Toniolo and Linder, Equation (13)

Average Accuracy: 45.9% → 58.7%

Time: 1.1min

Precision: binary64

Cost: 43528

Math

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

↓

\[\begin{array}{l} t_1 := \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{-86}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \mathsf{fma}\left(n, \frac{\ell}{Om} \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right), \mathsf{fma}\left(\ell \cdot \frac{\ell}{Om}, -2, t\right)\right)\right)}\\ \mathbf{elif}\;t_1 \leq 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \left(\frac{U \cdot \ell}{Om} \cdot \left(n \cdot \ell\right)\right)\right)}\\ \end{array} \]

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
         (sqrt
          (*
           (* (* 2.0 n) U)
           (+
            (- t (* 2.0 (/ (* l l) Om)))
            (* (* n (pow (/ l Om) 2.0)) (- U* U)))))))
   (if (<= t_1 5e-86)
     (sqrt
      (*
       (* 2.0 n)
       (*
        U
        (fma
         n
         (* (/ l Om) (* (/ l Om) (- U* U)))
         (fma (* l (/ l Om)) -2.0 t)))))
     (if (<= t_1 1e+149)
       t_1
       (sqrt (fma 2.0 (* n (* U t)) (* -4.0 (* (/ (* U l) Om) (* n 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 = sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) + ((n * pow((l / Om), 2.0)) * (U_42_ - U)))));
	double tmp;
	if (t_1 <= 5e-86) {
		tmp = sqrt(((2.0 * n) * (U * fma(n, ((l / Om) * ((l / Om) * (U_42_ - U))), fma((l * (l / Om)), -2.0, t)))));
	} else if (t_1 <= 1e+149) {
		tmp = t_1;
	} else {
		tmp = sqrt(fma(2.0, (n * (U * t)), (-4.0 * (((U * l) / Om) * (n * 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 = 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_42_ - U)))))
	tmp = 0.0
	if (t_1 <= 5e-86)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * fma(n, Float64(Float64(l / Om) * Float64(Float64(l / Om) * Float64(U_42_ - U))), fma(Float64(l * Float64(l / Om)), -2.0, t)))));
	elseif (t_1 <= 1e+149)
		tmp = t_1;
	else
		tmp = sqrt(fma(2.0, Float64(n * Float64(U * t)), Float64(-4.0 * Float64(Float64(Float64(U * l) / Om) * Float64(n * 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[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$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$1, 5e-86], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * N[(n * N[(N[(l / Om), $MachinePrecision] * N[(N[(l / Om), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision] * -2.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$1, 1e+149], t$95$1, N[Sqrt[N[(2.0 * N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(N[(N[(U * l), $MachinePrecision] / Om), $MachinePrecision] * N[(n * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. 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*))))) < 4.9999999999999999e-86

   1. Initial program 39.8%

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

   2. Simplified 52.9%

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

      [Start] 39.8	\[ \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
      associate-*l* [=>] 54.7	\[ \sqrt{\color{blue}{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}} \]
      cancel-sign-sub-inv [=>] 54.7	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(-n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\right)} \]
      +-commutative [=>] 54.7	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\left(\left(-n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right) + \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)}\right)} \]
      distribute-lft-neg-in [<=] 54.7	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\color{blue}{\left(-\left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} + \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)\right)} \]
      associate-*l* [=>] 52.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(-\color{blue}{n \cdot \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(U - U*\right)\right)}\right) + \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)\right)} \]
      distribute-rgt-neg-in [=>] 52.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\color{blue}{n \cdot \left(-{\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(U - U*\right)\right)} + \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)\right)} \]
      fma-def [=>] 52.9	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\mathsf{fma}\left(n, -{\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(U - U*\right), t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)}\right)} \]

   3. Applied egg-rr 52.9%

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

   4. Applied egg-rr 53.3%

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

   if 4.9999999999999999e-86 < (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*))))) < 1.00000000000000005e149

   1. Initial program 98.1%

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

   if 1.00000000000000005e149 < (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 1.3%

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

   2. Simplified 14.4%

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

      [Start] 1.3	\[ \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \]
      associate-*l* [=>] 3.1	\[ \sqrt{\color{blue}{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}} \]
      associate--l- [=>] 3.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\left(t - \left(2 \cdot \frac{\ell \cdot \ell}{Om} + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}\right)} \]
      sub-neg [=>] 3.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\left(t + \left(-\left(2 \cdot \frac{\ell \cdot \ell}{Om} + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)}\right)} \]
      sub-neg [<=] 3.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \color{blue}{\left(t - \left(2 \cdot \frac{\ell \cdot \ell}{Om} + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)}\right)} \]
      cancel-sign-sub [<=] 3.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t - \color{blue}{\left(2 \cdot \frac{\ell \cdot \ell}{Om} - \left(-n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\right)\right)} \]
      cancel-sign-sub [=>] 3.1	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t - \color{blue}{\left(2 \cdot \frac{\ell \cdot \ell}{Om} + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\right)\right)} \]
      associate-/l* [=>] 13.8	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t - \left(2 \cdot \color{blue}{\frac{\ell}{\frac{Om}{\ell}}} + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)\right)\right)} \]
      associate-*l* [=>] 14.4	\[ \sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t - \left(2 \cdot \frac{\ell}{\frac{Om}{\ell}} + \color{blue}{n \cdot \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(U - U*\right)\right)}\right)\right)\right)} \]

   3. Taylor expanded in Om around inf 7.0%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(n \cdot \left(t \cdot U\right)\right) + -4 \cdot \frac{n \cdot \left({\ell}^{2} \cdot U\right)}{Om}}} \]

   4. Simplified 16.6%

      \[\leadsto \sqrt{\color{blue}{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \frac{\ell \cdot \left(\ell \cdot U\right)}{\frac{Om}{n}}\right)}} \]
      Proof

      [Start] 7.0	\[ \sqrt{2 \cdot \left(n \cdot \left(t \cdot U\right)\right) + -4 \cdot \frac{n \cdot \left({\ell}^{2} \cdot U\right)}{Om}} \]
      fma-def [=>] 7.0	\[ \sqrt{\color{blue}{\mathsf{fma}\left(2, n \cdot \left(t \cdot U\right), -4 \cdot \frac{n \cdot \left({\ell}^{2} \cdot U\right)}{Om}\right)}} \]
      *-commutative [=>] 7.0	\[ \sqrt{\mathsf{fma}\left(2, n \cdot \color{blue}{\left(U \cdot t\right)}, -4 \cdot \frac{n \cdot \left({\ell}^{2} \cdot U\right)}{Om}\right)} \]
      *-commutative [=>] 7.0	\[ \sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \frac{\color{blue}{\left({\ell}^{2} \cdot U\right) \cdot n}}{Om}\right)} \]
      associate-/l* [=>] 8.1	\[ \sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \color{blue}{\frac{{\ell}^{2} \cdot U}{\frac{Om}{n}}}\right)} \]
      unpow2 [=>] 8.1	\[ \sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \frac{\color{blue}{\left(\ell \cdot \ell\right)} \cdot U}{\frac{Om}{n}}\right)} \]
      associate-*l* [=>] 16.6	\[ \sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \frac{\color{blue}{\ell \cdot \left(\ell \cdot U\right)}}{\frac{Om}{n}}\right)} \]

   5. Applied egg-rr 25.5%

      \[\leadsto \sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \color{blue}{\left(\frac{U \cdot \ell}{Om} \cdot \left(\frac{\ell}{1} \cdot n\right)\right)}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)} \leq 5 \cdot 10^{-86}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \mathsf{fma}\left(n, \frac{\ell}{Om} \cdot \left(\frac{\ell}{Om} \cdot \left(U* - U\right)\right), \mathsf{fma}\left(\ell \cdot \frac{\ell}{Om}, -2, t\right)\right)\right)}\\ \mathbf{elif}\;\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)} \leq 10^{+149}:\\ \;\;\;\;\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \left(\frac{U \cdot \ell}{Om} \cdot \left(n \cdot \ell\right)\right)\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	59.3%
Cost	43528

\[\begin{array}{l} t_1 := \frac{\ell \cdot \ell}{Om}\\ t_2 := \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot t_1\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)}\\ \mathbf{if}\;t_2 \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(-2 \cdot \frac{\ell}{\frac{Om}{\ell}} + n \cdot \left(t_1 \cdot \frac{U*}{Om} - t_1 \cdot \frac{U}{Om}\right)\right)\right)\right)}\\ \mathbf{elif}\;t_2 \leq 10^{+149}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \left(\frac{U \cdot \ell}{Om} \cdot \left(n \cdot \ell\right)\right)\right)}\\ \end{array} \]

Alternative 2
Accuracy	60.2%
Cost	30728

\[\begin{array}{l} t_1 := \left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\right)\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \mathsf{fma}\left(n, \frac{\ell}{Om} \cdot \left(\frac{\ell}{Om} \cdot U*\right), \mathsf{fma}\left(\ell \cdot \frac{\ell}{Om}, -2, t\right)\right)\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\sqrt{t_1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \left(\frac{U \cdot \ell}{Om} \cdot \left(n \cdot \ell\right)\right)\right)}\\ \end{array} \]

Alternative 3
Accuracy	54.3%
Cost	14732

\[\begin{array}{l} t_1 := \frac{U*}{Om} \cdot \frac{n}{Om} + \frac{-2}{Om}\\ \mathbf{if}\;\ell \leq -4.5 \cdot 10^{+49}:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \left(-\sqrt{n \cdot \left(U \cdot t_1\right)}\right)\right)\\ \mathbf{elif}\;\ell \leq 2.8 \cdot 10^{-247}:\\ \;\;\;\;\sqrt{\left(2 \cdot \left(n \cdot U\right)\right) \cdot \left(\mathsf{fma}\left(\ell \cdot \frac{\ell}{Om}, -2, t\right) + \frac{n}{\frac{Om}{\frac{\ell \cdot \left(\ell \cdot U*\right)}{Om}}}\right)}\\ \mathbf{elif}\;\ell \leq 3.4 \cdot 10^{-41}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(n \cdot \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot U*\right) + \frac{\ell}{Om} \cdot \left(\ell \cdot -2\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 2.9 \cdot 10^{-33}:\\ \;\;\;\;\frac{\left(\sqrt{2} \cdot \left(n \cdot \ell\right)\right) \cdot \sqrt{U \cdot \left(U* - U\right)}}{Om}\\ \mathbf{elif}\;\ell \leq 4.6 \cdot 10^{+149}:\\ \;\;\;\;\sqrt{U \cdot \left(-\mathsf{fma}\left(-2, n \cdot t, \frac{4}{\frac{Om}{n \cdot \left(\ell \cdot \ell\right)}}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \sqrt{U \cdot \left(n \cdot t_1\right)}\right)\\ \end{array} \]

Alternative 4
Accuracy	53.9%
Cost	14600

\[\begin{array}{l} t_1 := \frac{U*}{Om} \cdot \frac{n}{Om} + \frac{-2}{Om}\\ \mathbf{if}\;\ell \leq -2050000000000:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \left(-\sqrt{n \cdot \left(U \cdot t_1\right)}\right)\right)\\ \mathbf{elif}\;\ell \leq 5.5 \cdot 10^{-61}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(n \cdot \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot U*\right) + \frac{\ell}{Om} \cdot \left(\ell \cdot -2\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 8.2 \cdot 10^{+100}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \ell \cdot \left(\ell \cdot \left(\frac{-2}{Om} + \left(U* - U\right) \cdot \frac{n}{Om \cdot Om}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \sqrt{U \cdot \left(n \cdot t_1\right)}\right)\\ \end{array} \]

Alternative 5
Accuracy	51.5%
Cost	14544

\[\begin{array}{l} t_1 := \frac{\ell \cdot \ell}{Om}\\ \mathbf{if}\;\ell \leq -9 \cdot 10^{+106}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \left(\frac{U \cdot \ell}{Om} \cdot \left(n \cdot \ell\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq -4.3 \cdot 10^{-70}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(-2 \cdot \frac{\ell}{\frac{Om}{\ell}} + n \cdot \left(t_1 \cdot \frac{U*}{Om} - t_1 \cdot \frac{U}{Om}\right)\right)\right)\right)}\\ \mathbf{elif}\;\ell \leq 2.1 \cdot 10^{-62}:\\ \;\;\;\;\sqrt{2 \cdot \left|t \cdot \left(n \cdot U\right)\right|}\\ \mathbf{elif}\;\ell \leq 5.8 \cdot 10^{+99}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \ell \cdot \left(\ell \cdot \left(\frac{-2}{Om} + \left(U* - U\right) \cdot \frac{n}{Om \cdot Om}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \sqrt{U \cdot \left(n \cdot \left(\frac{U*}{Om} \cdot \frac{n}{Om} + \frac{-2}{Om}\right)\right)}\right)\\ \end{array} \]

Alternative 6
Accuracy	47.5%
Cost	14484

\[\begin{array}{l} t_1 := \ell \cdot \left(\ell \cdot \left(\frac{-2}{Om} + \left(U* - U\right) \cdot \frac{n}{Om \cdot Om}\right)\right)\\ \mathbf{if}\;Om \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{elif}\;Om \leq -3.1 \cdot 10^{-108}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + -4 \cdot \frac{\ell \cdot \left(U \cdot \ell\right)}{\frac{Om}{n}}}\\ \mathbf{elif}\;Om \leq -1.05 \cdot 10^{-161}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + U \cdot t_1\right)}\\ \mathbf{elif}\;Om \leq 1.7 \cdot 10^{-213}:\\ \;\;\;\;\frac{\left(\sqrt{2} \cdot \left(n \cdot \ell\right)\right) \cdot \sqrt{U \cdot \left(U* - U\right)}}{Om}\\ \mathbf{elif}\;Om \leq 2.7 \cdot 10^{+30}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(-2, n \cdot t, \frac{4}{\frac{Om}{n \cdot \left(\ell \cdot \ell\right)}}\right) \cdot \left(-U\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + t_1\right)\right)}\\ \end{array} \]

Alternative 7
Accuracy	50.6%
Cost	14412

\[\begin{array}{l} t_1 := \frac{U*}{Om} \cdot \frac{n}{Om} + \frac{-2}{Om}\\ \mathbf{if}\;\ell \leq -19000000000:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \left(-\sqrt{n \cdot \left(U \cdot t_1\right)}\right)\right)\\ \mathbf{elif}\;\ell \leq 1.55 \cdot 10^{-62}:\\ \;\;\;\;\sqrt{2 \cdot \left|t \cdot \left(n \cdot U\right)\right|}\\ \mathbf{elif}\;\ell \leq 6.3 \cdot 10^{+100}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \ell \cdot \left(\ell \cdot \left(\frac{-2}{Om} + \left(U* - U\right) \cdot \frac{n}{Om \cdot Om}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \sqrt{U \cdot \left(n \cdot t_1\right)}\right)\\ \end{array} \]

Alternative 8
Accuracy	48.5%
Cost	14352

\[\begin{array}{l} \mathbf{if}\;Om \leq -8.6 \cdot 10^{+42}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{elif}\;Om \leq -7.5 \cdot 10^{-168}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(2, n \cdot \left(U \cdot t\right), -4 \cdot \left(\ell \cdot \left(n \cdot \frac{U \cdot \ell}{Om}\right)\right)\right)}\\ \mathbf{elif}\;Om \leq 4.1 \cdot 10^{-213}:\\ \;\;\;\;\frac{\left(\sqrt{2} \cdot \left(n \cdot \ell\right)\right) \cdot \sqrt{U \cdot \left(U* - U\right)}}{Om}\\ \mathbf{elif}\;Om \leq 2.2 \cdot 10^{+25}:\\ \;\;\;\;\sqrt{\mathsf{fma}\left(-2, n \cdot t, \frac{4}{\frac{Om}{n \cdot \left(\ell \cdot \ell\right)}}\right) \cdot \left(-U\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \ell \cdot \left(\ell \cdot \left(\frac{-2}{Om} + \left(U* - U\right) \cdot \frac{n}{Om \cdot Om}\right)\right)\right)\right)}\\ \end{array} \]

Alternative 9
Accuracy	49.4%
Cost	14024

\[\begin{array}{l} t_1 := \frac{\ell \cdot \ell}{Om}\\ \mathbf{if}\;n \leq -1.2 \cdot 10^{-22}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(-2 \cdot \frac{\ell}{\frac{Om}{\ell}} + n \cdot \left(t_1 \cdot \frac{U*}{Om} - t_1 \cdot \frac{U}{Om}\right)\right)\right)\right)}\\ \mathbf{elif}\;n \leq 4.5 \cdot 10^{-200}:\\ \;\;\;\;\sqrt{U \cdot \mathsf{fma}\left(-4, n \cdot \left(\ell \cdot \frac{\ell}{Om}\right), n \cdot \left(2 \cdot t\right)\right)}\\ \mathbf{elif}\;n \leq 1.65 \cdot 10^{-187}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{U \cdot \left(n \cdot \frac{-2}{Om}\right)} \cdot \left(-\ell\right)\right)\\ \mathbf{elif}\;n \leq 6.5 \cdot 10^{+133}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot U\right)} \cdot \sqrt{n}\\ \end{array} \]

Alternative 10
Accuracy	49.3%
Cost	13964

\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ t_2 := \frac{\ell \cdot \ell}{Om}\\ \mathbf{if}\;n \leq -9.4 \cdot 10^{-24}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(-2 \cdot \frac{\ell}{\frac{Om}{\ell}} + n \cdot \left(t_2 \cdot \frac{U*}{Om} - t_2 \cdot \frac{U}{Om}\right)\right)\right)\right)}\\ \mathbf{elif}\;n \leq 1.75 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq 1.65 \cdot 10^{-187}:\\ \;\;\;\;\sqrt{2} \cdot \left(\ell \cdot \left(-\sqrt{-2 \cdot \frac{n \cdot U}{Om}}\right)\right)\\ \mathbf{elif}\;n \leq 3.2 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot U\right)} \cdot \sqrt{n}\\ \end{array} \]

Alternative 11
Accuracy	49.4%
Cost	13964

\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ t_2 := \frac{\ell \cdot \ell}{Om}\\ \mathbf{if}\;n \leq -5.4 \cdot 10^{-24}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(-2 \cdot \frac{\ell}{\frac{Om}{\ell}} + n \cdot \left(t_2 \cdot \frac{U*}{Om} - t_2 \cdot \frac{U}{Om}\right)\right)\right)\right)}\\ \mathbf{elif}\;n \leq 1.75 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq 1.65 \cdot 10^{-187}:\\ \;\;\;\;\sqrt{2} \cdot \left(\sqrt{U \cdot \left(n \cdot \frac{-2}{Om}\right)} \cdot \left(-\ell\right)\right)\\ \mathbf{elif}\;n \leq 7.2 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot U\right)} \cdot \sqrt{n}\\ \end{array} \]

Alternative 12
Accuracy	47.2%
Cost	9296

\[\begin{array}{l} t_1 := \frac{\ell \cdot \ell}{Om}\\ t_2 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ t_3 := \sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + -4 \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(U \cdot \ell\right)\right)\right)}\\ \mathbf{if}\;U* \leq -1.15 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;U* \leq 5.3 \cdot 10^{-197}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;U* \leq 2.2 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;U* \leq 2.2 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \left(-2 \cdot \frac{\ell}{\frac{Om}{\ell}} + n \cdot \left(t_1 \cdot \frac{U*}{Om} - t_1 \cdot \frac{U}{Om}\right)\right)\right)\right)}\\ \mathbf{elif}\;U* \leq 9 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;U* \leq 3.7 \cdot 10^{+168}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t + U \cdot \left(\ell \cdot \left(\ell \cdot \left(\frac{-2}{Om} + \left(U* - U\right) \cdot \frac{n}{Om \cdot Om}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	46.6%
Cost	8144

\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{if}\;Om \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Om \leq -2.05 \cdot 10^{-167}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)\right)}\\ \mathbf{elif}\;Om \leq -3.5 \cdot 10^{-215}:\\ \;\;\;\;\sqrt{2 \cdot \frac{\left(n \cdot \ell\right) \cdot \left(\left(U* - U\right) \cdot \frac{U}{Om}\right)}{\frac{Om}{n \cdot \ell}}}\\ \mathbf{elif}\;Om \leq 2.56 \cdot 10^{-187}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot t\right)\right) + -4 \cdot \left(\left(\ell \cdot \ell\right) \cdot \left(U \cdot \frac{n}{Om}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	47.5%
Cost	8144

\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ t_2 := 2 \cdot \left(n \cdot \left(U \cdot t\right)\right)\\ \mathbf{if}\;Om \leq -1.06 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Om \leq -7.2 \cdot 10^{-168}:\\ \;\;\;\;\sqrt{t_2 + -4 \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(U \cdot \ell\right)\right)\right)}\\ \mathbf{elif}\;Om \leq -1.25 \cdot 10^{-215}:\\ \;\;\;\;\sqrt{2 \cdot \frac{\left(n \cdot \ell\right) \cdot \left(\left(U* - U\right) \cdot \frac{U}{Om}\right)}{\frac{Om}{n \cdot \ell}}}\\ \mathbf{elif}\;Om \leq 2.56 \cdot 10^{-187}:\\ \;\;\;\;\sqrt{t_2 + -4 \cdot \left(\left(\ell \cdot \ell\right) \cdot \left(U \cdot \frac{n}{Om}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	48.9%
Cost	8144

\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ t_2 := 2 \cdot \left(n \cdot \left(U \cdot t\right)\right)\\ \mathbf{if}\;U \leq -2.2 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;U \leq -5.1 \cdot 10^{-275}:\\ \;\;\;\;\sqrt{t_2 + -4 \cdot \left(\frac{\ell}{Om} \cdot \left(n \cdot \left(U \cdot \ell\right)\right)\right)}\\ \mathbf{elif}\;U \leq 3.4 \cdot 10^{-238}:\\ \;\;\;\;\sqrt{t_2 + -4 \cdot \frac{\ell \cdot \left(U \cdot \ell\right)}{\frac{Om}{n}}}\\ \mathbf{elif}\;U \leq 4.6 \cdot 10^{-203}:\\ \;\;\;\;\sqrt{2 \cdot \frac{n \cdot \ell}{\frac{Om}{n \cdot \ell} \cdot \frac{Om}{U \cdot \left(U* - U\right)}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	46.1%
Cost	8012

\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{if}\;Om \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Om \leq -1.3 \cdot 10^{-167}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)\right)}\\ \mathbf{elif}\;Om \leq -6 \cdot 10^{-214}:\\ \;\;\;\;\sqrt{2 \cdot \frac{\left(n \cdot \ell\right) \cdot \left(\left(U* - U\right) \cdot \frac{U}{Om}\right)}{\frac{Om}{n \cdot \ell}}}\\ \mathbf{elif}\;Om \leq 2.7 \cdot 10^{-215}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Accuracy	45.9%
Cost	7888

\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{if}\;Om \leq -8.4 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Om \leq -4.2 \cdot 10^{-166}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)\right)}\\ \mathbf{elif}\;Om \leq -4.1 \cdot 10^{-216}:\\ \;\;\;\;\sqrt{2 \cdot \left(\frac{\left(n \cdot \ell\right) \cdot \left(n \cdot \ell\right)}{Om} \cdot \frac{U*}{\frac{Om}{U}}\right)}\\ \mathbf{elif}\;Om \leq 1.86 \cdot 10^{-215}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Accuracy	45.9%
Cost	7888

\[\begin{array}{l} t_1 := \sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{if}\;Om \leq -9.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Om \leq -7.2 \cdot 10^{-168}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)\right)}\\ \mathbf{elif}\;Om \leq -1.2 \cdot 10^{-213}:\\ \;\;\;\;\sqrt{2 \cdot \left(\frac{\left(n \cdot \ell\right) \cdot \left(n \cdot \ell\right)}{Om} \cdot \frac{U \cdot U*}{Om}\right)}\\ \mathbf{elif}\;Om \leq 5.5 \cdot 10^{-216}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Accuracy	46.7%
Cost	7625

\[\begin{array}{l} \mathbf{if}\;\ell \leq -6.4 \cdot 10^{-271} \lor \neg \left(\ell \leq 7.8 \cdot 10^{-246}\right):\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{t \cdot \left(n \cdot \left(2 \cdot U\right)\right)}\\ \end{array} \]

Alternative 20
Accuracy	46.5%
Cost	7625

\[\begin{array}{l} \mathbf{if}\;Om \leq -1 \cdot 10^{+43} \lor \neg \left(Om \leq 2.1 \cdot 10^{-237}\right):\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(n \cdot \left(U \cdot \left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right)\right)\right)}\\ \end{array} \]

Alternative 21
Accuracy	48.0%
Cost	7625

\[\begin{array}{l} \mathbf{if}\;U \leq -1.7 \cdot 10^{+98} \lor \neg \left(U \leq 1.26 \cdot 10^{-170}\right):\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t + \ell \cdot \frac{\ell \cdot -2}{Om}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t + \ell \cdot \left(\frac{\ell}{Om} \cdot -2\right)\right)\right)}\\ \end{array} \]

Alternative 22
Accuracy	37.4%
Cost	7500

\[\begin{array}{l} t_1 := \sqrt{U \cdot \frac{-4 \cdot \left(n \cdot \left(\ell \cdot \ell\right)\right)}{Om}}\\ \mathbf{if}\;\ell \leq -1250000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq 2.6 \cdot 10^{-247}:\\ \;\;\;\;\sqrt{t \cdot \left(n \cdot \left(2 \cdot U\right)\right)}\\ \mathbf{elif}\;\ell \leq 1.65 \cdot 10^{+62}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Accuracy	38.5%
Cost	7245

\[\begin{array}{l} \mathbf{if}\;U \leq -2.2 \cdot 10^{+101} \lor \neg \left(U \leq 1.95 \cdot 10^{-199}\right) \land U \leq 5 \cdot 10^{+209}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t\right)}\\ \end{array} \]

Alternative 24
Accuracy	39.1%
Cost	7112

\[\begin{array}{l} \mathbf{if}\;U \leq -2 \cdot 10^{-92}:\\ \;\;\;\;\sqrt{t \cdot \left(n \cdot \left(2 \cdot U\right)\right)}\\ \mathbf{elif}\;U \leq 1.8 \cdot 10^{-202}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t\right)\right)}\\ \end{array} \]

Alternative 25
Accuracy	37.9%
Cost	6848

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

Reproduce

herbie shell --seed 2023129 
(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*))))))