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

↓

\[\begin{array}{l} \mathbf{if}\;F \le -30784098139205.887:\\ \;\;\;\;\frac{\frac{1}{F \cdot F} - 1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \le 28455.400608266966:\\ \;\;\;\;\frac{{\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \frac{x}{\sin B} \cdot \cos B\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \frac{1}{F \cdot F}}{\sin B} - \frac{x}{\tan B}\\ \end{array}\]

double f(double F, double B, double x) {
        double r7051928 = x;
        double r7051929 = 1.0;
        double r7051930 = B;
        double r7051931 = tan(r7051930);
        double r7051932 = r7051929 / r7051931;
        double r7051933 = r7051928 * r7051932;
        double r7051934 = -r7051933;
        double r7051935 = F;
        double r7051936 = sin(r7051930);
        double r7051937 = r7051935 / r7051936;
        double r7051938 = r7051935 * r7051935;
        double r7051939 = 2.0;
        double r7051940 = r7051938 + r7051939;
        double r7051941 = r7051939 * r7051928;
        double r7051942 = r7051940 + r7051941;
        double r7051943 = r7051929 / r7051939;
        double r7051944 = -r7051943;
        double r7051945 = pow(r7051942, r7051944);
        double r7051946 = r7051937 * r7051945;
        double r7051947 = r7051934 + r7051946;
        return r7051947;
}

↓

double f(double F, double B, double x) {
        double r7051948 = F;
        double r7051949 = -30784098139205.887;
        bool r7051950 = r7051948 <= r7051949;
        double r7051951 = 1.0;
        double r7051952 = r7051948 * r7051948;
        double r7051953 = r7051951 / r7051952;
        double r7051954 = r7051953 - r7051951;
        double r7051955 = B;
        double r7051956 = sin(r7051955);
        double r7051957 = r7051954 / r7051956;
        double r7051958 = x;
        double r7051959 = tan(r7051955);
        double r7051960 = r7051958 / r7051959;
        double r7051961 = r7051957 - r7051960;
        double r7051962 = 28455.400608266966;
        bool r7051963 = r7051948 <= r7051962;
        double r7051964 = 2.0;
        double r7051965 = r7051952 + r7051964;
        double r7051966 = r7051964 * r7051958;
        double r7051967 = r7051965 + r7051966;
        double r7051968 = -0.5;
        double r7051969 = pow(r7051967, r7051968);
        double r7051970 = r7051969 * r7051948;
        double r7051971 = r7051970 / r7051956;
        double r7051972 = r7051958 / r7051956;
        double r7051973 = cos(r7051955);
        double r7051974 = r7051972 * r7051973;
        double r7051975 = r7051971 - r7051974;
        double r7051976 = r7051951 - r7051953;
        double r7051977 = r7051976 / r7051956;
        double r7051978 = r7051977 - r7051960;
        double r7051979 = r7051963 ? r7051975 : r7051978;
        double r7051980 = r7051950 ? r7051961 : r7051979;
        return r7051980;
}

\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 -30784098139205.887:\\
\;\;\;\;\frac{\frac{1}{F \cdot F} - 1}{\sin B} - \frac{x}{\tan B}\\

\mathbf{elif}\;F \le 28455.400608266966:\\
\;\;\;\;\frac{{\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \frac{x}{\sin B} \cdot \cos B\\

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

\end{array}

Derivation

Split input into 3 regimes
if F < -30784098139205.887
1. Initial program 26.3
  \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
2. Simplified21.1
  \[\leadsto \color{blue}{\frac{{\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \frac{x}{\tan B}}\]
3. Using strategy rm
4. Applied sqr-pow21.2
  \[\leadsto \frac{\color{blue}{\left({\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot {\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\left(\frac{\frac{-1}{2}}{2}\right)}\right)} \cdot F}{\sin B} - \frac{x}{\tan B}\]
5. Applied associate-*l*21.2
  \[\leadsto \frac{\color{blue}{{\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot \left({\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\left(\frac{\frac{-1}{2}}{2}\right)} \cdot F\right)}}{\sin B} - \frac{x}{\tan B}\]
6. Taylor expanded around -inf 0.1
  \[\leadsto \frac{\color{blue}{\frac{1}{{F}^{2}} - 1}}{\sin B} - \frac{x}{\tan B}\]
7. Simplified0.1
  \[\leadsto \frac{\color{blue}{\frac{1}{F \cdot F} - 1}}{\sin B} - \frac{x}{\tan B}\]
if -30784098139205.887 < F < 28455.400608266966
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
  \[\leadsto \color{blue}{\frac{{\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \frac{x}{\tan B}}\]
3. Using strategy rm
4. Applied tan-quot0.3
  \[\leadsto \frac{{\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \frac{x}{\color{blue}{\frac{\sin B}{\cos B}}}\]
5. Applied associate-/r/0.3
  \[\leadsto \frac{{\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \color{blue}{\frac{x}{\sin B} \cdot \cos B}\]
if 28455.400608266966 < F
1. Initial program 22.9
  \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
2. Simplified18.4
  \[\leadsto \color{blue}{\frac{{\left(\left(2 + F \cdot F\right) + 2 \cdot x\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \frac{x}{\tan B}}\]
3. Taylor expanded around inf 0.2
  \[\leadsto \frac{\color{blue}{1 - \frac{1}{{F}^{2}}}}{\sin B} - \frac{x}{\tan B}\]
4. Simplified0.2
  \[\leadsto \frac{\color{blue}{1 - \frac{1}{F \cdot F}}}{\sin B} - \frac{x}{\tan B}\]
Recombined 3 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;F \le -30784098139205.887:\\ \;\;\;\;\frac{\frac{1}{F \cdot F} - 1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \le 28455.400608266966:\\ \;\;\;\;\frac{{\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \frac{x}{\sin B} \cdot \cos B\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \frac{1}{F \cdot F}}{\sin B} - \frac{x}{\tan B}\\ \end{array}\]

Error

Derivation

`if F < -30784098139205.887`

`if -30784098139205.887 < F < 28455.400608266966`

`if 28455.400608266966 < F`

Reproduce