (pow.f64 x 3))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1/2 (/.f64 (+.f64 2 (pow.f64 (/.f64 -1 (sqrt.f64 -1)) 2)) (pow.f64 x 2))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) (/.f64 1 x))))): 0 points increase in error, 0 points decrease in error

   if -2.4e33 < t < -2.50000000000000006e-301

   1. Initial program 42.7

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}} \]

   2. Simplified 42.7

      \[\leadsto \color{blue}{\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x + -1} \cdot \mathsf{fma}\left(\ell, \ell, 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}} \]
      Proof
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x (Rewrite<= metadata-eval (neg.f64 1)))) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (Rewrite<= sub-neg_binary64 (-.f64 x 1))) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))) (*.f64 l l)))): 1 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (Rewrite=> fma-neg_binary64 (fma.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (neg.f64 (neg.f64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))) (neg.f64 (*.f64 l l)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite=> remove-double-neg_binary64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (neg.f64 (*.f64 l l))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in x around inf 18.8

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

   4. Simplified 18.8

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\color{blue}{\left(\frac{\ell \cdot \ell}{x} + 2 \cdot \left(\frac{t \cdot t}{x} + t \cdot t\right)\right) - \frac{-\left(2 \cdot \left(t \cdot t\right) + \ell \cdot \ell\right)}{x}}}} \]
      Proof
      (-.f64 (+.f64 (/.f64 (*.f64 l l) x) (*.f64 2 (+.f64 (/.f64 (*.f64 t t) x) (*.f64 t t)))) (/.f64 (neg.f64 (+.f64 (*.f64 2 (*.f64 t t)) (*.f64 l l))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 l 2)) x) (*.f64 2 (+.f64 (/.f64 (*.f64 t t) x) (*.f64 t t)))) (/.f64 (neg.f64 (+.f64 (*.f64 2 (*.f64 t t)) (*.f64 l l))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (*.f64 2 (+.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 t 2)) x) (*.f64 t t)))) (/.f64 (neg.f64 (+.f64 (*.f64 2 (*.f64 t t)) (*.f64 l l))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (*.f64 2 (+.f64 (/.f64 (pow.f64 t 2) x) (Rewrite<= unpow2_binary64 (pow.f64 t 2))))) (/.f64 (neg.f64 (+.f64 (*.f64 2 (*.f64 t t)) (*.f64 l l))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2))))) (/.f64 (neg.f64 (+.f64 (*.f64 2 (*.f64 t t)) (*.f64 l l))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2)))) (/.f64 (neg.f64 (+.f64 (*.f64 2 (Rewrite<= unpow2_binary64 (pow.f64 t 2))) (*.f64 l l))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2)))) (/.f64 (neg.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 l l) (*.f64 2 (pow.f64 t 2))))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2)))) (/.f64 (neg.f64 (+.f64 (Rewrite<= unpow2_binary64 (pow.f64 l 2)) (*.f64 2 (pow.f64 t 2)))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2)))) (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (+.f64 (pow.f64 l 2) (*.f64 2 (pow.f64 t 2))))) x)): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2)))) (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (+.f64 (pow.f64 l 2) (*.f64 2 (pow.f64 t 2))) x)))): 0 points increase in error, 0 points decrease in error

   if -2.50000000000000006e-301 < t < 3.99999999999999981e-177 or 5.5e13 < t

   1. Initial program 47.0

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}} \]

   2. Simplified 47.0

      \[\leadsto \color{blue}{\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x + -1} \cdot \mathsf{fma}\left(\ell, \ell, 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}} \]
      Proof
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x (Rewrite<= metadata-eval (neg.f64 1)))) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (Rewrite<= sub-neg_binary64 (-.f64 x 1))) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))) (*.f64 l l)))): 1 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))))) (*.f64 l l)))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (Rewrite=> fma-neg_binary64 (fma.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (neg.f64 (neg.f64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))) (neg.f64 (*.f64 l l)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (Rewrite=> remove-double-neg_binary64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (neg.f64 (*.f64 l l))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in x around inf 15.5

      \[\leadsto \color{blue}{\sqrt{2} \cdot \sqrt{0.5}} \]

   4. Applied egg-rr 14.7

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

   if 3.99999999999999981e-177 < t < 5.5e13

   1. Initial program 33.9

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}} \]

   2. Simplified 33.7

      \[\leadsto \color{blue}{\frac{\sqrt{2}}{\sqrt{\frac{\left(x + 1\right) \cdot \mathsf{fma}\left(2 \cdot t, t, \ell \cdot \ell\right)}{x + -1} - \ell \cdot \ell}} \cdot t} \]
      Proof
      (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 x 1) (fma.f64 (*.f64 2 t) t (*.f64 l l))) (+.f64 x -1)) (*.f64 l l)))) t): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 x 1) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (*.f64 2 t) t) (*.f64 l l)))) (+.f64 x -1)) (*.f64 l l)))) t): 0 points increase in error, 1 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 x 1) (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 2 (*.f64 t t))) (*.f64 l l))) (+.f64 x -1)) (*.f64 l l)))) t): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 x 1) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))) (+.f64 x -1)) (*.f64 l l)))) t): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 x 1) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (+.f64 x (Rewrite<= metadata-eval (neg.f64 1)))) (*.f64 l l)))) t): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 x 1) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (Rewrite<= sub-neg_binary64 (-.f64 x 1))) (*.f64 l l)))) t): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t))))) (*.f64 l l)))) t): 15 points increase in error, 34 points decrease in error
      (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))): 17 points increase in error, 7 points decrease in error

   3. Taylor expanded in x around inf 11.9

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

   4. Simplified 11.9

      \[\leadsto \frac{\sqrt{2}}{\sqrt{\color{blue}{\frac{\ell \cdot \ell}{x} + \left(2 \cdot \left(\frac{t \cdot t}{x} + t \cdot t\right) - \frac{-\mathsf{fma}\left(2, t \cdot t, \ell \cdot \ell\right)}{x}\right)}}} \cdot t \]
      Proof
      (+.f64 (/.f64 (*.f64 l l) x) (-.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 t t) x) (*.f64 t t))) (/.f64 (neg.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 l 2)) x) (-.f64 (*.f64 2 (+.f64 (/.f64 (*.f64 t t) x) (*.f64 t t))) (/.f64 (neg.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (*.f64 2 (+.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 t 2)) x) (*.f64 t t))) (/.f64 (neg.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (*.f64 2 (+.f64 (/.f64 (pow.f64 t 2) x) (Rewrite<= unpow2_binary64 (pow.f64 t 2)))) (/.f64 (neg.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2)))) (/.f64 (neg.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2))) (/.f64 (neg.f64 (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 2 (*.f64 t t)) (*.f64 l l)))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2))) (/.f64 (neg.f64 (+.f64 (*.f64 2 (Rewrite<= unpow2_binary64 (pow.f64 t 2))) (*.f64 l l))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2))) (/.f64 (neg.f64 (+.f64 (*.f64 2 (pow.f64 t 2)) (Rewrite<= unpow2_binary64 (pow.f64 l 2)))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2))) (/.f64 (neg.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 l 2) (*.f64 2 (pow.f64 t 2))))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2))) (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (+.f64 (pow.f64 l 2) (*.f64 2 (pow.f64 t 2))))) x))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (pow.f64 l 2) x) (-.f64 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2))) (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (+.f64 (pow.f64 l 2) (*.f64 2 (pow.f64 t 2))) x))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 (pow.f64 l 2) x) (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) x)) (*.f64 2 (pow.f64 t 2)))) (*.f64 -1 (/.f64 (+.f64 (pow.f64 l 2) (*.f64 2 (pow.f64 t 2))) x)))): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in t around 0 12.1

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

   6. Simplified 12.1

      \[\leadsto \frac{\sqrt{2}}{\sqrt{\frac{\ell \cdot \ell}{x} + \left(2 \cdot \left(\frac{t \cdot t}{x} + t \cdot t\right) - \color{blue}{\ell \cdot \frac{-\ell}{x}}\right)}} \cdot t \]
      Proof
      (*.f64 l (/.f64 (neg.f64 l) x)): 0 points increase in error, 0 points decrease in error
      (*.f64 l (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 l x)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 l (/.f64 l x)))): 0 points increase in error, 0 points decrease in error
      (neg.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 l l) x))): 49 points increase in error, 15 points decrease in error
      (neg.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 l 2)) x)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (pow.f64 l 2) x))): 0 points increase in error, 0 points decrease in error
3. Recombined 4 regimes into one program.

4. Final simplification 12.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{t \cdot \sqrt{2}}{\sqrt{\left(\frac{\ell \cdot \ell}{x} + 2 \cdot \left(t \cdot t + \frac{t \cdot t}{x}\right)\right) + \frac{\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)}{x}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-177}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 55000000000000:\\ \;\;\;\;t \cdot \frac{\sqrt{2}}{\sqrt{\frac{\ell \cdot \ell}{x} + \left(2 \cdot \left(t \cdot t + \frac{t \cdot t}{x}\right) + \ell \cdot \frac{\ell}{x}\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternatives

Alternative 1
Error	12.6
Cost	15176

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot t + \frac{t \cdot t}{x}\right)\\ t_2 := \frac{\ell \cdot \ell}{x}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;\sqrt{2} \cdot \frac{t}{\sqrt{t_2 + \left(t_1 + \frac{\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)}{x}\right)}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-176}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 23000000000000:\\ \;\;\;\;t \cdot \frac{\sqrt{2}}{\sqrt{t_2 + \left(t_1 + \ell \cdot \frac{\ell}{x}\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	12.8
Cost	15056

\[\begin{array}{l} t_1 := \frac{\ell \cdot \ell}{x}\\ t_2 := \sqrt{2} \cdot \frac{t}{\sqrt{t_1 + \left(t_1 + 2 \cdot \left(t \cdot t + \frac{t \cdot t}{x}\right)\right)}}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+33}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-176}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	12.6
Cost	15056

\[\begin{array}{l} t_1 := t \cdot \frac{\sqrt{2}}{\sqrt{\frac{\ell \cdot \ell}{x} + \left(2 \cdot \left(t \cdot t + \frac{t \cdot t}{x}\right) + \ell \cdot \frac{\ell}{x}\right)}}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+33}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-175}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 17500000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Error	12.6
Cost	15056

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot t + \frac{t \cdot t}{x}\right)\\ t_2 := \frac{\ell \cdot \ell}{x}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{t \cdot \sqrt{2}}{\sqrt{t_2 + \left(t_2 + t_1\right)}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-176}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 66000000000000:\\ \;\;\;\;t \cdot \frac{\sqrt{2}}{\sqrt{t_2 + \left(t_1 + \ell \cdot \frac{\ell}{x}\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	15.0
Cost	13768

\[\begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-165}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \frac{\sqrt{2}}{\sqrt{2 \cdot \frac{\ell}{\frac{x}{\ell}}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{x + -1}{x + 1}}\\ \end{array} \]

Alternative 6
Error	15.0
Cost	13768

\[\begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-159}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{t \cdot \sqrt{2}}{\sqrt{2 \cdot \left(\ell \cdot \frac{\ell}{x}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{x + -1}{x + 1}}\\ \end{array} \]

Alternative 7
Error	15.2
Cost	7556

\[\begin{array}{l} \mathbf{if}\;t \leq -3.85 \cdot 10^{-159}:\\ \;\;\;\;\frac{0.5}{{x}^{3}} + \left(-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{t}{\sqrt{\frac{\ell \cdot \ell}{x}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{x + -1}{x + 1}}\\ \end{array} \]

Alternative 8
Error	15.5
Cost	7112

\[\begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-165}:\\ \;\;\;\;-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;\frac{t}{\ell \cdot {x}^{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{x + -1}{x + 1}}\\ \end{array} \]

Alternative 9
Error	15.1
Cost	7112

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-165}:\\ \;\;\;\;-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{t}{\sqrt{\frac{\ell \cdot \ell}{x}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{x + -1}{x + 1}}\\ \end{array} \]

Alternative 10
Error	15.0
Cost	7112

\[\begin{array}{l} t_1 := \sqrt{\frac{x + -1}{x + 1}}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-163}:\\ \;\;\;\;-t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{t}{\sqrt{\frac{\ell \cdot \ell}{x}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	16.0
Cost	7048

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-160}:\\ \;\;\;\;-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;\frac{t}{\ell \cdot {x}^{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12
Error	16.1
Cost	6984

\[\begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-165}:\\ \;\;\;\;-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-308}:\\ \;\;\;\;\sqrt{x} \cdot \frac{t}{\ell}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13
Error	15.9
Cost	6984

\[\begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-165}:\\ \;\;\;\;-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;t \cdot \frac{\sqrt{x}}{\ell}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14
Error	16.0
Cost	6984

\[\begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-160}:\\ \;\;\;\;-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;\frac{t}{\frac{\ell}{\sqrt{x}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15
Error	16.1
Cost	836

\[\begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-309}:\\ \;\;\;\;-1 + \left(\frac{1}{x} + \frac{-0.5}{x \cdot x}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16
Error	16.2
Cost	452

\[\begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-309}:\\ \;\;\;\;-1 + \frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17
Error	16.4
Cost	196

\[\begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-309}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 18
Error	39.6
Cost	64

\[-1 \]

Reproduce

herbie shell --seed 2022329 
(FPCore (x l t)
  :name "Toniolo and Linder, Equation (7)"
  :precision binary64
  (/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))))