2tan (problem 3.3.2)

Average Error: 36.6 → 0.3

Time: 17.6s

Precision: binary64

Cost: 280520

Math

\[\tan \left(x + \varepsilon\right) - \tan x \]

↓

\[\begin{array}{l} t_0 := \frac{{\sin x}^{2}}{{\cos x}^{2}}\\ t_1 := -\tan x\\ t_2 := \tan x + \tan \varepsilon\\ t_3 := \frac{\sin x}{\cos x}\\ t_4 := {t_3}^{3}\\ t_5 := t_3 \cdot -0.3333333333333333 - t_4\\ \mathbf{if}\;\varepsilon \leq -0.00019:\\ \;\;\;\;\mathsf{fma}\left(t_2, \frac{1}{1 - \tan x \cdot \tan \varepsilon}, t_1\right)\\ \mathbf{elif}\;\varepsilon \leq 0.00021:\\ \;\;\;\;\mathsf{fma}\left({\varepsilon}^{4}, \mathsf{fma}\left(t_3, 0.3333333333333333, t_4 + t_3 \cdot \left(0.3333333333333333 - \mathsf{fma}\left(t_0, -0.3333333333333333, t_3 \cdot t_5\right)\right)\right), \mathsf{fma}\left(t_3 + t_4, \varepsilon \cdot \varepsilon, \mathsf{fma}\left({\varepsilon}^{3}, 0.3333333333333333 + t_3 \cdot \left(t_3 - t_5\right), \varepsilon + \varepsilon \cdot t_0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_2, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, t_1\right)\\ \end{array} \]

FPCore

(FPCore (x eps) :precision binary64 (- (tan (+ x eps)) (tan x)))

↓

(FPCore (x eps)
 :precision binary64
 (let* ((t_0 (/ (pow (sin x) 2.0) (pow (cos x) 2.0)))
        (t_1 (- (tan x)))
        (t_2 (+ (tan x) (tan eps)))
        (t_3 (/ (sin x) (cos x)))
        (t_4 (pow t_3 3.0))
        (t_5 (- (* t_3 -0.3333333333333333) t_4)))
   (if (<= eps -0.00019)
     (fma t_2 (/ 1.0 (- 1.0 (* (tan x) (tan eps)))) t_1)
     (if (<= eps 0.00021)
       (fma
        (pow eps 4.0)
        (fma
         t_3
         0.3333333333333333
         (+
          t_4
          (*
           t_3
           (- 0.3333333333333333 (fma t_0 -0.3333333333333333 (* t_3 t_5))))))
        (fma
         (+ t_3 t_4)
         (* eps eps)
         (fma
          (pow eps 3.0)
          (+ 0.3333333333333333 (* t_3 (- t_3 t_5)))
          (+ eps (* eps t_0)))))
       (fma t_2 (/ 1.0 (- 1.0 (/ (* (tan eps) (sin x)) (cos x)))) t_1)))))

C

double code(double x, double eps) {
	return tan((x + eps)) - tan(x);
}

↓

double code(double x, double eps) {
	double t_0 = pow(sin(x), 2.0) / pow(cos(x), 2.0);
	double t_1 = -tan(x);
	double t_2 = tan(x) + tan(eps);
	double t_3 = sin(x) / cos(x);
	double t_4 = pow(t_3, 3.0);
	double t_5 = (t_3 * -0.3333333333333333) - t_4;
	double tmp;
	if (eps <= -0.00019) {
		tmp = fma(t_2, (1.0 / (1.0 - (tan(x) * tan(eps)))), t_1);
	} else if (eps <= 0.00021) {
		tmp = fma(pow(eps, 4.0), fma(t_3, 0.3333333333333333, (t_4 + (t_3 * (0.3333333333333333 - fma(t_0, -0.3333333333333333, (t_3 * t_5)))))), fma((t_3 + t_4), (eps * eps), fma(pow(eps, 3.0), (0.3333333333333333 + (t_3 * (t_3 - t_5))), (eps + (eps * t_0)))));
	} else {
		tmp = fma(t_2, (1.0 / (1.0 - ((tan(eps) * sin(x)) / cos(x)))), t_1);
	}
	return tmp;
}

Julia

function code(x, eps)
	return Float64(tan(Float64(x + eps)) - tan(x))
end

↓

function code(x, eps)
	t_0 = Float64((sin(x) ^ 2.0) / (cos(x) ^ 2.0))
	t_1 = Float64(-tan(x))
	t_2 = Float64(tan(x) + tan(eps))
	t_3 = Float64(sin(x) / cos(x))
	t_4 = t_3 ^ 3.0
	t_5 = Float64(Float64(t_3 * -0.3333333333333333) - t_4)
	tmp = 0.0
	if (eps <= -0.00019)
		tmp = fma(t_2, Float64(1.0 / Float64(1.0 - Float64(tan(x) * tan(eps)))), t_1);
	elseif (eps <= 0.00021)
		tmp = fma((eps ^ 4.0), fma(t_3, 0.3333333333333333, Float64(t_4 + Float64(t_3 * Float64(0.3333333333333333 - fma(t_0, -0.3333333333333333, Float64(t_3 * t_5)))))), fma(Float64(t_3 + t_4), Float64(eps * eps), fma((eps ^ 3.0), Float64(0.3333333333333333 + Float64(t_3 * Float64(t_3 - t_5))), Float64(eps + Float64(eps * t_0)))));
	else
		tmp = fma(t_2, Float64(1.0 / Float64(1.0 - Float64(Float64(tan(eps) * sin(x)) / cos(x)))), t_1);
	end
	return tmp
end

Wolfram

code[x_, eps_] := N[(N[Tan[N[(x + eps), $MachinePrecision]], $MachinePrecision] - N[Tan[x], $MachinePrecision]), $MachinePrecision]

↓

code[x_, eps_] := Block[{t$95$0 = N[(N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision] / N[Power[N[Cos[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-N[Tan[x], $MachinePrecision])}, Block[{t$95$2 = N[(N[Tan[x], $MachinePrecision] + N[Tan[eps], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[Sin[x], $MachinePrecision] / N[Cos[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Power[t$95$3, 3.0], $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 * -0.3333333333333333), $MachinePrecision] - t$95$4), $MachinePrecision]}, If[LessEqual[eps, -0.00019], N[(t$95$2 * N[(1.0 / N[(1.0 - N[(N[Tan[x], $MachinePrecision] * N[Tan[eps], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[eps, 0.00021], N[(N[Power[eps, 4.0], $MachinePrecision] * N[(t$95$3 * 0.3333333333333333 + N[(t$95$4 + N[(t$95$3 * N[(0.3333333333333333 - N[(t$95$0 * -0.3333333333333333 + N[(t$95$3 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 + t$95$4), $MachinePrecision] * N[(eps * eps), $MachinePrecision] + N[(N[Power[eps, 3.0], $MachinePrecision] * N[(0.3333333333333333 + N[(t$95$3 * N[(t$95$3 - t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(eps + N[(eps * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 * N[(1.0 / N[(1.0 - N[(N[(N[Tan[eps], $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision] / N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]]

Target

Original	36.6
Target	14.9
Herbie	0.3

\[\frac{\sin \varepsilon}{\cos x \cdot \cos \left(x + \varepsilon\right)} \]

Derivation

1. Split input into 3 regimes

2. if eps < -1.9000000000000001e-4

   1. Initial program 29.5

      \[\tan \left(x + \varepsilon\right) - \tan x \]

   2. Applied egg-rr 0.4

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

   if -1.9000000000000001e-4 < eps < 2.1000000000000001e-4

   1. Initial program 44.3

      \[\tan \left(x + \varepsilon\right) - \tan x \]

   2. Applied egg-rr 43.7

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

   3. Applied egg-rr 43.7

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\sin \varepsilon, \frac{1}{\cos \varepsilon}, \tan x\right)}, \frac{1}{1 - \tan x \cdot \tan \varepsilon}, -\tan x\right) \]

   4. Simplified 43.7

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\sin \varepsilon}{\cos \varepsilon} + \tan x}, \frac{1}{1 - \tan x \cdot \tan \varepsilon}, -\tan x\right) \]
      Proof
      (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (tan.f64 x)): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (sin.f64 eps) 1)) (cos.f64 eps)) (tan.f64 x)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (sin.f64 eps) (/.f64 1 (cos.f64 eps)))) (tan.f64 x)): 16 points increase in error, 8 points decrease in error
      (Rewrite<= fma-udef_binary64 (fma.f64 (sin.f64 eps) (/.f64 1 (cos.f64 eps)) (tan.f64 x))): 5 points increase in error, 9 points decrease in error

   5. Taylor expanded in eps around 0 0.2

      \[\leadsto \color{blue}{{\varepsilon}^{4} \cdot \left(0.3333333333333333 \cdot \frac{\sin x}{\cos x} + \left(-1 \cdot \left(-1 \cdot \frac{{\sin x}^{3}}{{\cos x}^{3}} + -0.3333333333333333 \cdot \frac{\sin x}{\cos x}\right) + -1 \cdot \frac{\left(\frac{\left(-1 \cdot \frac{{\sin x}^{3}}{{\cos x}^{3}} + -0.3333333333333333 \cdot \frac{\sin x}{\cos x}\right) \cdot \sin x}{\cos x} + -0.3333333333333333 \cdot \frac{{\sin x}^{2}}{{\cos x}^{2}}\right) \cdot \sin x}{\cos x}\right)\right) + \left(\left(\frac{\sin x}{\cos x} + \frac{{\sin x}^{3}}{{\cos x}^{3}}\right) \cdot {\varepsilon}^{2} + \left(\varepsilon \cdot \left(1 + \frac{{\sin x}^{2}}{{\cos x}^{2}}\right) + {\varepsilon}^{3} \cdot \left(0.3333333333333333 + \left(-1 \cdot \frac{\left(-1 \cdot \frac{{\sin x}^{3}}{{\cos x}^{3}} + -0.3333333333333333 \cdot \frac{\sin x}{\cos x}\right) \cdot \sin x}{\cos x} + \frac{{\sin x}^{2}}{{\cos x}^{2}}\right)\right)\right)\right)} \]

   6. Simplified 0.2

      \[\leadsto \color{blue}{\mathsf{fma}\left({\varepsilon}^{4}, \mathsf{fma}\left(\frac{\sin x}{\cos x}, 0.3333333333333333, {\left(\frac{\sin x}{\cos x}\right)}^{3} + \left(-\frac{\sin x}{\cos x} \cdot \left(-0.3333333333333333 + \mathsf{fma}\left(\frac{{\sin x}^{2}}{{\cos x}^{2}}, -0.3333333333333333, \frac{\sin x}{\cos x} \cdot \left(\frac{\sin x}{\cos x} \cdot -0.3333333333333333 - {\left(\frac{\sin x}{\cos x}\right)}^{3}\right)\right)\right)\right)\right), \mathsf{fma}\left(\frac{\sin x}{\cos x} + {\left(\frac{\sin x}{\cos x}\right)}^{3}, \varepsilon \cdot \varepsilon, \mathsf{fma}\left({\varepsilon}^{3}, 0.3333333333333333 + \frac{\sin x}{\cos x} \cdot \left(\frac{\sin x}{\cos x} - \left(\frac{\sin x}{\cos x} \cdot -0.3333333333333333 - {\left(\frac{\sin x}{\cos x}\right)}^{3}\right)\right), \varepsilon + \varepsilon \cdot \frac{{\sin x}^{2}}{{\cos x}^{2}}\right)\right)\right)} \]
      Proof
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (Rewrite<= cube-unmult_binary64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 x))))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x))))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (cos.f64 x)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite<= unpow2_binary64 (pow.f64 (cos.f64 x) 2)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (/.f64 (*.f64 (sin.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (/.f64 (Rewrite<= cube-mult_binary64 (pow.f64 (sin.f64 x) 3)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (cos.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x))))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (Rewrite<= cube-mult_binary64 (pow.f64 (cos.f64 x) 3))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (Rewrite<= cube-unmult_binary64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 x))))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 2 points increase in error, 1 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x))))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 2 points increase in error, 3 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (cos.f64 x)))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite<= unpow2_binary64 (pow.f64 (cos.f64 x) 2)))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 1 points increase in error, 1 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (*.f64 (sin.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (Rewrite<= cube-mult_binary64 (pow.f64 (sin.f64 x) 3)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 1 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (cos.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x))))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 3) (Rewrite<= cube-mult_binary64 (pow.f64 (cos.f64 x) 3))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= /-rgt-identity_binary64 (/.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) 1))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (cos.f64 x) 1))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 1 points increase in error, 2 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x))) (*.f64 (cos.f64 x) 1)))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (Rewrite=> *-rgt-identity_binary64 (cos.f64 x))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) -1/3) (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 -1/3 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (/.f64 (sin.f64 x) (cos.f64 x)))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 2 points increase in error, 3 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) 1)) (/.f64 (sin.f64 x) (cos.f64 x))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (*.f64 1 (cos.f64 x)))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 2 points increase in error, 1 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (+.f64 (neg.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))) (neg.f64 (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (Rewrite=> *-lft-identity_binary64 (cos.f64 x))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (neg.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x)))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (+.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x)))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (fma.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x)))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 1/3) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x)))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 1 points increase in error, 1 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3)) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= cube-unmult_binary64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 x)))))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (cos.f64 x))))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite<= unpow2_binary64 (pow.f64 (cos.f64 x) 2))))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (*.f64 (sin.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= cube-mult_binary64 (pow.f64 (sin.f64 x) 3)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (cos.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x)))))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (Rewrite<= cube-mult_binary64 (pow.f64 (cos.f64 x) 3)))) (*.f64 eps eps) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (Rewrite<= unpow2_binary64 (pow.f64 eps 2)) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 3))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (Rewrite<= cube-unmult_binary64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 x))))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x))))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (cos.f64 x)))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite<= unpow2_binary64 (pow.f64 (cos.f64 x) 2)))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (*.f64 (sin.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (sin.f64 x) (sin.f64 x)))) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (Rewrite<= cube-mult_binary64 (pow.f64 (sin.f64 x) 3)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 3) (*.f64 (cos.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x))))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 3) (Rewrite<= cube-mult_binary64 (pow.f64 (cos.f64 x) 3))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3)))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (-.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (-.f64 (/.f64 (Rewrite<= unpow2_binary64 (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite<= unpow2_binary64 (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (Rewrite<= /-rgt-identity_binary64 (/.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) 1))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (sin.f64 x) (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 (cos.f64 x) 1))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x))) (*.f64 (cos.f64 x) 1)))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (Rewrite=> *-rgt-identity_binary64 (cos.f64 x))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (neg.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))) (+.f64 eps (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (+.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 eps 1)) (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (fma.f64 (pow.f64 eps 3) (+.f64 1/3 (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (Rewrite=> distribute-lft-out_binary64 (*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))))))): 19 points increase in error, 10 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (pow.f64 eps 3) (+.f64 1/3 (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))) (*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (fma.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (*.f64 (pow.f64 eps 3) (+.f64 1/3 (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x))))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2)) (+.f64 (*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (*.f64 (pow.f64 eps 3) (+.f64 1/3 (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (pow.f64 eps 4) (+.f64 (*.f64 1/3 (/.f64 (sin.f64 x) (cos.f64 x))) (+.f64 (*.f64 -1 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x))))) (*.f64 -1 (/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x)) (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (sin.f64 x)) (cos.f64 x)))))) (+.f64 (*.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (pow.f64 eps 2)) (+.f64 (*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (*.f64 (pow.f64 eps 3) (+.f64 1/3 (+.f64 (*.f64 -1 (/.f64 (*.f64 (+.f64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 3))) (*.f64 -1/3 (/.f64 (sin.f64 x) (cos.f64 x)))) (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))))))): 2 points increase in error, 2 points decrease in error

   if 2.1000000000000001e-4 < eps

   1. Initial program 29.0

      \[\tan \left(x + \varepsilon\right) - \tan x \]

   2. Applied egg-rr 0.3

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

   3. Applied egg-rr 0.4

      \[\leadsto \mathsf{fma}\left(\tan x + \tan \varepsilon, \frac{1}{1 - \color{blue}{\frac{\tan \varepsilon \cdot \sin x}{\cos x}}}, -\tan x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\varepsilon \leq -0.00019:\\ \;\;\;\;\mathsf{fma}\left(\tan x + \tan \varepsilon, \frac{1}{1 - \tan x \cdot \tan \varepsilon}, -\tan x\right)\\ \mathbf{elif}\;\varepsilon \leq 0.00021:\\ \;\;\;\;\mathsf{fma}\left({\varepsilon}^{4}, \mathsf{fma}\left(\frac{\sin x}{\cos x}, 0.3333333333333333, {\left(\frac{\sin x}{\cos x}\right)}^{3} + \frac{\sin x}{\cos x} \cdot \left(0.3333333333333333 - \mathsf{fma}\left(\frac{{\sin x}^{2}}{{\cos x}^{2}}, -0.3333333333333333, \frac{\sin x}{\cos x} \cdot \left(\frac{\sin x}{\cos x} \cdot -0.3333333333333333 - {\left(\frac{\sin x}{\cos x}\right)}^{3}\right)\right)\right)\right), \mathsf{fma}\left(\frac{\sin x}{\cos x} + {\left(\frac{\sin x}{\cos x}\right)}^{3}, \varepsilon \cdot \varepsilon, \mathsf{fma}\left({\varepsilon}^{3}, 0.3333333333333333 + \frac{\sin x}{\cos x} \cdot \left(\frac{\sin x}{\cos x} - \left(\frac{\sin x}{\cos x} \cdot -0.3333333333333333 - {\left(\frac{\sin x}{\cos x}\right)}^{3}\right)\right), \varepsilon + \varepsilon \cdot \frac{{\sin x}^{2}}{{\cos x}^{2}}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\tan x + \tan \varepsilon, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.3
Cost	59144

\[\begin{array}{l} t_0 := \frac{\sin x}{\cos x}\\ t_1 := \tan x + \tan \varepsilon\\ \mathbf{if}\;\varepsilon \leq -3.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{t_1}{1 - \tan x \cdot \tan \varepsilon} - \tan x\\ \mathbf{elif}\;\varepsilon \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;\varepsilon \cdot \left(\varepsilon \cdot \left(t_0 + {t_0}^{3}\right) + \left(1 + \frac{{\sin x}^{2}}{{\cos x}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_1, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \end{array} \]

Alternative 2
Error	0.3
Cost	59144

\[\begin{array}{l} t_0 := \tan x + \tan \varepsilon\\ t_1 := \frac{\sin x}{\cos x}\\ \mathbf{if}\;\varepsilon \leq -2.9 \cdot 10^{-7}:\\ \;\;\;\;\frac{t_0}{1 - \tan x \cdot \tan \varepsilon} - \tan x\\ \mathbf{elif}\;\varepsilon \leq 4 \cdot 10^{-7}:\\ \;\;\;\;\varepsilon + \varepsilon \cdot \left(\frac{{\sin x}^{2}}{{\cos x}^{2}} + \varepsilon \cdot \left(t_1 + {t_1}^{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_0, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \end{array} \]

Alternative 3
Error	0.4
Cost	45960

\[\begin{array}{l} t_0 := \tan x + \tan \varepsilon\\ \mathbf{if}\;\varepsilon \leq -3.65 \cdot 10^{-9}:\\ \;\;\;\;\frac{t_0}{1 - \tan x \cdot \tan \varepsilon} - \tan x\\ \mathbf{elif}\;\varepsilon \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;\varepsilon + \frac{\varepsilon \cdot {\sin x}^{2}}{{\cos x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_0, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \end{array} \]

Alternative 4
Error	0.4
Cost	39432

\[\begin{array}{l} t_0 := \tan x + \tan \varepsilon\\ t_1 := 1 - \tan x \cdot \tan \varepsilon\\ \mathbf{if}\;\varepsilon \leq -3.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{t_0}{t_1} - \tan x\\ \mathbf{elif}\;\varepsilon \leq 5.2 \cdot 10^{-9}:\\ \;\;\;\;\varepsilon + \frac{\varepsilon \cdot {\sin x}^{2}}{{\cos x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_0, \frac{1}{t_1}, -\tan x\right)\\ \end{array} \]

Alternative 5
Error	0.4
Cost	33096

\[\begin{array}{l} t_0 := \tan x + \tan \varepsilon\\ t_1 := 1 - \tan x \cdot \tan \varepsilon\\ \mathbf{if}\;\varepsilon \leq -3.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{t_0}{t_1} - \tan x\\ \mathbf{elif}\;\varepsilon \leq 5 \cdot 10^{-9}:\\ \;\;\;\;\varepsilon + \frac{\varepsilon \cdot {\sin x}^{2}}{{\cos x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{1}{t_1} - \tan x\\ \end{array} \]

Alternative 6
Error	0.4
Cost	32968

\[\begin{array}{l} t_0 := \frac{\tan x + \tan \varepsilon}{1 - \tan x \cdot \tan \varepsilon} - \tan x\\ \mathbf{if}\;\varepsilon \leq -5.2 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\varepsilon \leq 4.2 \cdot 10^{-9}:\\ \;\;\;\;\varepsilon + \frac{\varepsilon \cdot {\sin x}^{2}}{{\cos x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	14.2
Cost	26440

\[\begin{array}{l} \mathbf{if}\;\varepsilon \leq -6.5 \cdot 10^{-5}:\\ \;\;\;\;\tan \varepsilon\\ \mathbf{elif}\;\varepsilon \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;\varepsilon + \varepsilon \cdot \frac{{\sin x}^{2}}{{\cos x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\tan \varepsilon\\ \end{array} \]

Alternative 8
Error	14.2
Cost	26440

\[\begin{array}{l} \mathbf{if}\;\varepsilon \leq -7.4 \cdot 10^{-5}:\\ \;\;\;\;\tan \varepsilon\\ \mathbf{elif}\;\varepsilon \leq 1.05 \cdot 10^{-5}:\\ \;\;\;\;\varepsilon + \frac{\varepsilon \cdot {\sin x}^{2}}{{\cos x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\tan \varepsilon\\ \end{array} \]

Alternative 9
Error	14.2
Cost	19976

\[\begin{array}{l} \mathbf{if}\;\varepsilon \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\tan \varepsilon\\ \mathbf{elif}\;\varepsilon \leq 3.5 \cdot 10^{-6}:\\ \;\;\;\;\varepsilon + \varepsilon \cdot {\left(\frac{\cos x}{\sin x}\right)}^{-2}\\ \mathbf{else}:\\ \;\;\;\;\tan \varepsilon\\ \end{array} \]

Alternative 10
Error	26.3
Cost	6464

\[\tan \varepsilon \]

Alternative 11
Error	43.7
Cost	64

\[\varepsilon \]

Reproduce

herbie shell --seed 2022330 
(FPCore (x eps)
  :name "2tan (problem 3.3.2)"
  :precision binary64

  :herbie-target
  (/ (sin eps) (* (cos x) (cos (+ x eps))))

  (- (tan (+ x eps)) (tan x)))