Average Error: 36.9 → 0.3
Time: 30.4s
Precision: binary64
Cost: 216264
\[\tan \left(x + \varepsilon\right) - \tan x \]
↓
\[\begin{array}{l} t_0 := \frac{\sin x}{\cos x}\\ t_1 := \tan x \cdot \tan \varepsilon\\ t_2 := \frac{{\sin x}^{2}}{{\cos x}^{2}}\\ t_3 := 1 + t_2\\ t_4 := 0.3333333333333333 - t_2 \cdot \left(-0.3333333333333333 + \left(-1 - t_2\right)\right)\\ t_5 := \tan x + \tan \varepsilon\\ t_6 := 1 - t_1\\ \mathbf{if}\;\varepsilon \leq -0.000624941289150923:\\ \;\;\;\;\mathsf{fma}\left(t_5, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left({\varepsilon}^{3}, t_4, t_3 \cdot \left(\varepsilon + \frac{\varepsilon}{\frac{\cos x}{\varepsilon \cdot \sin x}}\right)\right) + {\varepsilon}^{4} \cdot \left(t_4 \cdot t_0 + t_3 \cdot \left(0.3333333333333333 \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_5 \cdot \cos x, \frac{\frac{1}{\cos x}}{t_6}, \tan x \cdot \frac{t_1 + -1}{t_6}\right)\\ \end{array} \]
(FPCore (x eps) :precision binary64 (- (tan (+ x eps)) (tan x)))
↓
(FPCore (x eps)
 :precision binary64
 (let* ((t_0 (/ (sin x) (cos x)))
        (t_1 (* (tan x) (tan eps)))
        (t_2 (/ (pow (sin x) 2.0) (pow (cos x) 2.0)))
        (t_3 (+ 1.0 t_2))
        (t_4
         (- 0.3333333333333333 (* t_2 (+ -0.3333333333333333 (- -1.0 t_2)))))
        (t_5 (+ (tan x) (tan eps)))
        (t_6 (- 1.0 t_1)))
   (if (<= eps -0.000624941289150923)
     (fma t_5 (/ 1.0 (- 1.0 (/ (* (tan eps) (sin x)) (cos x)))) (- (tan x)))
     (if (<= eps 1.4747620014679831e-6)
       (+
        (fma
         (pow eps 3.0)
         t_4
         (* t_3 (+ eps (/ eps (/ (cos x) (* eps (sin x)))))))
        (* (pow eps 4.0) (+ (* t_4 t_0) (* t_3 (* 0.3333333333333333 t_0)))))
       (fma
        (* t_5 (cos x))
        (/ (/ 1.0 (cos x)) t_6)
        (* (tan x) (/ (+ t_1 -1.0) t_6)))))))
double code(double x, double eps) {
	return tan((x + eps)) - tan(x);
}
↓
double code(double x, double eps) {
	double t_0 = sin(x) / cos(x);
	double t_1 = tan(x) * tan(eps);
	double t_2 = pow(sin(x), 2.0) / pow(cos(x), 2.0);
	double t_3 = 1.0 + t_2;
	double t_4 = 0.3333333333333333 - (t_2 * (-0.3333333333333333 + (-1.0 - t_2)));
	double t_5 = tan(x) + tan(eps);
	double t_6 = 1.0 - t_1;
	double tmp;
	if (eps <= -0.000624941289150923) {
		tmp = fma(t_5, (1.0 / (1.0 - ((tan(eps) * sin(x)) / cos(x)))), -tan(x));
	} else if (eps <= 1.4747620014679831e-6) {
		tmp = fma(pow(eps, 3.0), t_4, (t_3 * (eps + (eps / (cos(x) / (eps * sin(x))))))) + (pow(eps, 4.0) * ((t_4 * t_0) + (t_3 * (0.3333333333333333 * t_0))));
	} else {
		tmp = fma((t_5 * cos(x)), ((1.0 / cos(x)) / t_6), (tan(x) * ((t_1 + -1.0) / t_6)));
	}
	return tmp;
}

function code(x, eps)
	return Float64(tan(Float64(x + eps)) - tan(x))
end
↓
function code(x, eps)
	t_0 = Float64(sin(x) / cos(x))
	t_1 = Float64(tan(x) * tan(eps))
	t_2 = Float64((sin(x) ^ 2.0) / (cos(x) ^ 2.0))
	t_3 = Float64(1.0 + t_2)
	t_4 = Float64(0.3333333333333333 - Float64(t_2 * Float64(-0.3333333333333333 + Float64(-1.0 - t_2))))
	t_5 = Float64(tan(x) + tan(eps))
	t_6 = Float64(1.0 - t_1)
	tmp = 0.0
	if (eps <= -0.000624941289150923)
		tmp = fma(t_5, Float64(1.0 / Float64(1.0 - Float64(Float64(tan(eps) * sin(x)) / cos(x)))), Float64(-tan(x)));
	elseif (eps <= 1.4747620014679831e-6)
		tmp = Float64(fma((eps ^ 3.0), t_4, Float64(t_3 * Float64(eps + Float64(eps / Float64(cos(x) / Float64(eps * sin(x))))))) + Float64((eps ^ 4.0) * Float64(Float64(t_4 * t_0) + Float64(t_3 * Float64(0.3333333333333333 * t_0)))));
	else
		tmp = fma(Float64(t_5 * cos(x)), Float64(Float64(1.0 / cos(x)) / t_6), Float64(tan(x) * Float64(Float64(t_1 + -1.0) / t_6)));
	end
	return tmp
end

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[Sin[x], $MachinePrecision] / N[Cos[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Tan[x], $MachinePrecision] * N[Tan[eps], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[N[Sin[x], $MachinePrecision], 2.0], $MachinePrecision] / N[Power[N[Cos[x], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(0.3333333333333333 - N[(t$95$2 * N[(-0.3333333333333333 + N[(-1.0 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[Tan[x], $MachinePrecision] + N[Tan[eps], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(1.0 - t$95$1), $MachinePrecision]}, If[LessEqual[eps, -0.000624941289150923], N[(t$95$5 * N[(1.0 / N[(1.0 - N[(N[(N[Tan[eps], $MachinePrecision] * N[Sin[x], $MachinePrecision]), $MachinePrecision] / N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + (-N[Tan[x], $MachinePrecision])), $MachinePrecision], If[LessEqual[eps, 1.4747620014679831e-6], N[(N[(N[Power[eps, 3.0], $MachinePrecision] * t$95$4 + N[(t$95$3 * N[(eps + N[(eps / N[(N[Cos[x], $MachinePrecision] / N[(eps * N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[eps, 4.0], $MachinePrecision] * N[(N[(t$95$4 * t$95$0), $MachinePrecision] + N[(t$95$3 * N[(0.3333333333333333 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$5 * N[Cos[x], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 / N[Cos[x], $MachinePrecision]), $MachinePrecision] / t$95$6), $MachinePrecision] + N[(N[Tan[x], $MachinePrecision] * N[(N[(t$95$1 + -1.0), $MachinePrecision] / t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

\tan \left(x + \varepsilon\right) - \tan x
↓
\begin{array}{l}
t_0 := \frac{\sin x}{\cos x}\\
t_1 := \tan x \cdot \tan \varepsilon\\
t_2 := \frac{{\sin x}^{2}}{{\cos x}^{2}}\\
t_3 := 1 + t_2\\
t_4 := 0.3333333333333333 - t_2 \cdot \left(-0.3333333333333333 + \left(-1 - t_2\right)\right)\\
t_5 := \tan x + \tan \varepsilon\\
t_6 := 1 - t_1\\
\mathbf{if}\;\varepsilon \leq -0.000624941289150923:\\
\;\;\;\;\mathsf{fma}\left(t_5, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\

\mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\
\;\;\;\;\mathsf{fma}\left({\varepsilon}^{3}, t_4, t_3 \cdot \left(\varepsilon + \frac{\varepsilon}{\frac{\cos x}{\varepsilon \cdot \sin x}}\right)\right) + {\varepsilon}^{4} \cdot \left(t_4 \cdot t_0 + t_3 \cdot \left(0.3333333333333333 \cdot t_0\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(t_5 \cdot \cos x, \frac{\frac{1}{\cos x}}{t_6}, \tan x \cdot \frac{t_1 + -1}{t_6}\right)\\


\end{array}

Error

Target

Original36.9
Target15.3
Herbie0.3
\[\frac{\sin \varepsilon}{\cos x \cdot \cos \left(x + \varepsilon\right)} \]

Derivation

  1. Split input into 3 regimes

  2. if eps < -6.2494128915092299e-4

    1. Initial program 29.5

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

    2. Applied egg-rr0.4

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

    3. Applied egg-rr0.4

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

    if -6.2494128915092299e-4 < eps < 1.4747620014679831e-6

    1. Initial program 44.0

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

    2. Applied egg-rr44.5

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan \left(x + \varepsilon\right)\right)\right)} - \tan x \]

    3. Applied egg-rr43.7

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

    4. Taylor expanded in eps around 0 0.3

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

    5. Simplified0.3

      \[\leadsto \color{blue}{\mathsf{fma}\left({\varepsilon}^{3}, 0.3333333333333333 - \frac{{\sin x}^{2}}{{\cos x}^{2}} \cdot \left(-0.3333333333333333 - \left(1 - \frac{-{\sin x}^{2}}{{\cos x}^{2}}\right)\right), \left(1 - \frac{-{\sin x}^{2}}{{\cos x}^{2}}\right) \cdot \left(\varepsilon + \frac{\varepsilon}{\frac{\cos x}{\varepsilon \cdot \sin x}}\right)\right) - {\varepsilon}^{4} \cdot \left(\left(1 - \frac{-{\sin x}^{2}}{{\cos x}^{2}}\right) \cdot \left(\frac{\sin x}{\cos x} \cdot -0.3333333333333333\right) - \frac{\sin x}{\cos x} \cdot \left(0.3333333333333333 - \frac{{\sin x}^{2}}{{\cos x}^{2}} \cdot \left(-0.3333333333333333 - \left(1 - \frac{-{\sin x}^{2}}{{\cos x}^{2}}\right)\right)\right)\right)} \]
      Proof
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (Rewrite<= *-inverses_binary64 (/.f64 (cos.f64 x) (cos.f64 x))) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x))))))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (neg.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x)))))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (cos.f64 x))))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (-.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (-.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x))))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (-.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (Rewrite<= cube-mult_binary64 (pow.f64 (cos.f64 x) 3))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (neg.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3)))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3)))))) (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (-.f64 (Rewrite<= *-inverses_binary64 (/.f64 (cos.f64 x) (cos.f64 x))) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x)))))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (neg.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x))))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 4 points increase in error, 5 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (cos.f64 x)))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x))) (+.f64 eps (/.f64 eps (/.f64 (cos.f64 x) (*.f64 eps (sin.f64 x))))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 12 points increase in error, 6 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) (+.f64 eps (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 eps (*.f64 eps (sin.f64 x))) (cos.f64 x)))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) (+.f64 eps (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 eps eps) (sin.f64 x))) (cos.f64 x))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) (+.f64 eps (/.f64 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 eps 2)) (sin.f64 x)) (cos.f64 x))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) eps) (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (+.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x))) (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 19 points increase in error, 13 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (*.f64 (pow.f64 eps 2) (sin.f64 x))) (*.f64 (cos.f64 x) (cos.f64 x)))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (Rewrite=> *-commutative_binary64 (*.f64 (sin.f64 x) (pow.f64 eps 2)))) (*.f64 (cos.f64 x) (cos.f64 x))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 eps 2))) (*.f64 (cos.f64 x) (cos.f64 x))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)))) (*.f64 (cos.f64 x) (cos.f64 x))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (Rewrite<= unpow2_binary64 (pow.f64 (cos.f64 x) 2))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (fma.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (pow.f64 eps 3) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3)))))) (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 1 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3))) (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x))) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3))))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 (Rewrite<= *-inverses_binary64 (/.f64 (cos.f64 x) (cos.f64 x))) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x)))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (neg.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x))))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (cos.f64 x)))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 2 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) (/.f64 (sin.f64 x) (cos.f64 x))) -1/3)) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 2 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (*.f64 (cos.f64 x) (cos.f64 x)))) -1/3) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 1 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (Rewrite<= unpow2_binary64 (pow.f64 (cos.f64 x) 2))) -1/3) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2)))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 1 (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (Rewrite<= *-inverses_binary64 (/.f64 (cos.f64 x) (cos.f64 x))) (/.f64 (neg.f64 (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x))))))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (neg.f64 (Rewrite=> associate-/r*_binary64 (/.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x)))))))))))): 0 points increase in error, 1 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (cos.f64 x))))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (-.f64 (/.f64 (cos.f64 x) (cos.f64 x)) (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (-.f64 -1/3 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)))))))))): 3 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))))))))): 1 points increase in error, 1 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (-.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (pow.f64 (cos.f64 x) 2)))))))))): 0 points increase in error, 2 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (-.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (*.f64 (cos.f64 x) (Rewrite=> unpow2_binary64 (*.f64 (cos.f64 x) (cos.f64 x))))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (-.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (Rewrite<= cube-mult_binary64 (pow.f64 (cos.f64 x) 3))))))))): 1 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (neg.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3)))))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (Rewrite<= associate-/r/_binary64 (/.f64 (sin.f64 x) (/.f64 (cos.f64 x) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))))))))): 2 points increase in error, 3 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (sin.f64 x) (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3)))))) (cos.f64 x)))))): 2 points increase in error, 1 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (-.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (sin.f64 x))) (cos.f64 x))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (neg.f64 (/.f64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (sin.f64 x)) (cos.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (*.f64 (pow.f64 eps 4) (+.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (sin.f64 x)) (cos.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (neg.f64 (*.f64 (pow.f64 eps 4) (+.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (sin.f64 x)) (cos.f64 x)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (*.f64 (pow.f64 eps 4) (+.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (sin.f64 x)) (cos.f64 x)))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (+.f64 (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3))) (*.f64 -1 (*.f64 (pow.f64 eps 4) (+.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (sin.f64 x)) (cos.f64 x))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x))) (pow.f64 (cos.f64 x) 2)) (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) eps) (cos.f64 x)) (+.f64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (pow.f64 eps 3)) (*.f64 -1 (*.f64 (pow.f64 eps 4) (+.f64 (*.f64 -1/3 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (sin.f64 x)) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 1/3 (+.f64 (*.f64 -1/3 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (*.f64 -1 (/.f64 (*.f64 (-.f64 (cos.f64 x) (*.f64 -1 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 3))))) (sin.f64 x)) (cos.f64 x)))))))))): 1 points increase in error, 0 points decrease in error

    if 1.4747620014679831e-6 < eps

    1. Initial program 30.5

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

    2. Applied egg-rr38.6

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan \left(x + \varepsilon\right)\right)\right)} - \tan x \]

    3. Applied egg-rr0.5

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

    4. Applied egg-rr0.5

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\varepsilon \leq -0.000624941289150923:\\ \;\;\;\;\mathsf{fma}\left(\tan x + \tan \varepsilon, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left({\varepsilon}^{3}, 0.3333333333333333 - \frac{{\sin x}^{2}}{{\cos x}^{2}} \cdot \left(-0.3333333333333333 + \left(-1 - \frac{{\sin x}^{2}}{{\cos x}^{2}}\right)\right), \left(1 + \frac{{\sin x}^{2}}{{\cos x}^{2}}\right) \cdot \left(\varepsilon + \frac{\varepsilon}{\frac{\cos x}{\varepsilon \cdot \sin x}}\right)\right) + {\varepsilon}^{4} \cdot \left(\left(0.3333333333333333 - \frac{{\sin x}^{2}}{{\cos x}^{2}} \cdot \left(-0.3333333333333333 + \left(-1 - \frac{{\sin x}^{2}}{{\cos x}^{2}}\right)\right)\right) \cdot \frac{\sin x}{\cos x} + \left(1 + \frac{{\sin x}^{2}}{{\cos x}^{2}}\right) \cdot \left(0.3333333333333333 \cdot \frac{\sin x}{\cos x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(\tan x + \tan \varepsilon\right) \cdot \cos x, \frac{\frac{1}{\cos x}}{1 - \tan x \cdot \tan \varepsilon}, \tan x \cdot \frac{\tan x \cdot \tan \varepsilon + -1}{1 - \tan x \cdot \tan \varepsilon}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error0.3
Cost157000
\[\begin{array}{l} t_0 := \tan x \cdot \tan \varepsilon\\ t_1 := \tan x + \tan \varepsilon\\ t_2 := \frac{\sin x}{\cos x}\\ t_3 := \frac{{\sin x}^{3}}{{\cos x}^{3}}\\ t_4 := \frac{{\sin x}^{2}}{{\cos x}^{2}}\\ t_5 := 1 - t_0\\ \mathbf{if}\;\varepsilon \leq -0.000624941289150923:\\ \;\;\;\;\mathsf{fma}\left(t_1, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\ \;\;\;\;\left(t_2 + t_3\right) \cdot {\varepsilon}^{2} + \left(\varepsilon \cdot \left(1 + t_4\right) + {\varepsilon}^{3} \cdot \left(0.3333333333333333 + \left(t_4 + \frac{\sin x \cdot \left(t_3 + 0.3333333333333333 \cdot t_2\right)}{\cos x}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_1 \cdot \cos x, \frac{\frac{1}{\cos x}}{t_5}, \tan x \cdot \frac{t_0 + -1}{t_5}\right)\\ \end{array} \]
Alternative 2
Error0.4
Cost111880
\[\begin{array}{l} t_0 := \frac{{\sin x}^{2}}{\cos x}\\ t_1 := \tan x + \tan \varepsilon\\ t_2 := \tan x \cdot \tan \varepsilon\\ t_3 := 1 - t_2\\ \mathbf{if}\;\varepsilon \leq -10.176222388331277:\\ \;\;\;\;\frac{t_1}{\mathsf{fma}\left(\tan \varepsilon, -\tan x, 1\right)} - \tan x\\ \mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\ \;\;\;\;\frac{\varepsilon \cdot \left(\cos x + t_0\right) + \left({\varepsilon}^{3} \cdot \left(\cos x \cdot 0.3333333333333333 + 0.3333333333333333 \cdot t_0\right) + {\varepsilon}^{5} \cdot \left(\cos x \cdot 0.13333333333333333 + t_0 \cdot 0.13333333333333333\right)\right)}{\cos x \cdot t_3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_1 \cdot \cos x, \frac{\frac{1}{\cos x}}{t_3}, \tan x \cdot \frac{t_2 + -1}{t_3}\right)\\ \end{array} \]
Alternative 3
Error0.4
Cost78984
\[\begin{array}{l} t_0 := \tan x \cdot \tan \varepsilon\\ t_1 := 1 - t_0\\ t_2 := \tan x + \tan \varepsilon\\ t_3 := \frac{{\sin x}^{2}}{\cos x}\\ \mathbf{if}\;\varepsilon \leq -0.000624941289150923:\\ \;\;\;\;\mathsf{fma}\left(t_2, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\ \;\;\;\;\frac{\varepsilon \cdot \left(\cos x + t_3\right) + {\varepsilon}^{3} \cdot \left(\cos x \cdot 0.3333333333333333 + 0.3333333333333333 \cdot t_3\right)}{\cos x \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_2 \cdot \cos x, \frac{\frac{1}{\cos x}}{t_1}, \tan x \cdot \frac{t_0 + -1}{t_1}\right)\\ \end{array} \]
Alternative 4
Error0.5
Cost78792
\[\begin{array}{l} t_0 := \tan x \cdot \tan \varepsilon\\ t_1 := 1 - t_0\\ t_2 := \tan x + \tan \varepsilon\\ t_3 := \frac{\sin x}{\cos x}\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(t_2, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, -\tan x\right)\\ \mathbf{elif}\;\varepsilon \leq 1.6898551015484493 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(\varepsilon, \varepsilon \cdot \left(t_3 + {t_3}^{3}\right), \mathsf{fma}\left(\varepsilon, \frac{{\sin x}^{2}}{{\cos x}^{2}}, \varepsilon\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_2 \cdot \cos x, \frac{\frac{1}{\cos x}}{t_1}, \tan x \cdot \frac{t_0 + -1}{t_1}\right)\\ \end{array} \]
Alternative 5
Error0.5
Cost71816
\[\begin{array}{l} t_0 := -\tan x\\ t_1 := \tan x + \tan \varepsilon\\ t_2 := \frac{\sin x}{\cos x}\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(t_1, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, t_0\right)\\ \mathbf{elif}\;\varepsilon \leq 1.6898551015484493 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(\varepsilon, \varepsilon \cdot \left(t_2 + {t_2}^{3}\right), \mathsf{fma}\left(\varepsilon, \frac{{\sin x}^{2}}{{\cos x}^{2}}, \varepsilon\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{\mathsf{fma}\left(\tan \varepsilon, t_0, 1\right)} - \tan x\\ \end{array} \]
Alternative 6
Error0.5
Cost45828
\[\begin{array}{l} t_0 := -\tan x\\ t_1 := \tan x + \tan \varepsilon\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(t_1, \frac{1}{1 - \frac{\tan \varepsilon \cdot \sin x}{\cos x}}, t_0\right)\\ \mathbf{elif}\;\varepsilon \leq 1.6898551015484493 \cdot 10^{-21}:\\ \;\;\;\;\left(1 + \frac{{\sin x}^{2}}{{\cos x}^{2}}\right) \cdot \left(\varepsilon + \frac{\varepsilon}{\frac{\cos x}{\varepsilon \cdot \sin x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{\mathsf{fma}\left(\tan \varepsilon, t_0, 1\right)} - \tan x\\ \end{array} \]
Alternative 7
Error0.5
Cost39752
\[\begin{array}{l} t_0 := \frac{\tan x + \tan \varepsilon}{\mathsf{fma}\left(\tan \varepsilon, -\tan x, 1\right)} - \tan x\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\varepsilon \leq 1.6898551015484493 \cdot 10^{-21}:\\ \;\;\;\;\left(1 + \frac{{\sin x}^{2}}{{\cos x}^{2}}\right) \cdot \left(\varepsilon + \frac{\varepsilon}{\frac{\cos x}{\varepsilon \cdot \sin x}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 8
Error0.6
Cost39304
\[\begin{array}{l} t_0 := \frac{\tan x + \tan \varepsilon}{\mathsf{fma}\left(\tan \varepsilon, -\tan x, 1\right)} - \tan x\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\varepsilon \leq 1.6898551015484493 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(\varepsilon, \frac{{\sin x}^{2}}{{\cos x}^{2}}, \varepsilon\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 9
Error0.5
Cost33096
\[\begin{array}{l} t_0 := \tan x + \tan \varepsilon\\ t_1 := 1 - \tan x \cdot \tan \varepsilon\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;\frac{t_0}{t_1} - \tan x\\ \mathbf{elif}\;\varepsilon \leq 1.3229232815913695 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(\varepsilon, \frac{{\sin x}^{2}}{{\cos x}^{2}}, \varepsilon\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{t_1}{t_0}} - \tan x\\ \end{array} \]
Alternative 10
Error0.6
Cost32968
\[\begin{array}{l} t_0 := \frac{\tan x + \tan \varepsilon}{1 - \tan x \cdot \tan \varepsilon} - \tan x\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\varepsilon \leq 1.6898551015484493 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(\varepsilon, \frac{{\sin x}^{2}}{{\cos x}^{2}}, \varepsilon\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 11
Error14.6
Cost32712
\[\begin{array}{l} t_0 := \left(\tan x + \tan \varepsilon\right) - \tan x\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(\varepsilon, \frac{{\sin x}^{2}}{{\cos x}^{2}}, \varepsilon\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 12
Error14.6
Cost20360
\[\begin{array}{l} t_0 := \left(\tan x + \tan \varepsilon\right) - \tan x\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\ \;\;\;\;\varepsilon + \varepsilon \cdot \frac{0.5 - 0.5 \cdot \cos \left(x \cdot 2\right)}{{\cos x}^{2}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 13
Error14.6
Cost19976
\[\begin{array}{l} t_0 := \left(\tan x + \tan \varepsilon\right) - \tan x\\ \mathbf{if}\;\varepsilon \leq -8.957248511955102 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\varepsilon \leq 1.4747620014679831 \cdot 10^{-6}:\\ \;\;\;\;\varepsilon + \varepsilon \cdot {\left(\frac{\sin x}{\cos x}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 14
Error27.0
Cost12992
\[\frac{\sin \varepsilon}{\cos \varepsilon} \]
Alternative 15
Error44.1
Cost64
\[\varepsilon \]

Error

Reproduce

herbie shell --seed 2022313 
(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)))