\[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]

↓

\[\begin{array}{l} t_1 := {\left(\frac{\ell}{Om}\right)}^{2}\\ t_2 := \sqrt{\left(U \cdot \left(2 \cdot n\right)\right) \cdot \left(\left(t + \frac{\ell \cdot \ell}{Om} \cdot -2\right) + \left(n \cdot t_1\right) \cdot \left(U* - U\right)\right)}\\ \mathbf{if}\;t_2 \leq 0:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, n \cdot \left(t_1 \cdot \left(U - U*\right)\right)\right)\right)}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right) + 2 \cdot \left(t \cdot \left(n \cdot U\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + 2 \cdot \frac{\left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right) \cdot \left(n \cdot \left(U \cdot \ell\right)\right)}{Om}}\\ \end{array} \]

(FPCore (n U t l Om U*)
 :precision binary64
 (sqrt
  (*
   (* (* 2.0 n) U)
   (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

↓

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (pow (/ l Om) 2.0))
        (t_2
         (sqrt
          (*
           (* U (* 2.0 n))
           (+ (+ t (* (/ (* l l) Om) -2.0)) (* (* n t_1) (- U* U)))))))
   (if (<= t_2 0.0)
     (*
      (sqrt (* 2.0 n))
      (sqrt (* U (- t (fma 2.0 (* l (/ l Om)) (* n (* t_1 (- U U*))))))))
     (if (<= t_2 INFINITY)
       (sqrt
        (+
         (*
          (fma l -2.0 (* n (* (/ l Om) (- U* U))))
          (* (/ l Om) (* n (* 2.0 U))))
         (* 2.0 (* t (* n U)))))
       (sqrt
        (+
         (* 2.0 (* n (* U t)))
         (*
          2.0
          (/ (* (- (* l -2.0) (* (/ n Om) (* U l))) (* n (* U l))) Om))))))))

double code(double n, double U, double t, double l, double Om, double U_42_) {
	return sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * pow((l / Om), 2.0)) * (U - U_42_)))));
}

↓

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = pow((l / Om), 2.0);
	double t_2 = sqrt(((U * (2.0 * n)) * ((t + (((l * l) / Om) * -2.0)) + ((n * t_1) * (U_42_ - U)))));
	double tmp;
	if (t_2 <= 0.0) {
		tmp = sqrt((2.0 * n)) * sqrt((U * (t - fma(2.0, (l * (l / Om)), (n * (t_1 * (U - U_42_)))))));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = sqrt(((fma(l, -2.0, (n * ((l / Om) * (U_42_ - U)))) * ((l / Om) * (n * (2.0 * U)))) + (2.0 * (t * (n * U)))));
	} else {
		tmp = sqrt(((2.0 * (n * (U * t))) + (2.0 * ((((l * -2.0) - ((n / Om) * (U * l))) * (n * (U * l))) / Om))));
	}
	return tmp;
}

function code(n, U, t, l, Om, U_42_)
	return sqrt(Float64(Float64(Float64(2.0 * n) * U) * Float64(Float64(t - Float64(2.0 * Float64(Float64(l * l) / Om))) - Float64(Float64(n * (Float64(l / Om) ^ 2.0)) * Float64(U - U_42_)))))
end

↓

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(l / Om) ^ 2.0
	t_2 = sqrt(Float64(Float64(U * Float64(2.0 * n)) * Float64(Float64(t + Float64(Float64(Float64(l * l) / Om) * -2.0)) + Float64(Float64(n * t_1) * Float64(U_42_ - U)))))
	tmp = 0.0
	if (t_2 <= 0.0)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - fma(2.0, Float64(l * Float64(l / Om)), Float64(n * Float64(t_1 * Float64(U - U_42_))))))));
	elseif (t_2 <= Inf)
		tmp = sqrt(Float64(Float64(fma(l, -2.0, Float64(n * Float64(Float64(l / Om) * Float64(U_42_ - U)))) * Float64(Float64(l / Om) * Float64(n * Float64(2.0 * U)))) + Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = sqrt(Float64(Float64(2.0 * Float64(n * Float64(U * t))) + Float64(2.0 * Float64(Float64(Float64(Float64(l * -2.0) - Float64(Float64(n / Om) * Float64(U * l))) * Float64(n * Float64(U * l))) / Om))));
	end
	return tmp
end

code[n_, U_, t_, l_, Om_, U$42$_] := N[Sqrt[N[(N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision] * N[(N[(t - N[(2.0 * N[(N[(l * l), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(n * N[Power[N[(l / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U - U$42$), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

↓

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[Power[N[(l / Om), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(N[(U * N[(2.0 * n), $MachinePrecision]), $MachinePrecision] * N[(N[(t + N[(N[(N[(l * l), $MachinePrecision] / Om), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(n * t$95$1), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$2, 0.0], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(U * N[(t - N[(2.0 * N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision] + N[(n * N[(t$95$1 * N[(U - U$42$), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[Sqrt[N[(N[(N[(l * -2.0 + N[(n * N[(N[(l / Om), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(l / Om), $MachinePrecision] * N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[(N[(2.0 * N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(N[(N[(N[(l * -2.0), $MachinePrecision] - N[(N[(n / Om), $MachinePrecision] * N[(U * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(n * N[(U * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]]

\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}

↓

\begin{array}{l}
t_1 := {\left(\frac{\ell}{Om}\right)}^{2}\\
t_2 := \sqrt{\left(U \cdot \left(2 \cdot n\right)\right) \cdot \left(\left(t + \frac{\ell \cdot \ell}{Om} \cdot -2\right) + \left(n \cdot t_1\right) \cdot \left(U* - U\right)\right)}\\
\mathbf{if}\;t_2 \leq 0:\\
\;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, n \cdot \left(t_1 \cdot \left(U - U*\right)\right)\right)\right)}\\

\mathbf{elif}\;t_2 \leq \infty:\\
\;\;\;\;\sqrt{\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right) + 2 \cdot \left(t \cdot \left(n \cdot U\right)\right)}\\

\mathbf{else}:\\
\;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + 2 \cdot \frac{\left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right) \cdot \left(n \cdot \left(U \cdot \ell\right)\right)}{Om}}\\


\end{array}

Derivation

Split input into 3 regimes
if (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))) < 0.0
1. Initial program 56.3
  \[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
2. Applied egg-rr39.4
  \[\leadsto \color{blue}{\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, n \cdot \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(U - U*\right)\right)\right)\right)}} \]
if 0.0 < (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))) < +inf.0
1. Initial program 24.3
  \[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
2. Simplified23.6
  \[\leadsto \color{blue}{\sqrt{\left(2 \cdot \left(n \cdot U\right)\right) \cdot \left(t + \frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, n \cdot \frac{\ell \cdot \left(U* - U\right)}{Om}\right)\right)}} \]
  Proof
  (sqrt.f64 (*.f64 (*.f64 2 (*.f64 n U)) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 n (/.f64 (*.f64 l (-.f64 U* U)) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 n) U)) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 n (/.f64 (*.f64 l (-.f64 U* U)) Om))))))): 0 points increase in error, 1 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (Rewrite<= metadata-eval (neg.f64 2)) (*.f64 n (/.f64 (*.f64 l (-.f64 U* U)) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (Rewrite=> sub-neg_binary64 (+.f64 U* (neg.f64 U)))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (+.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 U*))) (neg.f64 U))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (neg.f64 U*) U)))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (neg.f64 (Rewrite<= +-commutative_binary64 (+.f64 U (neg.f64 U*))))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 U U*)))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 l Om) (neg.f64 (-.f64 U U*)))))))))): 0 points increase in error, 8 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)))))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U U*)))))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 l (neg.f64 2)) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 2) l)) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 l Om) (*.f64 (neg.f64 2) l)) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 l (*.f64 (neg.f64 2) l)) Om)) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 10 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (neg.f64 2) l) l)) Om) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (neg.f64 2) (*.f64 l l))) Om) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (neg.f64 2) (/.f64 (*.f64 l l) Om))) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om)))) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 l Om) (*.f64 (/.f64 l Om) (-.f64 U U*))) n)))))): 7 points increase in error, 2 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 l Om) (/.f64 l Om)) (-.f64 U U*))) n))))): 10 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)) n))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (Rewrite<= *-commutative_binary64 (*.f64 n (*.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U*)))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))))): 2 points increase in error, 7 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 t (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om)))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (Rewrite<= sub-neg_binary64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om)))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))): 0 points increase in error, 0 points decrease in error
3. Applied egg-rr19.4
  \[\leadsto \sqrt{\color{blue}{\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(U \cdot 2\right)\right)\right) + 2 \cdot \left(\left(n \cdot U\right) \cdot t\right)}} \]
if +inf.0 < (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))))
1. Initial program 64.0
  \[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
2. Simplified58.4
  \[\leadsto \color{blue}{\sqrt{\left(2 \cdot \left(n \cdot U\right)\right) \cdot \left(t + \frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, n \cdot \frac{\ell \cdot \left(U* - U\right)}{Om}\right)\right)}} \]
  Proof
  (sqrt.f64 (*.f64 (*.f64 2 (*.f64 n U)) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 n (/.f64 (*.f64 l (-.f64 U* U)) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 n) U)) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 n (/.f64 (*.f64 l (-.f64 U* U)) Om))))))): 0 points increase in error, 1 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (Rewrite<= metadata-eval (neg.f64 2)) (*.f64 n (/.f64 (*.f64 l (-.f64 U* U)) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (Rewrite=> sub-neg_binary64 (+.f64 U* (neg.f64 U)))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (+.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 U*))) (neg.f64 U))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (neg.f64 U*) U)))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (neg.f64 (Rewrite<= +-commutative_binary64 (+.f64 U (neg.f64 U*))))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (/.f64 (*.f64 l (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 U U*)))) Om))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 l Om) (neg.f64 (-.f64 U U*)))))))))): 0 points increase in error, 8 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (*.f64 n (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)))))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 n (*.f64 (/.f64 l Om) (-.f64 U U*)))))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l (neg.f64 2) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 l (neg.f64 2)) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 2) l)) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 l Om) (*.f64 (neg.f64 2) l)) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 l (*.f64 (neg.f64 2) l)) Om)) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 10 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (neg.f64 2) l) l)) Om) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (neg.f64 2) (*.f64 l l))) Om) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (neg.f64 2) (/.f64 (*.f64 l l) Om))) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om)))) (*.f64 (/.f64 l Om) (*.f64 (*.f64 (/.f64 l Om) (-.f64 U U*)) n)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 l Om) (*.f64 (/.f64 l Om) (-.f64 U U*))) n)))))): 7 points increase in error, 2 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 l Om) (/.f64 l Om)) (-.f64 U U*))) n))))): 10 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)) n))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (Rewrite<= *-commutative_binary64 (*.f64 n (*.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U*)))))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (-.f64 (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))))): 2 points increase in error, 7 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 t (neg.f64 (*.f64 2 (/.f64 (*.f64 l l) Om)))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))))): 0 points increase in error, 0 points decrease in error
  (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (Rewrite<= sub-neg_binary64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om)))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))): 0 points increase in error, 0 points decrease in error
3. Taylor expanded in t around inf 42.9
  \[\leadsto \sqrt{\color{blue}{2 \cdot \left(n \cdot \left(t \cdot U\right)\right) + 2 \cdot \frac{\left(\frac{n \cdot \left(\ell \cdot \left(U* - U\right)\right)}{Om} + -2 \cdot \ell\right) \cdot \left(n \cdot \left(\ell \cdot U\right)\right)}{Om}}} \]
4. Taylor expanded in U* around 0 41.2
  \[\leadsto \sqrt{2 \cdot \left(n \cdot \left(t \cdot U\right)\right) + 2 \cdot \frac{\left(\color{blue}{-1 \cdot \frac{n \cdot \left(\ell \cdot U\right)}{Om}} + -2 \cdot \ell\right) \cdot \left(n \cdot \left(\ell \cdot U\right)\right)}{Om}} \]
5. Simplified41.4
  \[\leadsto \sqrt{2 \cdot \left(n \cdot \left(t \cdot U\right)\right) + 2 \cdot \frac{\left(\color{blue}{\frac{n}{Om} \cdot \left(-\ell \cdot U\right)} + -2 \cdot \ell\right) \cdot \left(n \cdot \left(\ell \cdot U\right)\right)}{Om}} \]
  Proof
  (*.f64 (/.f64 n Om) (neg.f64 (*.f64 l U))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 n Om) (*.f64 l U)))): 0 points increase in error, 0 points decrease in error
  (neg.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 n (*.f64 l U)) Om))): 46 points increase in error, 37 points decrease in error
  (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 n (*.f64 l U)) Om))): 0 points increase in error, 0 points decrease in error
Recombined 3 regimes into one program.
Final simplification25.5
\[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt{\left(U \cdot \left(2 \cdot n\right)\right) \cdot \left(\left(t + \frac{\ell \cdot \ell}{Om} \cdot -2\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)} \leq 0:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, n \cdot \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(U - U*\right)\right)\right)\right)}\\ \mathbf{elif}\;\sqrt{\left(U \cdot \left(2 \cdot n\right)\right) \cdot \left(\left(t + \frac{\ell \cdot \ell}{Om} \cdot -2\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)} \leq \infty:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right) + 2 \cdot \left(t \cdot \left(n \cdot U\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + 2 \cdot \frac{\left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right) \cdot \left(n \cdot \left(U \cdot \ell\right)\right)}{Om}}\\ \end{array} \]

Alternatives

Alternative 1
Error	26.1
Cost	43720

\[\begin{array}{l} t_1 := \sqrt{\left(U \cdot \left(2 \cdot n\right)\right) \cdot \left(\left(t + \frac{\ell \cdot \ell}{Om} \cdot -2\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot t}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right) + 2 \cdot \left(t \cdot \left(n \cdot U\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + 2 \cdot \frac{\left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right) \cdot \left(n \cdot \left(U \cdot \ell\right)\right)}{Om}}\\ \end{array} \]

Alternative 2
Error	26.6
Cost	30536

\[\begin{array}{l} t_1 := \left(U \cdot \left(2 \cdot n\right)\right) \cdot \left(\left(t + \frac{\ell \cdot \ell}{Om} \cdot -2\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\sqrt{\left(2 \cdot \left(n \cdot U\right)\right) \cdot \left(t + \frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot U*\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(\left(n \cdot \mathsf{fma}\left(\ell, -2, \frac{\left(U* - U\right) \cdot \left(n \cdot \ell\right)}{Om}\right)\right) \cdot \left(\left(U \cdot \ell\right) \cdot \frac{1}{Om}\right)\right)}\\ \end{array} \]

Alternative 3
Error	30.2
Cost	14680

\[\begin{array}{l} t_1 := n \cdot \left(U \cdot \ell\right)\\ t_2 := \left(\ell \cdot \sqrt{2}\right) \cdot \sqrt{\frac{n \cdot \left(U \cdot \left(-2 + \frac{n \cdot U*}{Om}\right)\right)}{Om}}\\ \mathbf{if}\;\ell \leq -2.4 \cdot 10^{-67}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + 2 \cdot \frac{t_1 \cdot \left(\frac{n}{Om} \cdot \left(\ell \cdot U*\right) + \ell \cdot -2\right)}{Om}}\\ \mathbf{elif}\;\ell \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t + \frac{\ell \cdot \left(\frac{n \cdot \left(\ell \cdot U*\right)}{Om} + \ell \cdot -2\right)}{Om}\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 2.2 \cdot 10^{+109}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(-4, \frac{\left(\ell \cdot \ell\right) \cdot \left(n \cdot U\right)}{Om}, 2 \cdot \left(U \cdot \left(n \cdot t\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 1.15 \cdot 10^{+220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\ell \leq 10^{+262}:\\ \;\;\;\;\sqrt{-2 \cdot \left(\frac{t_1}{Om} \cdot \left(\frac{n}{Om} \cdot \left(U \cdot \ell\right) + 2 \cdot \ell\right)\right)}\\ \mathbf{elif}\;\ell \leq 8.2 \cdot 10^{+272}:\\ \;\;\;\;\sqrt{2 \cdot \left(\left(n \cdot U\right) \cdot \mathsf{fma}\left(-2, \frac{\ell}{\frac{Om}{\ell}}, t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	30.1
Cost	14540

\[\begin{array}{l} t_1 := \sqrt{\left(2 \cdot \left(n \cdot U\right)\right) \cdot \left(t + \frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot U*\right)\right)\right)}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-215}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + 2 \cdot \frac{\left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right) \cdot \left(n \cdot \left(U \cdot \ell\right)\right)}{Om}}\\ \mathbf{elif}\;t \leq 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot t} \cdot \sqrt{n \cdot U}\\ \end{array} \]

Alternative 5
Error	30.8
Cost	14416

\[\begin{array}{l} \mathbf{if}\;\ell \leq -2.4 \cdot 10^{-67}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + 2 \cdot \frac{\left(n \cdot \left(U \cdot \ell\right)\right) \cdot \left(\frac{n}{Om} \cdot \left(\ell \cdot U*\right) + \ell \cdot -2\right)}{Om}}\\ \mathbf{elif}\;\ell \leq 3.7 \cdot 10^{-228}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t + \frac{\ell \cdot \left(\frac{n \cdot \left(\ell \cdot U*\right)}{Om} + \ell \cdot -2\right)}{Om}\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 1.8 \cdot 10^{+79}:\\ \;\;\;\;\sqrt{-2 \cdot \left(\left(n \cdot U\right) \cdot \left(\frac{2}{\frac{Om}{\ell \cdot \ell}} - t\right)\right)}\\ \mathbf{elif}\;\ell \leq 2.3 \cdot 10^{+134}:\\ \;\;\;\;\sqrt{2 \cdot \left(\frac{n}{Om} \cdot \left(\left(\ell \cdot \left(U \cdot \ell\right)\right) \cdot \left(-2 + U* \cdot \frac{n}{Om}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\ell \cdot \sqrt{2}\right) \cdot \sqrt{\frac{n \cdot \left(U \cdot \left(-2 + \frac{n \cdot U*}{Om}\right)\right)}{Om}}\\ \end{array} \]

Alternative 6
Error	32.9
Cost	8392

\[\begin{array}{l} \mathbf{if}\;\ell \leq -3.1 \cdot 10^{+114}:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot -2}{\frac{\frac{Om}{\ell}}{U \cdot \ell}}}\\ \mathbf{elif}\;\ell \leq -4.4 \cdot 10^{-114}:\\ \;\;\;\;\sqrt{\left(U \cdot \left(2 \cdot n\right)\right) \cdot \left(\left(t + \frac{\ell \cdot \ell}{Om} \cdot -2\right) + \frac{n \cdot \left(\ell \cdot \ell\right)}{Om} \cdot \frac{U*}{Om}\right)}\\ \mathbf{elif}\;\ell \leq 3.7 \cdot 10^{-228}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t + \frac{\ell \cdot \left(\frac{n \cdot \left(\ell \cdot U*\right)}{Om} + \ell \cdot -2\right)}{Om}\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 9.5 \cdot 10^{+86}:\\ \;\;\;\;\sqrt{-2 \cdot \left(\left(n \cdot U\right) \cdot \left(\frac{2}{\frac{Om}{\ell \cdot \ell}} - t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-2 \cdot \left(\frac{n \cdot \left(U \cdot \ell\right)}{Om} \cdot \left(\frac{n}{Om} \cdot \left(U \cdot \ell\right) + 2 \cdot \ell\right)\right)}\\ \end{array} \]

Alternative 7
Error	32.3
Cost	8388

\[\begin{array}{l} t_1 := n \cdot \left(U \cdot \ell\right)\\ \mathbf{if}\;\ell \leq -2.4 \cdot 10^{-67}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + 2 \cdot \frac{t_1 \cdot \left(\frac{n}{Om} \cdot \left(\ell \cdot U*\right) + \ell \cdot -2\right)}{Om}}\\ \mathbf{elif}\;\ell \leq 3.7 \cdot 10^{-228}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t + \frac{\ell \cdot \left(\frac{n \cdot \left(\ell \cdot U*\right)}{Om} + \ell \cdot -2\right)}{Om}\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 1.8 \cdot 10^{+79}:\\ \;\;\;\;\sqrt{-2 \cdot \left(\left(n \cdot U\right) \cdot \left(\frac{2}{\frac{Om}{\ell \cdot \ell}} - t\right)\right)}\\ \mathbf{elif}\;\ell \leq 6.4 \cdot 10^{+128}:\\ \;\;\;\;\sqrt{2 \cdot \left(\frac{n}{Om} \cdot \left(\left(\ell \cdot \left(U \cdot \ell\right)\right) \cdot \left(-2 + U* \cdot \frac{n}{Om}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-2 \cdot \left(\frac{t_1}{Om} \cdot \left(\frac{n}{Om} \cdot \left(U \cdot \ell\right) + 2 \cdot \ell\right)\right)}\\ \end{array} \]

Alternative 8
Error	32.7
Cost	8140

\[\begin{array}{l} \mathbf{if}\;\ell \leq -2 \cdot 10^{+138}:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot -2}{\frac{\frac{Om}{\ell}}{U \cdot \ell}}}\\ \mathbf{elif}\;\ell \leq 3.7 \cdot 10^{-228}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t + \frac{\ell \cdot \left(\frac{n \cdot \left(\ell \cdot U*\right)}{Om} + \ell \cdot -2\right)}{Om}\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 9.5 \cdot 10^{+86}:\\ \;\;\;\;\sqrt{-2 \cdot \left(\left(n \cdot U\right) \cdot \left(\frac{2}{\frac{Om}{\ell \cdot \ell}} - t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-2 \cdot \left(\frac{n \cdot \left(U \cdot \ell\right)}{Om} \cdot \left(\frac{n}{Om} \cdot \left(U \cdot \ell\right) + 2 \cdot \ell\right)\right)}\\ \end{array} \]

Alternative 9
Error	34.4
Cost	8008

Alternative 10
Error	34.7
Cost	7624

Alternative 11
Error	36.9
Cost	7496

\[\begin{array}{l} \mathbf{if}\;\ell \leq -1.85 \cdot 10^{+123}:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot -2}{\frac{\frac{Om}{\ell}}{U \cdot \ell}}}\\ \mathbf{elif}\;\ell \leq 9.5 \cdot 10^{+86}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(\left(\ell \cdot -2\right) \cdot \left(\frac{n}{Om} \cdot \left(U \cdot \ell\right)\right)\right)}\\ \end{array} \]

Alternative 12
Error	39.2
Cost	7364

\[\begin{array}{l} \mathbf{if}\;\ell \leq 9.5 \cdot 10^{+86}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(-2 \cdot \left(\ell \cdot \left(\ell \cdot \left(U \cdot \frac{n}{Om}\right)\right)\right)\right)}\\ \end{array} \]

Alternative 13
Error	38.6
Cost	7364

\[\begin{array}{l} \mathbf{if}\;\ell \leq 9.5 \cdot 10^{+86}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(\left(\ell \cdot -2\right) \cdot \left(\frac{n}{Om} \cdot \left(U \cdot \ell\right)\right)\right)}\\ \end{array} \]

Alternative 14
Error	40.0
Cost	6848

\[\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right)} \]

Alternative 15
Error	40.0
Cost	6848

\[\sqrt{t \cdot \left(2 \cdot \left(n \cdot U\right)\right)} \]

Error

Derivation

`if (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))) < 0.0`

`if 0.0 < (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))) < +inf.0`

`if +inf.0 < (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))`

Alternatives

Error

Reproduce

Error

Derivation

if (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))) < 0.0

if 0.0 < (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))))) < +inf.0

if +inf.0 < (sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))))

Alternatives

Error

Reproduce

`if (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))) < 0.0`

`if 0.0 < (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))) < +inf.0`

`if +inf.0 < (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))`