\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]

↓

\[\begin{array}{l} \mathbf{if}\;F \le -858534606529.7429:\\ \;\;\;\;\frac{\frac{1}{F \cdot F} - 1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \le 3467869.845259974:\\ \;\;\;\;\frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\frac{\sin B}{F}} - \cos B \cdot \frac{x}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{\sin B} - \frac{\frac{1}{\sin B}}{F \cdot F}\right) - \frac{x}{\tan B}\\ \end{array}\]

double f(double F, double B, double x) {
        double r24495222 = x;
        double r24495223 = 1.0;
        double r24495224 = B;
        double r24495225 = tan(r24495224);
        double r24495226 = r24495223 / r24495225;
        double r24495227 = r24495222 * r24495226;
        double r24495228 = -r24495227;
        double r24495229 = F;
        double r24495230 = sin(r24495224);
        double r24495231 = r24495229 / r24495230;
        double r24495232 = r24495229 * r24495229;
        double r24495233 = 2.0;
        double r24495234 = r24495232 + r24495233;
        double r24495235 = r24495233 * r24495222;
        double r24495236 = r24495234 + r24495235;
        double r24495237 = r24495223 / r24495233;
        double r24495238 = -r24495237;
        double r24495239 = pow(r24495236, r24495238);
        double r24495240 = r24495231 * r24495239;
        double r24495241 = r24495228 + r24495240;
        return r24495241;
}

↓

double f(double F, double B, double x) {
        double r24495242 = F;
        double r24495243 = -858534606529.7429;
        bool r24495244 = r24495242 <= r24495243;
        double r24495245 = 1.0;
        double r24495246 = r24495242 * r24495242;
        double r24495247 = r24495245 / r24495246;
        double r24495248 = r24495247 - r24495245;
        double r24495249 = B;
        double r24495250 = sin(r24495249);
        double r24495251 = r24495248 / r24495250;
        double r24495252 = x;
        double r24495253 = tan(r24495249);
        double r24495254 = r24495252 / r24495253;
        double r24495255 = r24495251 - r24495254;
        double r24495256 = 3467869.845259974;
        bool r24495257 = r24495242 <= r24495256;
        double r24495258 = 2.0;
        double r24495259 = fma(r24495242, r24495242, r24495258);
        double r24495260 = fma(r24495258, r24495252, r24495259);
        double r24495261 = -0.5;
        double r24495262 = pow(r24495260, r24495261);
        double r24495263 = r24495250 / r24495242;
        double r24495264 = r24495262 / r24495263;
        double r24495265 = cos(r24495249);
        double r24495266 = r24495252 / r24495250;
        double r24495267 = r24495265 * r24495266;
        double r24495268 = r24495264 - r24495267;
        double r24495269 = r24495245 / r24495250;
        double r24495270 = r24495269 / r24495246;
        double r24495271 = r24495269 - r24495270;
        double r24495272 = r24495271 - r24495254;
        double r24495273 = r24495257 ? r24495268 : r24495272;
        double r24495274 = r24495244 ? r24495255 : r24495273;
        return r24495274;
}

\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}

↓

\begin{array}{l}
\mathbf{if}\;F \le -858534606529.7429:\\
\;\;\;\;\frac{\frac{1}{F \cdot F} - 1}{\sin B} - \frac{x}{\tan B}\\

\mathbf{elif}\;F \le 3467869.845259974:\\
\;\;\;\;\frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\frac{\sin B}{F}} - \cos B \cdot \frac{x}{\sin B}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{1}{\sin B} - \frac{\frac{1}{\sin B}}{F \cdot F}\right) - \frac{x}{\tan B}\\

\end{array}

Derivation

Split input into 3 regimes
if F < -858534606529.7429
1. Initial program 26.1
  \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
2. Simplified25.4
  \[\leadsto \color{blue}{\frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\frac{\sin B}{F}} - \frac{x}{\tan B}}\]
3. Using strategy rm
4. Applied div-inv25.4
  \[\leadsto \frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\color{blue}{\sin B \cdot \frac{1}{F}}} - \frac{x}{\tan B}\]
5. Applied add-sqr-sqrt25.4
  \[\leadsto \frac{{\color{blue}{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*} \cdot \sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}}^{\frac{-1}{2}}}{\sin B \cdot \frac{1}{F}} - \frac{x}{\tan B}\]
6. Applied unpow-prod-down25.5
  \[\leadsto \frac{\color{blue}{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}} \cdot {\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}}}}{\sin B \cdot \frac{1}{F}} - \frac{x}{\tan B}\]
7. Applied times-frac21.1
  \[\leadsto \color{blue}{\frac{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}}}{\sin B} \cdot \frac{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}}}{\frac{1}{F}}} - \frac{x}{\tan B}\]
8. Using strategy rm
9. Applied associate-*l/21.1
  \[\leadsto \color{blue}{\frac{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}} \cdot \frac{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}}}{\frac{1}{F}}}{\sin B}} - \frac{x}{\tan B}\]
10. Simplified21.0
  \[\leadsto \frac{\color{blue}{\frac{1 \cdot F}{\sqrt{(x \cdot 2 + \left((F \cdot F + 2)_*\right))_*}}}}{\sin B} - \frac{x}{\tan B}\]
11. Taylor expanded around -inf 0.1
  \[\leadsto \frac{\color{blue}{\frac{1}{{F}^{2}} - 1}}{\sin B} - \frac{x}{\tan B}\]
12. Simplified0.1
  \[\leadsto \frac{\color{blue}{\frac{1}{F \cdot F} - 1}}{\sin B} - \frac{x}{\tan B}\]
if -858534606529.7429 < F < 3467869.845259974
1. Initial program 0.4
  \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
2. Simplified0.3
  \[\leadsto \color{blue}{\frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\frac{\sin B}{F}} - \frac{x}{\tan B}}\]
3. Using strategy rm
4. Applied tan-quot0.3
  \[\leadsto \frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\frac{\sin B}{F}} - \frac{x}{\color{blue}{\frac{\sin B}{\cos B}}}\]
5. Applied associate-/r/0.3
  \[\leadsto \frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\frac{\sin B}{F}} - \color{blue}{\frac{x}{\sin B} \cdot \cos B}\]
if 3467869.845259974 < F
1. Initial program 23.0
  \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
2. Simplified22.3
  \[\leadsto \color{blue}{\frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\frac{\sin B}{F}} - \frac{x}{\tan B}}\]
3. Using strategy rm
4. Applied div-inv22.3
  \[\leadsto \frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\color{blue}{\sin B \cdot \frac{1}{F}}} - \frac{x}{\tan B}\]
5. Applied add-sqr-sqrt22.3
  \[\leadsto \frac{{\color{blue}{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*} \cdot \sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}}^{\frac{-1}{2}}}{\sin B \cdot \frac{1}{F}} - \frac{x}{\tan B}\]
6. Applied unpow-prod-down22.4
  \[\leadsto \frac{\color{blue}{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}} \cdot {\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}}}}{\sin B \cdot \frac{1}{F}} - \frac{x}{\tan B}\]
7. Applied times-frac18.6
  \[\leadsto \color{blue}{\frac{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}}}{\sin B} \cdot \frac{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}}}{\frac{1}{F}}} - \frac{x}{\tan B}\]
8. Using strategy rm
9. Applied associate-*l/18.6
  \[\leadsto \color{blue}{\frac{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}} \cdot \frac{{\left(\sqrt{(2 \cdot x + \left((F \cdot F + 2)_*\right))_*}\right)}^{\frac{-1}{2}}}{\frac{1}{F}}}{\sin B}} - \frac{x}{\tan B}\]
10. Simplified18.5
  \[\leadsto \frac{\color{blue}{\frac{1 \cdot F}{\sqrt{(x \cdot 2 + \left((F \cdot F + 2)_*\right))_*}}}}{\sin B} - \frac{x}{\tan B}\]
11. Using strategy rm
12. Applied associate-/l/18.5
  \[\leadsto \color{blue}{\frac{1 \cdot F}{\sin B \cdot \sqrt{(x \cdot 2 + \left((F \cdot F + 2)_*\right))_*}}} - \frac{x}{\tan B}\]
13. Simplified18.5
  \[\leadsto \frac{\color{blue}{F}}{\sin B \cdot \sqrt{(x \cdot 2 + \left((F \cdot F + 2)_*\right))_*}} - \frac{x}{\tan B}\]
14. Taylor expanded around inf 0.2
  \[\leadsto \color{blue}{\left(\frac{1}{\sin B} - \frac{1}{{F}^{2} \cdot \sin B}\right)} - \frac{x}{\tan B}\]
15. Simplified0.2
  \[\leadsto \color{blue}{\left(\frac{1}{\sin B} - \frac{\frac{1}{\sin B}}{F \cdot F}\right)} - \frac{x}{\tan B}\]
Recombined 3 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;F \le -858534606529.7429:\\ \;\;\;\;\frac{\frac{1}{F \cdot F} - 1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \le 3467869.845259974:\\ \;\;\;\;\frac{{\left((2 \cdot x + \left((F \cdot F + 2)_*\right))_*\right)}^{\frac{-1}{2}}}{\frac{\sin B}{F}} - \cos B \cdot \frac{x}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{\sin B} - \frac{\frac{1}{\sin B}}{F \cdot F}\right) - \frac{x}{\tan B}\\ \end{array}\]

Error

Derivation

`if F < -858534606529.7429`

`if -858534606529.7429 < F < 3467869.845259974`

`if 3467869.845259974 < F`

Reproduce