Average Error: 42.6 → 9.1
Time: 1.6m
Precision: 64
\[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.4341990158619707 \cdot 10^{+119}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\left(\frac{1}{\sqrt{2}} - \frac{2}{\sqrt{2}}\right) \cdot \frac{t}{x \cdot x} - \left(\frac{t}{x \cdot \sqrt{2}} \cdot 2 + \sqrt{2} \cdot t\right)}\\ \mathbf{elif}\;t \le -9.99137278910249 \cdot 10^{-171}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\sqrt{t \cdot \left(t \cdot \left(2 + \frac{4}{x}\right)\right) + \frac{\ell}{x} \cdot \left(2 \cdot \ell\right)}}\\ \mathbf{elif}\;t \le -3.9310422125379254 \cdot 10^{-294}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\left(\frac{1}{\sqrt{2}} - \frac{2}{\sqrt{2}}\right) \cdot \frac{t}{x \cdot x} - \left(\frac{t}{x \cdot \sqrt{2}} \cdot 2 + \sqrt{2} \cdot t\right)}\\ \mathbf{elif}\;t \le 2.062636072758067 \cdot 10^{-203}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\frac{\sqrt{x \cdot \left(\left(\frac{\frac{64}{x \cdot x}}{x} + 8\right) \cdot \left(t \cdot t\right)\right) + \left(\left(2 \cdot \ell\right) \cdot \ell\right) \cdot \left(4 - \left(2 - \frac{4}{x}\right) \cdot \frac{4}{x}\right)}}{\sqrt{\left(\frac{4}{x} + x\right) \cdot 4 + -8}}}\\ \mathbf{elif}\;t \le 3.1992285379389345 \cdot 10^{-162}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{t \cdot \left(\frac{\frac{2}{x}}{\sqrt{2}} + \sqrt{2}\right) - \frac{\frac{t}{\sqrt{2}}}{x \cdot x}}\\ \mathbf{elif}\;t \le 1.8906144109064744 \cdot 10^{+99}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\sqrt{t \cdot \left(t \cdot \left(2 + \frac{4}{x}\right)\right) + \frac{\ell}{x} \cdot \left(2 \cdot \ell\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{t \cdot \left(\frac{\frac{2}{x}}{\sqrt{2}} + \sqrt{2}\right) - \frac{\frac{t}{\sqrt{2}}}{x \cdot x}}\\ \end{array}\]
\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.4341990158619707 \cdot 10^{+119}:\\
\;\;\;\;\frac{\sqrt{2} \cdot t}{\left(\frac{1}{\sqrt{2}} - \frac{2}{\sqrt{2}}\right) \cdot \frac{t}{x \cdot x} - \left(\frac{t}{x \cdot \sqrt{2}} \cdot 2 + \sqrt{2} \cdot t\right)}\\

\mathbf{elif}\;t \le -9.99137278910249 \cdot 10^{-171}:\\
\;\;\;\;\frac{\sqrt{2} \cdot t}{\sqrt{t \cdot \left(t \cdot \left(2 + \frac{4}{x}\right)\right) + \frac{\ell}{x} \cdot \left(2 \cdot \ell\right)}}\\

\mathbf{elif}\;t \le -3.9310422125379254 \cdot 10^{-294}:\\
\;\;\;\;\frac{\sqrt{2} \cdot t}{\left(\frac{1}{\sqrt{2}} - \frac{2}{\sqrt{2}}\right) \cdot \frac{t}{x \cdot x} - \left(\frac{t}{x \cdot \sqrt{2}} \cdot 2 + \sqrt{2} \cdot t\right)}\\

\mathbf{elif}\;t \le 2.062636072758067 \cdot 10^{-203}:\\
\;\;\;\;\frac{\sqrt{2} \cdot t}{\frac{\sqrt{x \cdot \left(\left(\frac{\frac{64}{x \cdot x}}{x} + 8\right) \cdot \left(t \cdot t\right)\right) + \left(\left(2 \cdot \ell\right) \cdot \ell\right) \cdot \left(4 - \left(2 - \frac{4}{x}\right) \cdot \frac{4}{x}\right)}}{\sqrt{\left(\frac{4}{x} + x\right) \cdot 4 + -8}}}\\

\mathbf{elif}\;t \le 3.1992285379389345 \cdot 10^{-162}:\\
\;\;\;\;\frac{\sqrt{2} \cdot t}{t \cdot \left(\frac{\frac{2}{x}}{\sqrt{2}} + \sqrt{2}\right) - \frac{\frac{t}{\sqrt{2}}}{x \cdot x}}\\

\mathbf{elif}\;t \le 1.8906144109064744 \cdot 10^{+99}:\\
\;\;\;\;\frac{\sqrt{2} \cdot t}{\sqrt{t \cdot \left(t \cdot \left(2 + \frac{4}{x}\right)\right) + \frac{\ell}{x} \cdot \left(2 \cdot \ell\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt{2} \cdot t}{t \cdot \left(\frac{\frac{2}{x}}{\sqrt{2}} + \sqrt{2}\right) - \frac{\frac{t}{\sqrt{2}}}{x \cdot x}}\\

\end{array}
double f(double x, double l, double t) {
        double r7303109 = 2.0;
        double r7303110 = sqrt(r7303109);
        double r7303111 = t;
        double r7303112 = r7303110 * r7303111;
        double r7303113 = x;
        double r7303114 = 1.0;
        double r7303115 = r7303113 + r7303114;
        double r7303116 = r7303113 - r7303114;
        double r7303117 = r7303115 / r7303116;
        double r7303118 = l;
        double r7303119 = r7303118 * r7303118;
        double r7303120 = r7303111 * r7303111;
        double r7303121 = r7303109 * r7303120;
        double r7303122 = r7303119 + r7303121;
        double r7303123 = r7303117 * r7303122;
        double r7303124 = r7303123 - r7303119;
        double r7303125 = sqrt(r7303124);
        double r7303126 = r7303112 / r7303125;
        return r7303126;
}
↓
double f(double x, double l, double t) {
        double r7303127 = t;
        double r7303128 = -1.4341990158619707e+119;
        bool r7303129 = r7303127 <= r7303128;
        double r7303130 = 2.0;
        double r7303131 = sqrt(r7303130);
        double r7303132 = r7303131 * r7303127;
        double r7303133 = 1.0;
        double r7303134 = r7303133 / r7303131;
        double r7303135 = r7303130 / r7303131;
        double r7303136 = r7303134 - r7303135;
        double r7303137 = x;
        double r7303138 = r7303137 * r7303137;
        double r7303139 = r7303127 / r7303138;
        double r7303140 = r7303136 * r7303139;
        double r7303141 = r7303137 * r7303131;
        double r7303142 = r7303127 / r7303141;
        double r7303143 = r7303142 * r7303130;
        double r7303144 = r7303143 + r7303132;
        double r7303145 = r7303140 - r7303144;
        double r7303146 = r7303132 / r7303145;
        double r7303147 = -9.99137278910249e-171;
        bool r7303148 = r7303127 <= r7303147;
        double r7303149 = 4.0;
        double r7303150 = r7303149 / r7303137;
        double r7303151 = r7303130 + r7303150;
        double r7303152 = r7303127 * r7303151;
        double r7303153 = r7303127 * r7303152;
        double r7303154 = l;
        double r7303155 = r7303154 / r7303137;
        double r7303156 = r7303130 * r7303154;
        double r7303157 = r7303155 * r7303156;
        double r7303158 = r7303153 + r7303157;
        double r7303159 = sqrt(r7303158);
        double r7303160 = r7303132 / r7303159;
        double r7303161 = -3.9310422125379254e-294;
        bool r7303162 = r7303127 <= r7303161;
        double r7303163 = 2.062636072758067e-203;
        bool r7303164 = r7303127 <= r7303163;
        double r7303165 = 64.0;
        double r7303166 = r7303165 / r7303138;
        double r7303167 = r7303166 / r7303137;
        double r7303168 = 8.0;
        double r7303169 = r7303167 + r7303168;
        double r7303170 = r7303127 * r7303127;
        double r7303171 = r7303169 * r7303170;
        double r7303172 = r7303137 * r7303171;
        double r7303173 = r7303156 * r7303154;
        double r7303174 = r7303130 - r7303150;
        double r7303175 = r7303174 * r7303150;
        double r7303176 = r7303149 - r7303175;
        double r7303177 = r7303173 * r7303176;
        double r7303178 = r7303172 + r7303177;
        double r7303179 = sqrt(r7303178);
        double r7303180 = r7303150 + r7303137;
        double r7303181 = r7303180 * r7303149;
        double r7303182 = -8.0;
        double r7303183 = r7303181 + r7303182;
        double r7303184 = sqrt(r7303183);
        double r7303185 = r7303179 / r7303184;
        double r7303186 = r7303132 / r7303185;
        double r7303187 = 3.1992285379389345e-162;
        bool r7303188 = r7303127 <= r7303187;
        double r7303189 = r7303130 / r7303137;
        double r7303190 = r7303189 / r7303131;
        double r7303191 = r7303190 + r7303131;
        double r7303192 = r7303127 * r7303191;
        double r7303193 = r7303127 / r7303131;
        double r7303194 = r7303193 / r7303138;
        double r7303195 = r7303192 - r7303194;
        double r7303196 = r7303132 / r7303195;
        double r7303197 = 1.8906144109064744e+99;
        bool r7303198 = r7303127 <= r7303197;
        double r7303199 = r7303198 ? r7303160 : r7303196;
        double r7303200 = r7303188 ? r7303196 : r7303199;
        double r7303201 = r7303164 ? r7303186 : r7303200;
        double r7303202 = r7303162 ? r7303146 : r7303201;
        double r7303203 = r7303148 ? r7303160 : r7303202;
        double r7303204 = r7303129 ? r7303146 : r7303203;
        return r7303204;
}

Error

Bits error versus x

Bits error versus l

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if t < -1.4341990158619707e+119 or -9.99137278910249e-171 < t < -3.9310422125379254e-294

    1. Initial program 56.0

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]

    2. Taylor expanded around -inf 13.4

      \[\leadsto \frac{\sqrt{2} \cdot t}{\color{blue}{2 \cdot \frac{t}{{\left(\sqrt{2}\right)}^{3} \cdot {x}^{2}} - \left(2 \cdot \frac{t}{\sqrt{2} \cdot {x}^{2}} + \left(t \cdot \sqrt{2} + 2 \cdot \frac{t}{\sqrt{2} \cdot x}\right)\right)}}\]

    3. Simplified13.4

      \[\leadsto \frac{\sqrt{2} \cdot t}{\color{blue}{\frac{t}{x \cdot x} \cdot \left(\frac{1}{\sqrt{2}} - \frac{2}{\sqrt{2}}\right) - \left(\sqrt{2} \cdot t + \frac{t}{\sqrt{2} \cdot x} \cdot 2\right)}}\]

    if -1.4341990158619707e+119 < t < -9.99137278910249e-171 or 3.1992285379389345e-162 < t < 1.8906144109064744e+99

    1. Initial program 26.6

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]

    2. Taylor expanded around inf 10.8

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

    3. Simplified5.5

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\color{blue}{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \left(\ell \cdot 2\right) \cdot \frac{\ell}{x}}}}\]

    if -3.9310422125379254e-294 < t < 2.062636072758067e-203

    1. Initial program 61.9

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]

    2. Taylor expanded around inf 30.2

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

    3. Simplified28.8

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\color{blue}{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \left(\ell \cdot 2\right) \cdot \frac{\ell}{x}}}}\]
    4. Using strategy rm

    5. Applied associate-*r/30.2

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \color{blue}{\frac{\left(\ell \cdot 2\right) \cdot \ell}{x}}}}\]

    6. Applied flip3-+30.2

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\left(\color{blue}{\frac{{\left(\frac{4}{x}\right)}^{3} + {2}^{3}}{\frac{4}{x} \cdot \frac{4}{x} + \left(2 \cdot 2 - \frac{4}{x} \cdot 2\right)}} \cdot t\right) \cdot t + \frac{\left(\ell \cdot 2\right) \cdot \ell}{x}}}\]

    7. Applied associate-*l/30.2

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\color{blue}{\frac{\left({\left(\frac{4}{x}\right)}^{3} + {2}^{3}\right) \cdot t}{\frac{4}{x} \cdot \frac{4}{x} + \left(2 \cdot 2 - \frac{4}{x} \cdot 2\right)}} \cdot t + \frac{\left(\ell \cdot 2\right) \cdot \ell}{x}}}\]

    8. Applied associate-*l/30.2

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\color{blue}{\frac{\left(\left({\left(\frac{4}{x}\right)}^{3} + {2}^{3}\right) \cdot t\right) \cdot t}{\frac{4}{x} \cdot \frac{4}{x} + \left(2 \cdot 2 - \frac{4}{x} \cdot 2\right)}} + \frac{\left(\ell \cdot 2\right) \cdot \ell}{x}}}\]

    9. Applied frac-add30.5

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\color{blue}{\frac{\left(\left(\left({\left(\frac{4}{x}\right)}^{3} + {2}^{3}\right) \cdot t\right) \cdot t\right) \cdot x + \left(\frac{4}{x} \cdot \frac{4}{x} + \left(2 \cdot 2 - \frac{4}{x} \cdot 2\right)\right) \cdot \left(\left(\ell \cdot 2\right) \cdot \ell\right)}{\left(\frac{4}{x} \cdot \frac{4}{x} + \left(2 \cdot 2 - \frac{4}{x} \cdot 2\right)\right) \cdot x}}}}\]

    10. Applied sqrt-div25.3

      \[\leadsto \frac{\sqrt{2} \cdot t}{\color{blue}{\frac{\sqrt{\left(\left(\left({\left(\frac{4}{x}\right)}^{3} + {2}^{3}\right) \cdot t\right) \cdot t\right) \cdot x + \left(\frac{4}{x} \cdot \frac{4}{x} + \left(2 \cdot 2 - \frac{4}{x} \cdot 2\right)\right) \cdot \left(\left(\ell \cdot 2\right) \cdot \ell\right)}}{\sqrt{\left(\frac{4}{x} \cdot \frac{4}{x} + \left(2 \cdot 2 - \frac{4}{x} \cdot 2\right)\right) \cdot x}}}}\]

    11. Simplified25.3

      \[\leadsto \frac{\sqrt{2} \cdot t}{\frac{\color{blue}{\sqrt{\left(4 - \frac{4}{x} \cdot \left(2 - \frac{4}{x}\right)\right) \cdot \left(\left(2 \cdot \ell\right) \cdot \ell\right) + \left(\left(t \cdot t\right) \cdot \left(\frac{\frac{64}{x \cdot x}}{x} + 8\right)\right) \cdot x}}}{\sqrt{\left(\frac{4}{x} \cdot \frac{4}{x} + \left(2 \cdot 2 - \frac{4}{x} \cdot 2\right)\right) \cdot x}}}\]

    12. Simplified25.3

      \[\leadsto \frac{\sqrt{2} \cdot t}{\frac{\sqrt{\left(4 - \frac{4}{x} \cdot \left(2 - \frac{4}{x}\right)\right) \cdot \left(\left(2 \cdot \ell\right) \cdot \ell\right) + \left(\left(t \cdot t\right) \cdot \left(\frac{\frac{64}{x \cdot x}}{x} + 8\right)\right) \cdot x}}{\color{blue}{\sqrt{-8 + 4 \cdot \left(x + \frac{4}{x}\right)}}}}\]

    if 2.062636072758067e-203 < t < 3.1992285379389345e-162 or 1.8906144109064744e+99 < t

    1. Initial program 51.3

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]

    2. Taylor expanded around inf 48.6

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

    3. Simplified46.7

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\color{blue}{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \left(\ell \cdot 2\right) \cdot \frac{\ell}{x}}}}\]
    4. Using strategy rm

    5. Applied add-cube-cbrt46.7

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \left(\ell \cdot 2\right) \cdot \frac{\ell}{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}}}\]

    6. Applied add-cube-cbrt46.7

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \left(\ell \cdot 2\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}}\]

    7. Applied times-frac46.7

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \left(\ell \cdot 2\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{\sqrt[3]{\ell}}{\sqrt[3]{x}}\right)}}}\]

    8. Applied associate-*r*46.7

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \color{blue}{\left(\left(\ell \cdot 2\right) \cdot \frac{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \frac{\sqrt[3]{\ell}}{\sqrt[3]{x}}}}}\]

    9. Simplified46.7

      \[\leadsto \frac{\sqrt{2} \cdot t}{\sqrt{\left(\left(\frac{4}{x} + 2\right) \cdot t\right) \cdot t + \color{blue}{\left(\left(\ell \cdot 2\right) \cdot \left(\frac{\sqrt[3]{\ell}}{\sqrt[3]{x}} \cdot \frac{\sqrt[3]{\ell}}{\sqrt[3]{x}}\right)\right)} \cdot \frac{\sqrt[3]{\ell}}{\sqrt[3]{x}}}}\]

    10. Taylor expanded around inf 5.4

      \[\leadsto \frac{\sqrt{2} \cdot t}{\color{blue}{\left(t \cdot \sqrt{2} + 2 \cdot \frac{t}{\sqrt{2} \cdot x}\right) - 2 \cdot \frac{t}{{\left(\sqrt{2}\right)}^{3} \cdot {x}^{2}}}}\]

    11. Simplified5.4

      \[\leadsto \frac{\sqrt{2} \cdot t}{\color{blue}{t \cdot \left(\sqrt{2} + \frac{\frac{2}{x}}{\sqrt{2}}\right) - \frac{\frac{t}{\sqrt{2}}}{x \cdot x}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification9.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.4341990158619707 \cdot 10^{+119}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\left(\frac{1}{\sqrt{2}} - \frac{2}{\sqrt{2}}\right) \cdot \frac{t}{x \cdot x} - \left(\frac{t}{x \cdot \sqrt{2}} \cdot 2 + \sqrt{2} \cdot t\right)}\\ \mathbf{elif}\;t \le -9.99137278910249 \cdot 10^{-171}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\sqrt{t \cdot \left(t \cdot \left(2 + \frac{4}{x}\right)\right) + \frac{\ell}{x} \cdot \left(2 \cdot \ell\right)}}\\ \mathbf{elif}\;t \le -3.9310422125379254 \cdot 10^{-294}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\left(\frac{1}{\sqrt{2}} - \frac{2}{\sqrt{2}}\right) \cdot \frac{t}{x \cdot x} - \left(\frac{t}{x \cdot \sqrt{2}} \cdot 2 + \sqrt{2} \cdot t\right)}\\ \mathbf{elif}\;t \le 2.062636072758067 \cdot 10^{-203}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\frac{\sqrt{x \cdot \left(\left(\frac{\frac{64}{x \cdot x}}{x} + 8\right) \cdot \left(t \cdot t\right)\right) + \left(\left(2 \cdot \ell\right) \cdot \ell\right) \cdot \left(4 - \left(2 - \frac{4}{x}\right) \cdot \frac{4}{x}\right)}}{\sqrt{\left(\frac{4}{x} + x\right) \cdot 4 + -8}}}\\ \mathbf{elif}\;t \le 3.1992285379389345 \cdot 10^{-162}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{t \cdot \left(\frac{\frac{2}{x}}{\sqrt{2}} + \sqrt{2}\right) - \frac{\frac{t}{\sqrt{2}}}{x \cdot x}}\\ \mathbf{elif}\;t \le 1.8906144109064744 \cdot 10^{+99}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\sqrt{t \cdot \left(t \cdot \left(2 + \frac{4}{x}\right)\right) + \frac{\ell}{x} \cdot \left(2 \cdot \ell\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{t \cdot \left(\frac{\frac{2}{x}}{\sqrt{2}} + \sqrt{2}\right) - \frac{\frac{t}{\sqrt{2}}}{x \cdot x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (x l t)
  :name "Toniolo and Linder, Equation (7)"
  (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))