Average Error: 13.6 → 0.3
Time: 40.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;F \le -2.016907704755291348515550104729865295568 \cdot 10^{99}:\\ \;\;\;\;\frac{1}{\sin B \cdot {\left(\frac{1}{{-1}^{1}}\right)}^{1}} - \frac{1 \cdot x}{\tan B}\\ \mathbf{elif}\;F \le 12308.79316332406233414076268672943115234:\\ \;\;\;\;\frac{F}{{\left(x \cdot 2 + \left(F \cdot F + 2\right)\right)}^{\left(\frac{1}{2}\right)} \cdot \sin B} - \cos B \cdot \frac{1 \cdot x}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\sin B \cdot F + \left({\left(\frac{1}{{F}^{1}}\right)}^{1} \cdot \sin B\right) \cdot 1}{F}} - \frac{1 \cdot x}{\tan B}\\ \end{array}\]
\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 -2.016907704755291348515550104729865295568 \cdot 10^{99}:\\
\;\;\;\;\frac{1}{\sin B \cdot {\left(\frac{1}{{-1}^{1}}\right)}^{1}} - \frac{1 \cdot x}{\tan B}\\

\mathbf{elif}\;F \le 12308.79316332406233414076268672943115234:\\
\;\;\;\;\frac{F}{{\left(x \cdot 2 + \left(F \cdot F + 2\right)\right)}^{\left(\frac{1}{2}\right)} \cdot \sin B} - \cos B \cdot \frac{1 \cdot x}{\sin B}\\

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

\end{array}
double f(double F, double B, double x) {
        double r2481271 = x;
        double r2481272 = 1.0;
        double r2481273 = B;
        double r2481274 = tan(r2481273);
        double r2481275 = r2481272 / r2481274;
        double r2481276 = r2481271 * r2481275;
        double r2481277 = -r2481276;
        double r2481278 = F;
        double r2481279 = sin(r2481273);
        double r2481280 = r2481278 / r2481279;
        double r2481281 = r2481278 * r2481278;
        double r2481282 = 2.0;
        double r2481283 = r2481281 + r2481282;
        double r2481284 = r2481282 * r2481271;
        double r2481285 = r2481283 + r2481284;
        double r2481286 = r2481272 / r2481282;
        double r2481287 = -r2481286;
        double r2481288 = pow(r2481285, r2481287);
        double r2481289 = r2481280 * r2481288;
        double r2481290 = r2481277 + r2481289;
        return r2481290;
}
↓
double f(double F, double B, double x) {
        double r2481291 = F;
        double r2481292 = -2.0169077047552913e+99;
        bool r2481293 = r2481291 <= r2481292;
        double r2481294 = 1.0;
        double r2481295 = B;
        double r2481296 = sin(r2481295);
        double r2481297 = -1.0;
        double r2481298 = 1.0;
        double r2481299 = pow(r2481297, r2481298);
        double r2481300 = r2481294 / r2481299;
        double r2481301 = pow(r2481300, r2481298);
        double r2481302 = r2481296 * r2481301;
        double r2481303 = r2481294 / r2481302;
        double r2481304 = x;
        double r2481305 = r2481298 * r2481304;
        double r2481306 = tan(r2481295);
        double r2481307 = r2481305 / r2481306;
        double r2481308 = r2481303 - r2481307;
        double r2481309 = 12308.793163324062;
        bool r2481310 = r2481291 <= r2481309;
        double r2481311 = 2.0;
        double r2481312 = r2481304 * r2481311;
        double r2481313 = r2481291 * r2481291;
        double r2481314 = r2481313 + r2481311;
        double r2481315 = r2481312 + r2481314;
        double r2481316 = r2481298 / r2481311;
        double r2481317 = pow(r2481315, r2481316);
        double r2481318 = r2481317 * r2481296;
        double r2481319 = r2481291 / r2481318;
        double r2481320 = cos(r2481295);
        double r2481321 = r2481305 / r2481296;
        double r2481322 = r2481320 * r2481321;
        double r2481323 = r2481319 - r2481322;
        double r2481324 = r2481296 * r2481291;
        double r2481325 = pow(r2481291, r2481298);
        double r2481326 = r2481294 / r2481325;
        double r2481327 = pow(r2481326, r2481298);
        double r2481328 = r2481327 * r2481296;
        double r2481329 = r2481328 * r2481298;
        double r2481330 = r2481324 + r2481329;
        double r2481331 = r2481330 / r2481291;
        double r2481332 = r2481294 / r2481331;
        double r2481333 = r2481332 - r2481307;
        double r2481334 = r2481310 ? r2481323 : r2481333;
        double r2481335 = r2481293 ? r2481308 : r2481334;
        return r2481335;
}

Error

Bits error versus F

Bits error versus B

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if F < -2.0169077047552913e+99

    1. Initial program 33.0

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

    2. Simplified26.8

      \[\leadsto \color{blue}{\frac{F}{\frac{\sin B}{{\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{\left(-\frac{1}{2}\right)}}} - \frac{x \cdot 1}{\tan B}}\]
    3. Using strategy rm

    4. Applied pow-neg26.8

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

    5. Applied associate-/r/26.8

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

    6. Simplified26.8

      \[\leadsto \frac{F}{\color{blue}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{\left(\frac{1}{2}\right)}} - \frac{x \cdot 1}{\tan B}\]
    7. Using strategy rm

    8. Applied clear-num26.8

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

    9. Taylor expanded around -inf 0.2

      \[\leadsto \frac{1}{\color{blue}{\sin B \cdot {\left(\frac{1}{{-1}^{1}}\right)}^{1}}} - \frac{x \cdot 1}{\tan B}\]

    if -2.0169077047552913e+99 < F < 12308.793163324062

    1. Initial program 0.8

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

    2. Simplified0.3

      \[\leadsto \color{blue}{\frac{F}{\frac{\sin B}{{\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{\left(-\frac{1}{2}\right)}}} - \frac{x \cdot 1}{\tan B}}\]
    3. Using strategy rm

    4. Applied pow-neg0.3

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

    5. Applied associate-/r/0.3

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

    6. Simplified0.3

      \[\leadsto \frac{F}{\color{blue}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{\left(\frac{1}{2}\right)}} - \frac{x \cdot 1}{\tan B}\]
    7. Using strategy rm

    8. Applied tan-quot0.3

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

    9. Applied associate-/r/0.3

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

    if 12308.793163324062 < F

    1. Initial program 24.2

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

    2. Simplified18.2

      \[\leadsto \color{blue}{\frac{F}{\frac{\sin B}{{\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{\left(-\frac{1}{2}\right)}}} - \frac{x \cdot 1}{\tan B}}\]
    3. Using strategy rm

    4. Applied pow-neg18.2

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

    5. Applied associate-/r/18.2

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

    6. Simplified18.2

      \[\leadsto \frac{F}{\color{blue}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{\left(\frac{1}{2}\right)}} - \frac{x \cdot 1}{\tan B}\]
    7. Using strategy rm

    8. Applied clear-num18.1

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

    9. Taylor expanded around inf 0.2

      \[\leadsto \frac{1}{\frac{\color{blue}{F \cdot \sin B + 1 \cdot \left({\left(\frac{1}{{F}^{1}}\right)}^{1} \cdot \sin B\right)}}{F}} - \frac{x \cdot 1}{\tan B}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;F \le -2.016907704755291348515550104729865295568 \cdot 10^{99}:\\ \;\;\;\;\frac{1}{\sin B \cdot {\left(\frac{1}{{-1}^{1}}\right)}^{1}} - \frac{1 \cdot x}{\tan B}\\ \mathbf{elif}\;F \le 12308.79316332406233414076268672943115234:\\ \;\;\;\;\frac{F}{{\left(x \cdot 2 + \left(F \cdot F + 2\right)\right)}^{\left(\frac{1}{2}\right)} \cdot \sin B} - \cos B \cdot \frac{1 \cdot x}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\sin B \cdot F + \left({\left(\frac{1}{{F}^{1}}\right)}^{1} \cdot \sin B\right) \cdot 1}{F}} - \frac{1 \cdot x}{\tan B}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  (+ (- (* x (/ 1.0 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))