Toniolo and Linder, Equation (13)

Average Accuracy: 40.9% → 52.9%

Time: 1.5min

Precision: binary64

Cost: 51532

Math

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

↓

\[\begin{array}{l} t_1 := {\left(\frac{\ell}{Om}\right)}^{2}\\ t_2 := \left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot t_1\right) \cdot \left(U* - U\right)\right)\\ \mathbf{if}\;t_2 \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(U \cdot \frac{\ell}{Om}\right) + U \cdot t\right)}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\sqrt{t_2}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, n \cdot \left(t_1 \cdot \left(U - U*\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{\frac{n}{\frac{Om}{U \cdot \left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right)}}} \cdot \left(-\ell\right)\right)\\ \end{array} \]

FPCore

(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
         (*
          (* (* 2.0 n) U)
          (+ (- t (* 2.0 (/ (* l l) Om))) (* (* n t_1) (- U* U))))))
   (if (<= t_2 0.0)
     (sqrt
      (*
       (* 2.0 n)
       (+
        (* (fma l -2.0 (* n (* (/ l Om) (- U* U)))) (* U (/ l Om)))
        (* U t))))
     (if (<= t_2 2e+297)
       (sqrt t_2)
       (if (<= t_2 INFINITY)
         (*
          (sqrt (* 2.0 (* n U)))
          (sqrt (- t (fma 2.0 (* l (/ l Om)) (* n (* t_1 (- U U*)))))))
         (*
          (sqrt 2.0)
          (*
           (sqrt (/ n (/ Om (* U (+ -2.0 (* (- U* U) (/ n Om)))))))
           (- l))))))))

C

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 = ((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) + ((n * t_1) * (U_42_ - U)));
	double tmp;
	if (t_2 <= 0.0) {
		tmp = sqrt(((2.0 * n) * ((fma(l, -2.0, (n * ((l / Om) * (U_42_ - U)))) * (U * (l / Om))) + (U * t))));
	} else if (t_2 <= 2e+297) {
		tmp = sqrt(t_2);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = sqrt((2.0 * (n * U))) * sqrt((t - fma(2.0, (l * (l / Om)), (n * (t_1 * (U - U_42_))))));
	} else {
		tmp = sqrt(2.0) * (sqrt((n / (Om / (U * (-2.0 + ((U_42_ - U) * (n / Om))))))) * -l);
	}
	return tmp;
}

Julia

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 = Float64(Float64(Float64(2.0 * n) * U) * Float64(Float64(t - Float64(2.0 * Float64(Float64(l * l) / Om))) + Float64(Float64(n * t_1) * Float64(U_42_ - U))))
	tmp = 0.0
	if (t_2 <= 0.0)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(Float64(fma(l, -2.0, Float64(n * Float64(Float64(l / Om) * Float64(U_42_ - U)))) * Float64(U * Float64(l / Om))) + Float64(U * t))));
	elseif (t_2 <= 2e+297)
		tmp = sqrt(t_2);
	elseif (t_2 <= Inf)
		tmp = Float64(sqrt(Float64(2.0 * Float64(n * U))) * sqrt(Float64(t - fma(2.0, Float64(l * Float64(l / Om)), Float64(n * Float64(t_1 * Float64(U - U_42_)))))));
	else
		tmp = Float64(sqrt(2.0) * Float64(sqrt(Float64(n / Float64(Om / Float64(U * Float64(-2.0 + Float64(Float64(U_42_ - U) * Float64(n / Om))))))) * Float64(-l)));
	end
	return tmp
end

Wolfram

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[(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 * t$95$1), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.0], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(N[(N[(l * -2.0 + N[(n * N[(N[(l / Om), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(U * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(U * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$2, 2e+297], N[Sqrt[t$95$2], $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[Sqrt[N[(2.0 * N[(n * U), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[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], N[(N[Sqrt[2.0], $MachinePrecision] * N[(N[Sqrt[N[(n / N[(Om / N[(U * N[(-2.0 + N[(N[(U$42$ - U), $MachinePrecision] * N[(n / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-l)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.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 15.9%

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

   2. Simplified 43.9%

      \[\leadsto \color{blue}{\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, \frac{\ell}{Om} \cdot \left(n \cdot \left(U* - U\right)\right)\right)\right)\right)}} \]
      Proof

      [Start] 15.9	\[ \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
      associate-*l* [=>] 40.1	\[ \sqrt{\color{blue}{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}} \]
      sub-neg [=>] 40.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\color{blue}{\left(t + \left(-2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)} - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)} \]
      associate--l+ [=>] 40.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\left(t + \left(\left(-2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}\right)} \]
      *-commutative [=>] 40.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\left(-\color{blue}{\frac{\ell \cdot \ell}{Om} \cdot 2}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      distribute-rgt-neg-in [=>] 40.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\color{blue}{\frac{\ell \cdot \ell}{Om} \cdot \left(-2\right)} - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      associate-*l/ [<=] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\color{blue}{\left(\frac{\ell}{Om} \cdot \ell\right)} \cdot \left(-2\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      associate-*l* [=>] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\color{blue}{\frac{\ell}{Om} \cdot \left(\ell \cdot \left(-2\right)\right)} - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      *-commutative [<=] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \color{blue}{\left(\left(-2\right) \cdot \ell\right)} - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      *-commutative [=>] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \left(\left(-2\right) \cdot \ell\right) - \color{blue}{\left({\left(\frac{\ell}{Om}\right)}^{2} \cdot n\right)} \cdot \left(U - U*\right)\right)\right)\right)} \]
      associate-*l* [=>] 40.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \left(\left(-2\right) \cdot \ell\right) - \color{blue}{{\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(n \cdot \left(U - U*\right)\right)}\right)\right)\right)} \]
      unpow2 [=>] 40.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \left(\left(-2\right) \cdot \ell\right) - \color{blue}{\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right)} \cdot \left(n \cdot \left(U - U*\right)\right)\right)\right)\right)} \]
      associate-*l* [=>] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \left(\left(-2\right) \cdot \ell\right) - \color{blue}{\frac{\ell}{Om} \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(U - U*\right)\right)\right)}\right)\right)\right)} \]

   3. Applied egg-rr 47.8%

      \[\leadsto \sqrt{\left(2 \cdot n\right) \cdot \color{blue}{\left(\mathsf{fma}\left(\ell, -2, n \cdot \left(\left(U* - U\right) \cdot \frac{\ell}{Om}\right)\right) \cdot \left(\frac{\ell}{Om} \cdot U\right) + U \cdot t\right)}} \]
      Proof

      [Start] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, \frac{\ell}{Om} \cdot \left(n \cdot \left(U* - U\right)\right)\right)\right)\right)} \]
      +-commutative [=>] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\left(\frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, \frac{\ell}{Om} \cdot \left(n \cdot \left(U* - U\right)\right)\right) + t\right)}\right)} \]
      distribute-lft-in [=>] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \color{blue}{\left(U \cdot \left(\frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, \frac{\ell}{Om} \cdot \left(n \cdot \left(U* - U\right)\right)\right)\right) + U \cdot t\right)}} \]
      *-commutative [=>] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(\color{blue}{\left(\frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, \frac{\ell}{Om} \cdot \left(n \cdot \left(U* - U\right)\right)\right)\right) \cdot U} + U \cdot t\right)} \]
      *-commutative [=>] 43.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(\color{blue}{\left(\mathsf{fma}\left(\ell, -2, \frac{\ell}{Om} \cdot \left(n \cdot \left(U* - U\right)\right)\right) \cdot \frac{\ell}{Om}\right)} \cdot U + U \cdot t\right)} \]
      associate-*l* [=>] 44.0	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(\color{blue}{\mathsf{fma}\left(\ell, -2, \frac{\ell}{Om} \cdot \left(n \cdot \left(U* - U\right)\right)\right) \cdot \left(\frac{\ell}{Om} \cdot U\right)} + U \cdot t\right)} \]
      *-commutative [=>] 44.0	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(\mathsf{fma}\left(\ell, -2, \color{blue}{\left(n \cdot \left(U* - U\right)\right) \cdot \frac{\ell}{Om}}\right) \cdot \left(\frac{\ell}{Om} \cdot U\right) + U \cdot t\right)} \]
      associate-*l* [=>] 47.8	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(\mathsf{fma}\left(\ell, -2, \color{blue}{n \cdot \left(\left(U* - U\right) \cdot \frac{\ell}{Om}\right)}\right) \cdot \left(\frac{\ell}{Om} \cdot U\right) + U \cdot t\right)} \]

   if 0.0 < (*.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*)))) < 2e297

   1. Initial program 96.6%

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

   if 2e297 < (*.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 0.0%

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

   2. Applied egg-rr 17.0%

      \[\leadsto \color{blue}{\sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, {\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(n \cdot \left(U - U*\right)\right)\right)}} \]
      Proof

      [Start] 0.0	\[ \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
      sqrt-prod [=>] 16.6	\[ \color{blue}{\sqrt{\left(2 \cdot n\right) \cdot U} \cdot \sqrt{\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)}} \]
      associate-*l* [=>] 16.6	\[ \sqrt{\color{blue}{2 \cdot \left(n \cdot U\right)}} \cdot \sqrt{\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)} \]
      associate--l- [=>] 16.6	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{\color{blue}{t - \left(2 \cdot \frac{\ell \cdot \ell}{Om} + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}} \]
      fma-def [=>] 16.6	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \color{blue}{\mathsf{fma}\left(2, \frac{\ell \cdot \ell}{Om}, \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}} \]
      associate-/l* [=>] 19.8	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \color{blue}{\frac{\ell}{\frac{Om}{\ell}}}, \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
      div-inv [=>] 19.8	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \color{blue}{\ell \cdot \frac{1}{\frac{Om}{\ell}}}, \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
      clear-num [<=] 19.8	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \color{blue}{\frac{\ell}{Om}}, \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
      *-commutative [=>] 19.8	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, \color{blue}{\left({\left(\frac{\ell}{Om}\right)}^{2} \cdot n\right)} \cdot \left(U - U*\right)\right)} \]
      associate-*l* [=>] 17.0	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, \color{blue}{{\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(n \cdot \left(U - U*\right)\right)}\right)} \]

   3. Simplified 19.4%

      \[\leadsto \color{blue}{\sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, n \cdot \left(\left(U - U*\right) \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right)\right)}} \]
      Proof

      [Start] 17.0	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, {\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(n \cdot \left(U - U*\right)\right)\right)} \]
      *-commutative [=>] 17.0	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, \color{blue}{\left(n \cdot \left(U - U*\right)\right) \cdot {\left(\frac{\ell}{Om}\right)}^{2}}\right)} \]
      associate-*l* [=>] 19.4	\[ \sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, \color{blue}{n \cdot \left(\left(U - U*\right) \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right)}\right)} \]

   if +inf.0 < (*.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 0.0%

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

   2. Simplified 10.3%

      \[\leadsto \color{blue}{\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell}{Om} \cdot \mathsf{fma}\left(\ell, -2, \frac{\ell}{Om} \cdot \left(n \cdot \left(U* - U\right)\right)\right)\right)\right)}} \]
      Proof

      [Start] 0.0	\[ \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
      associate-*l* [=>] 0.0	\[ \sqrt{\color{blue}{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}} \]
      sub-neg [=>] 0.0	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\color{blue}{\left(t + \left(-2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)} - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)} \]
      associate--l+ [=>] 0.0	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\left(t + \left(\left(-2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}\right)} \]
      *-commutative [=>] 0.0	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\left(-\color{blue}{\frac{\ell \cdot \ell}{Om} \cdot 2}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      distribute-rgt-neg-in [=>] 0.0	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\color{blue}{\frac{\ell \cdot \ell}{Om} \cdot \left(-2\right)} - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      associate-*l/ [<=] 10.3	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\color{blue}{\left(\frac{\ell}{Om} \cdot \ell\right)} \cdot \left(-2\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      associate-*l* [=>] 10.3	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\color{blue}{\frac{\ell}{Om} \cdot \left(\ell \cdot \left(-2\right)\right)} - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      *-commutative [<=] 10.3	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \color{blue}{\left(\left(-2\right) \cdot \ell\right)} - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      *-commutative [=>] 10.3	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \left(\left(-2\right) \cdot \ell\right) - \color{blue}{\left({\left(\frac{\ell}{Om}\right)}^{2} \cdot n\right)} \cdot \left(U - U*\right)\right)\right)\right)} \]
      associate-*l* [=>] 10.3	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \left(\left(-2\right) \cdot \ell\right) - \color{blue}{{\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(n \cdot \left(U - U*\right)\right)}\right)\right)\right)} \]
      unpow2 [=>] 10.3	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \left(\left(-2\right) \cdot \ell\right) - \color{blue}{\left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right)} \cdot \left(n \cdot \left(U - U*\right)\right)\right)\right)\right)} \]
      associate-*l* [=>] 10.3	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(\frac{\ell}{Om} \cdot \left(\left(-2\right) \cdot \ell\right) - \color{blue}{\frac{\ell}{Om} \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(U - U*\right)\right)\right)}\right)\right)\right)} \]

   3. Taylor expanded in l around -inf 3.4%

      \[\leadsto \sqrt{\left(2 \cdot n\right) \cdot \color{blue}{\left(-1 \cdot \frac{\left(2 + -1 \cdot \frac{n \cdot \left(U* - U\right)}{Om}\right) \cdot \left({\ell}^{2} \cdot U\right)}{Om}\right)}} \]

   4. Simplified 3.4%

      \[\leadsto \sqrt{\left(2 \cdot n\right) \cdot \color{blue}{\frac{-\left(2 - \frac{n}{Om} \cdot \left(U* - U\right)\right)}{\frac{\frac{Om}{U}}{\ell \cdot \ell}}}} \]
      Proof

      [Start] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(-1 \cdot \frac{\left(2 + -1 \cdot \frac{n \cdot \left(U* - U\right)}{Om}\right) \cdot \left({\ell}^{2} \cdot U\right)}{Om}\right)} \]
      mul-1-neg [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \color{blue}{\left(-\frac{\left(2 + -1 \cdot \frac{n \cdot \left(U* - U\right)}{Om}\right) \cdot \left({\ell}^{2} \cdot U\right)}{Om}\right)}} \]
      associate-/l* [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(-\color{blue}{\frac{2 + -1 \cdot \frac{n \cdot \left(U* - U\right)}{Om}}{\frac{Om}{{\ell}^{2} \cdot U}}}\right)} \]
      distribute-neg-frac [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \color{blue}{\frac{-\left(2 + -1 \cdot \frac{n \cdot \left(U* - U\right)}{Om}\right)}{\frac{Om}{{\ell}^{2} \cdot U}}}} \]
      mul-1-neg [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \frac{-\left(2 + \color{blue}{\left(-\frac{n \cdot \left(U* - U\right)}{Om}\right)}\right)}{\frac{Om}{{\ell}^{2} \cdot U}}} \]
      unsub-neg [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \frac{-\color{blue}{\left(2 - \frac{n \cdot \left(U* - U\right)}{Om}\right)}}{\frac{Om}{{\ell}^{2} \cdot U}}} \]
      associate-/l* [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \frac{-\left(2 - \color{blue}{\frac{n}{\frac{Om}{U* - U}}}\right)}{\frac{Om}{{\ell}^{2} \cdot U}}} \]
      associate-/r/ [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \frac{-\left(2 - \color{blue}{\frac{n}{Om} \cdot \left(U* - U\right)}\right)}{\frac{Om}{{\ell}^{2} \cdot U}}} \]
      *-commutative [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \frac{-\left(2 - \frac{n}{Om} \cdot \left(U* - U\right)\right)}{\frac{Om}{\color{blue}{U \cdot {\ell}^{2}}}}} \]
      associate-/r* [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \frac{-\left(2 - \frac{n}{Om} \cdot \left(U* - U\right)\right)}{\color{blue}{\frac{\frac{Om}{U}}{{\ell}^{2}}}}} \]
      unpow2 [=>] 3.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \frac{-\left(2 - \frac{n}{Om} \cdot \left(U* - U\right)\right)}{\frac{\frac{Om}{U}}{\color{blue}{\ell \cdot \ell}}}} \]

   5. Taylor expanded in l around -inf 35.5%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(\sqrt{2} \cdot \ell\right) \cdot \sqrt{\frac{n \cdot \left(\left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right) \cdot U\right)}{Om}}\right)} \]

   6. Simplified 38.6%

      \[\leadsto \color{blue}{-\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{n}{\frac{Om}{U \cdot \left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right)}}}\right)} \]
      Proof

      [Start] 35.5	\[ -1 \cdot \left(\left(\sqrt{2} \cdot \ell\right) \cdot \sqrt{\frac{n \cdot \left(\left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right) \cdot U\right)}{Om}}\right) \]
      mul-1-neg [=>] 35.5	\[ \color{blue}{-\left(\sqrt{2} \cdot \ell\right) \cdot \sqrt{\frac{n \cdot \left(\left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right) \cdot U\right)}{Om}}} \]
      associate-*l* [=>] 35.2	\[ -\color{blue}{\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{n \cdot \left(\left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right) \cdot U\right)}{Om}}\right)} \]
      associate-/l* [=>] 38.6	\[ -\sqrt{2} \cdot \left(\ell \cdot \sqrt{\color{blue}{\frac{n}{\frac{Om}{\left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right) \cdot U}}}}\right) \]
      *-commutative [=>] 38.6	\[ -\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{n}{\frac{Om}{\color{blue}{U \cdot \left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right)}}}}\right) \]
      sub-neg [=>] 38.6	\[ -\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{n}{\frac{Om}{U \cdot \color{blue}{\left(\frac{n \cdot \left(U* - U\right)}{Om} + \left(-2\right)\right)}}}}\right) \]
      associate-*l/ [<=] 38.6	\[ -\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{n}{\frac{Om}{U \cdot \left(\color{blue}{\frac{n}{Om} \cdot \left(U* - U\right)} + \left(-2\right)\right)}}}\right) \]
      metadata-eval [=>] 38.6	\[ -\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{n}{\frac{Om}{U \cdot \left(\frac{n}{Om} \cdot \left(U* - U\right) + \color{blue}{-2}\right)}}}\right) \]
      +-commutative [<=] 38.6	\[ -\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{n}{\frac{Om}{U \cdot \color{blue}{\left(-2 + \frac{n}{Om} \cdot \left(U* - U\right)\right)}}}}\right) \]
      *-commutative [=>] 38.6	\[ -\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{n}{\frac{Om}{U \cdot \left(-2 + \color{blue}{\left(U* - U\right) \cdot \frac{n}{Om}}\right)}}}\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right) \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(U \cdot \frac{\ell}{Om}\right) + U \cdot t\right)}\\ \mathbf{elif}\;\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right) \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)}\\ \mathbf{elif}\;\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right) \leq \infty:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot U\right)} \cdot \sqrt{t - \mathsf{fma}\left(2, \ell \cdot \frac{\ell}{Om}, n \cdot \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(U - U*\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{\frac{n}{\frac{Om}{U \cdot \left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right)}}} \cdot \left(-\ell\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	53.0%
Cost	51340

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := t_2 \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)\\ \mathbf{if}\;t_3 \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(t_1 \cdot \left(U \cdot \frac{\ell}{Om}\right) + U \cdot t\right)}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\sqrt{t_3}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(\frac{\ell}{Om}, t_1, t\right)} \cdot \sqrt{t_2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{\frac{n}{\frac{Om}{U \cdot \left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right)}}} \cdot \left(-\ell\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	51.8%
Cost	44428

\[\begin{array}{l} t_1 := \left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(U \cdot \frac{\ell}{Om}\right) + U \cdot t\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\sqrt{t_1}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \mathsf{fma}\left(-2, \ell \cdot \frac{\ell}{Om}, t\right)\right)} \cdot \sqrt{U}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{\frac{n}{\frac{Om}{U \cdot \left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right)}}} \cdot \left(-\ell\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	53.1%
Cost	38476

\[\begin{array}{l} t_1 := \left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(U \cdot \frac{\ell}{Om}\right) + U \cdot t\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\sqrt{t_1}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right) + \frac{\ell \cdot -2 + \frac{\left(U* - U\right) \cdot \left(n \cdot \ell\right)}{Om}}{\frac{Om}{\ell \cdot \left(n \cdot U\right)}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{\frac{n}{\frac{Om}{U \cdot \left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right)}}} \cdot \left(-\ell\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	49.5%
Cost	14672

\[\begin{array}{l} \mathbf{if}\;\ell \leq -3 \cdot 10^{+110}:\\ \;\;\;\;\sqrt{\frac{n \cdot \left(U \cdot \left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right)\right)}{Om}} \cdot \left(\ell \cdot \left(-\sqrt{2}\right)\right)\\ \mathbf{elif}\;\ell \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell}{Om} \cdot \left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 15500000000000:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot \left(\ell \cdot \left(U \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}\right)\right)\right)}{Om} + t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{elif}\;\ell \leq 3.5 \cdot 10^{+163}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \mathsf{fma}\left(-2, \frac{\ell}{\frac{Om}{\ell}}, t\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\ell \cdot \sqrt{2}\right) \cdot \sqrt{n \cdot \left(U \cdot \left(\frac{n}{Om} \cdot \frac{U* - U}{Om} + \frac{-2}{Om}\right)\right)}\\ \end{array} \]

Alternative 5
Accuracy	50.0%
Cost	14672

\[\begin{array}{l} \mathbf{if}\;\ell \leq -2.1 \cdot 10^{+105}:\\ \;\;\;\;\sqrt{\frac{n \cdot \left(U \cdot \left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right)\right)}{Om}} \cdot \left(\ell \cdot \left(-\sqrt{2}\right)\right)\\ \mathbf{elif}\;\ell \leq -1.5 \cdot 10^{-140}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(\mathsf{fma}\left(\ell, -2, n \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right)\right) \cdot \left(U \cdot \frac{\ell}{Om}\right) + U \cdot t\right)}\\ \mathbf{elif}\;\ell \leq 16500000000000:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot \left(\ell \cdot \left(U \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}\right)\right)\right)}{Om} + t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{elif}\;\ell \leq 7.1 \cdot 10^{+162}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \mathsf{fma}\left(-2, \frac{\ell}{\frac{Om}{\ell}}, t\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\ell \cdot \sqrt{2}\right) \cdot \sqrt{n \cdot \left(U \cdot \left(\frac{n}{Om} \cdot \frac{U* - U}{Om} + \frac{-2}{Om}\right)\right)}\\ \end{array} \]

Alternative 6
Accuracy	43.7%
Cost	14548

\[\begin{array}{l} t_1 := n \cdot \left(U \cdot t\right)\\ t_2 := \sqrt{2 \cdot \left(t_1 + \frac{\ell \cdot -2 + \frac{\left(U* - U\right) \cdot \left(n \cdot \ell\right)}{Om}}{\frac{Om}{\ell \cdot \left(n \cdot U\right)}}\right)}\\ \mathbf{if}\;U \leq -2 \cdot 10^{+122}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ \mathbf{elif}\;U \leq -4.3 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;U \leq -1.02 \cdot 10^{-230}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \frac{\left(U* - U\right) \cdot \frac{n}{Om} - 2}{\frac{Om}{\ell} \cdot \frac{\frac{1}{U}}{\ell}}}\\ \mathbf{elif}\;U \leq -9.5 \cdot 10^{-281}:\\ \;\;\;\;\sqrt{2 \cdot t_1 + 2 \cdot \frac{\left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot \left(U* - U\right)\right)}{Om}\right) \cdot \left(n \cdot \left(U \cdot \ell\right)\right)}{Om}}\\ \mathbf{elif}\;U \leq 2.45 \cdot 10^{-154}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(-4, \frac{\ell \cdot \left(U \cdot \ell\right)}{\frac{Om}{n}}, 2 \cdot \left(U \cdot \left(n \cdot t\right)\right)\right)}\\ \mathbf{elif}\;U \leq 1.25 \cdot 10^{+159} \lor \neg \left(U \leq 2.7 \cdot 10^{+278}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{U + U} \cdot \sqrt{n \cdot t}\\ \end{array} \]

Alternative 7
Accuracy	50.2%
Cost	14544

\[\begin{array}{l} \mathbf{if}\;\ell \leq -5.5 \cdot 10^{+116}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{\frac{n}{\frac{Om}{U \cdot \left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right)}}} \cdot \left(-\ell\right)\right)\\ \mathbf{elif}\;\ell \leq -5.5 \cdot 10^{+36}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell}{Om} \cdot \left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 28000000000000:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot \left(\ell \cdot \left(U \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}\right)\right)\right)}{Om} + t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{elif}\;\ell \leq 9.5 \cdot 10^{+162}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \mathsf{fma}\left(-2, \frac{\ell}{\frac{Om}{\ell}}, t\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{\left(n \cdot U\right) \cdot \left(-2 + \frac{n}{\frac{Om}{U* - U}}\right)}{Om}}\right)\\ \end{array} \]

Alternative 8
Accuracy	49.7%
Cost	14544

\[\begin{array}{l} \mathbf{if}\;\ell \leq -3.5 \cdot 10^{+112}:\\ \;\;\;\;\sqrt{\frac{n \cdot \left(U \cdot \left(\frac{n \cdot \left(U* - U\right)}{Om} - 2\right)\right)}{Om}} \cdot \left(\ell \cdot \left(-\sqrt{2}\right)\right)\\ \mathbf{elif}\;\ell \leq -1.4 \cdot 10^{+36}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell}{Om} \cdot \left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 31000000000000:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot \left(\ell \cdot \left(U \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}\right)\right)\right)}{Om} + t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{elif}\;\ell \leq 2 \cdot 10^{+163}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \mathsf{fma}\left(-2, \frac{\ell}{\frac{Om}{\ell}}, t\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \sqrt{\frac{\left(n \cdot U\right) \cdot \left(-2 + \frac{n}{\frac{Om}{U* - U}}\right)}{Om}}\right)\\ \end{array} \]

Alternative 9
Accuracy	43.2%
Cost	14436

\[\begin{array}{l} t_1 := \ell \cdot -2 + \frac{\left(U* - U\right) \cdot \left(n \cdot \ell\right)}{Om}\\ t_2 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ t_3 := \sqrt{2 \cdot \frac{n \cdot \left(\ell \cdot \left(U \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}\right)\right)\right)}{Om} + t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ t_4 := n \cdot \left(U \cdot t\right)\\ t_5 := \sqrt{2 \cdot \left(t_4 + \frac{t_1}{\frac{Om}{\ell \cdot \left(n \cdot U\right)}}\right)}\\ \mathbf{if}\;U \leq -6.6 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;U \leq -4.3 \cdot 10^{-130}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;U \leq -1.02 \cdot 10^{-230}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \frac{\left(U* - U\right) \cdot \frac{n}{Om} - 2}{\frac{Om}{\ell} \cdot \frac{\frac{1}{U}}{\ell}}}\\ \mathbf{elif}\;U \leq 3.4 \cdot 10^{-307}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \frac{\left(U \cdot \ell\right) \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot \left(U* - U\right)\right)}{Om}\right)}{Om}\right)}\\ \mathbf{elif}\;U \leq 3.7 \cdot 10^{-289}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;U \leq 4 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;U \leq 1.1 \cdot 10^{-141}:\\ \;\;\;\;\sqrt{2 \cdot \left(t_4 + \frac{t_1}{\frac{Om}{n \cdot \left(U \cdot \ell\right)}}\right)}\\ \mathbf{elif}\;U \leq 1.35 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;U \leq 3.1 \cdot 10^{+278}:\\ \;\;\;\;\sqrt{U + U} \cdot \sqrt{n \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 10
Accuracy	43.2%
Cost	9180

\[\begin{array}{l} t_1 := \ell \cdot -2 + \frac{\left(U* - U\right) \cdot \left(n \cdot \ell\right)}{Om}\\ t_2 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ t_3 := n \cdot \left(U \cdot t\right)\\ t_4 := \sqrt{2 \cdot \left(t_3 + \frac{t_1}{\frac{Om}{\ell \cdot \left(n \cdot U\right)}}\right)}\\ \mathbf{if}\;U \leq -5.7 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;U \leq -4.3 \cdot 10^{-130}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;U \leq -8.8 \cdot 10^{-231}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \frac{\left(U* - U\right) \cdot \frac{n}{Om} - 2}{\frac{Om}{\ell} \cdot \frac{\frac{1}{U}}{\ell}}}\\ \mathbf{elif}\;U \leq 3.5 \cdot 10^{-307}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \frac{\left(U \cdot \ell\right) \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot \left(U* - U\right)\right)}{Om}\right)}{Om}\right)}\\ \mathbf{elif}\;U \leq 1.9 \cdot 10^{-288}:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot \left(\ell \cdot \left(U \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}\right)\right)\right)}{Om} + t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{elif}\;U \leq 2.9 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;U \leq 2 \cdot 10^{-173}:\\ \;\;\;\;\sqrt{2 \cdot \left(t_3 + \frac{t_1}{\frac{Om}{n \cdot \left(U \cdot \ell\right)}}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 11
Accuracy	44.8%
Cost	8920

\[\begin{array}{l} t_1 := \frac{Om}{n \cdot \left(U \cdot \ell\right)}\\ t_2 := n \cdot \left(U \cdot t\right)\\ t_3 := \left(U* - U\right) \cdot \frac{n}{Om}\\ \mathbf{if}\;\ell \leq -9.2 \cdot 10^{+176}:\\ \;\;\;\;\sqrt{\left(-2 + t_3\right) \cdot \left(\left(2 \cdot n\right) \cdot \left(\ell \cdot \frac{U}{\frac{Om}{\ell}}\right)\right)}\\ \mathbf{elif}\;\ell \leq -5 \cdot 10^{-25}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \left(U \cdot \left(\ell \cdot \ell\right)\right) \cdot \frac{t_3 - 2}{Om}\right)}\\ \mathbf{elif}\;\ell \leq -5.8 \cdot 10^{-140}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \frac{\left(U \cdot \ell\right) \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot \left(U* - U\right)\right)}{Om}\right)}{Om}\right)}\\ \mathbf{elif}\;\ell \leq 8.6 \cdot 10^{-73}:\\ \;\;\;\;\sqrt{2 \cdot \left(\left(n \cdot U\right) \cdot \left(t + \left(\frac{n}{Om} \cdot \frac{\ell \cdot \left(\ell \cdot U*\right)}{Om} - \frac{2}{\frac{Om}{\ell \cdot \ell}}\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 1.85 \cdot 10^{+65}:\\ \;\;\;\;\sqrt{2 \cdot \left(t_2 + \frac{\ell \cdot -2 + \frac{\left(U* - U\right) \cdot \left(n \cdot \ell\right)}{Om}}{t_1}\right)}\\ \mathbf{elif}\;\ell \leq 4.4 \cdot 10^{+109}:\\ \;\;\;\;\sqrt{\left(-2 + U* \cdot \frac{n}{Om}\right) \cdot \left(\left(2 \cdot n\right) \cdot \left(\ell \cdot \left(\ell \cdot \frac{U}{Om}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(t_2 + \frac{\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}}{t_1}\right)}\\ \end{array} \]

Alternative 12
Accuracy	44.8%
Cost	8788

\[\begin{array}{l} t_1 := \left(U* - U\right) \cdot \frac{n}{Om}\\ t_2 := t_1 - 2\\ \mathbf{if}\;\ell \leq -9.2 \cdot 10^{+176}:\\ \;\;\;\;\sqrt{\left(-2 + t_1\right) \cdot \left(\left(2 \cdot n\right) \cdot \left(\ell \cdot \frac{U}{\frac{Om}{\ell}}\right)\right)}\\ \mathbf{elif}\;\ell \leq -1 \cdot 10^{-138}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \left(U \cdot \left(\ell \cdot \ell\right)\right) \cdot \frac{t_2}{Om}\right)}\\ \mathbf{elif}\;\ell \leq 5 \cdot 10^{-272}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \mathbf{elif}\;\ell \leq 8.2 \cdot 10^{-73}:\\ \;\;\;\;\sqrt{2 \cdot \left(\left(n \cdot U\right) \cdot \left(t + \left(\frac{n}{Om} \cdot \frac{\ell \cdot \left(\ell \cdot U*\right)}{Om} - \frac{2}{\frac{Om}{\ell \cdot \ell}}\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 2.8 \cdot 10^{+15}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \frac{\left(U \cdot \ell\right) \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot \left(U* - U\right)\right)}{Om}\right)}{Om}\right)}\\ \mathbf{elif}\;\ell \leq 2.85 \cdot 10^{+134}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \frac{t_2}{\frac{Om}{\ell} \cdot \frac{\frac{1}{U}}{\ell}}}\\ \end{array} \]

Alternative 13
Accuracy	44.9%
Cost	8785

\[\begin{array}{l} t_1 := \left(U* - U\right) \cdot \frac{n}{Om}\\ \mathbf{if}\;\ell \leq -9.2 \cdot 10^{+176}:\\ \;\;\;\;\sqrt{\left(-2 + t_1\right) \cdot \left(\left(2 \cdot n\right) \cdot \left(\ell \cdot \frac{U}{\frac{Om}{\ell}}\right)\right)}\\ \mathbf{elif}\;\ell \leq -4 \cdot 10^{-30}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \left(U \cdot \left(\ell \cdot \ell\right)\right) \cdot \frac{t_1 - 2}{Om}\right)}\\ \mathbf{elif}\;\ell \leq -8.6 \cdot 10^{-139} \lor \neg \left(\ell \leq 8.2 \cdot 10^{-73}\right):\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right) + \frac{\ell \cdot -2 + \frac{\left(U* - U\right) \cdot \left(n \cdot \ell\right)}{Om}}{\frac{Om}{\ell \cdot \left(n \cdot U\right)}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(\left(n \cdot U\right) \cdot \left(t + \left(\frac{n}{Om} \cdot \frac{\ell \cdot \left(\ell \cdot U*\right)}{Om} - \frac{2}{\frac{Om}{\ell \cdot \ell}}\right)\right)\right)}\\ \end{array} \]

Alternative 14
Accuracy	44.2%
Cost	8656

\[\begin{array}{l} t_1 := \left(U* - U\right) \cdot \frac{n}{Om}\\ \mathbf{if}\;\ell \leq -9.2 \cdot 10^{+176}:\\ \;\;\;\;\sqrt{\left(-2 + t_1\right) \cdot \left(\left(2 \cdot n\right) \cdot \left(\ell \cdot \frac{U}{\frac{Om}{\ell}}\right)\right)}\\ \mathbf{elif}\;\ell \leq -8 \cdot 10^{-141}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \left(U \cdot \left(\ell \cdot \ell\right)\right) \cdot \frac{t_1 - 2}{Om}\right)}\\ \mathbf{elif}\;\ell \leq 10^{-268}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \mathbf{elif}\;\ell \leq 6 \cdot 10^{-73}:\\ \;\;\;\;\sqrt{2 \cdot \left(\left(n \cdot U\right) \cdot \left(t + \left(\frac{n}{Om} \cdot \frac{\ell \cdot \left(\ell \cdot U*\right)}{Om} - \frac{2}{\frac{Om}{\ell \cdot \ell}}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right) + \frac{\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}}{\frac{Om}{n \cdot \left(U \cdot \ell\right)}}\right)}\\ \end{array} \]

Alternative 15
Accuracy	42.8%
Cost	8400

\[\begin{array}{l} \mathbf{if}\;\ell \leq -1 \cdot 10^{+182}:\\ \;\;\;\;\sqrt{\left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right) \cdot \left(\left(2 \cdot n\right) \cdot \left(\ell \cdot \frac{U}{\frac{Om}{\ell}}\right)\right)}\\ \mathbf{elif}\;\ell \leq -7.6 \cdot 10^{-140}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell}{Om} \cdot \left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 5.2 \cdot 10^{-132}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \mathbf{elif}\;\ell \leq 6000000000000:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}\right)}{Om}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ \end{array} \]

Alternative 16
Accuracy	43.8%
Cost	8400

\[\begin{array}{l} t_1 := \left(U* - U\right) \cdot \frac{n}{Om}\\ \mathbf{if}\;\ell \leq -9.2 \cdot 10^{+176}:\\ \;\;\;\;\sqrt{\left(-2 + t_1\right) \cdot \left(\left(2 \cdot n\right) \cdot \left(\ell \cdot \frac{U}{\frac{Om}{\ell}}\right)\right)}\\ \mathbf{elif}\;\ell \leq -1 \cdot 10^{-125}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + \left(U \cdot \left(\ell \cdot \ell\right)\right) \cdot \frac{t_1 - 2}{Om}\right)}\\ \mathbf{elif}\;\ell \leq 3.1 \cdot 10^{-260}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \mathbf{elif}\;\ell \leq 8200000000000:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell \cdot \left(\ell \cdot -2 + \frac{n \cdot \left(\ell \cdot U*\right)}{Om}\right)}{Om}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ \end{array} \]

Alternative 17
Accuracy	41.2%
Cost	8141

\[\begin{array}{l} \mathbf{if}\;n \leq -1.9 \cdot 10^{-51}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot \left(n \cdot U\right)\right) + -4 \cdot \frac{n \cdot \left(U \cdot \left(\ell \cdot \ell\right)\right)}{Om}}\\ \mathbf{elif}\;n \leq -6.2 \cdot 10^{-256} \lor \neg \left(n \leq -7.5 \cdot 10^{-280}\right):\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right) \cdot \frac{\left(U \cdot \ell\right) \cdot \left(n \cdot \left(2 \cdot \ell\right)\right)}{Om}}\\ \end{array} \]

Alternative 18
Accuracy	41.7%
Cost	8136

\[\begin{array}{l} \mathbf{if}\;\ell \leq -1.35 \cdot 10^{+180}:\\ \;\;\;\;\sqrt{\left(-2 + \left(U* - U\right) \cdot \frac{n}{Om}\right) \cdot \left(\left(2 \cdot n\right) \cdot \left(\ell \cdot \frac{U}{\frac{Om}{\ell}}\right)\right)}\\ \mathbf{elif}\;\ell \leq -1.16 \cdot 10^{-139}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \frac{\ell}{Om} \cdot \left(\ell \cdot -2 - \frac{n}{Om} \cdot \left(U \cdot \ell\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 6.6 \cdot 10^{-32}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ \end{array} \]

Alternative 19
Accuracy	41.4%
Cost	7753

\[\begin{array}{l} \mathbf{if}\;\ell \leq -1 \cdot 10^{-15} \lor \neg \left(\ell \leq 3.5 \cdot 10^{-32}\right):\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(-2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + n \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \end{array} \]

Alternative 20
Accuracy	41.2%
Cost	7625

\[\begin{array}{l} \mathbf{if}\;\ell \leq -9.6 \cdot 10^{-126} \lor \neg \left(\ell \leq 8.6 \cdot 10^{-73}\right):\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t + \ell \cdot \left(\frac{\ell}{Om} \cdot -2\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \end{array} \]

Alternative 21
Accuracy	41.2%
Cost	7624

\[\begin{array}{l} \mathbf{if}\;\ell \leq -1.02 \cdot 10^{-125}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t + \ell \cdot \left(\frac{\ell}{Om} \cdot -2\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 8.6 \cdot 10^{-73}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{n \cdot \left(2 \cdot \left(U \cdot \left(t + -2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right)\right)\right)}\\ \end{array} \]

Alternative 22
Accuracy	36.9%
Cost	7497

\[\begin{array}{l} \mathbf{if}\;\ell \leq -3.3 \cdot 10^{+67} \lor \neg \left(\ell \leq 3 \cdot 10^{+56}\right):\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(\frac{\ell}{Om} \cdot \left(\ell \cdot -2\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \end{array} \]

Alternative 23
Accuracy	34.7%
Cost	7113

\[\begin{array}{l} \mathbf{if}\;n \leq -1.6 \cdot 10^{-153} \lor \neg \left(n \leq 5 \cdot 10^{-59}\right):\\ \;\;\;\;\sqrt{\left(n \cdot U\right) \cdot \left(2 \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t\right)\right)}\\ \end{array} \]

Alternative 24
Accuracy	32.7%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;\ell \leq -6.6 \cdot 10^{-105}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t\right)\right)}\\ \end{array} \]

Alternative 25
Accuracy	33.0%
Cost	6848

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

Alternative 26
Accuracy	5.3%
Cost	448

\[t \cdot \left(U \cdot \left(n + n\right)\right) \]

Alternative 27
Accuracy	4.6%
Cost	320

\[\left(n \cdot n\right) \cdot 4 \]

Alternative 28
Accuracy	2.5%
Cost	192

\[n + -2 \]

Alternative 29
Accuracy	3.7%
Cost	192

\[n + n \]

Reproduce

herbie shell --seed 2023153 
(FPCore (n U t l Om U*)
  :name "Toniolo and Linder, Equation (13)"
  :precision binary64
  (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))