Average Error: 0.2 → 0.2
Time: 33.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r1992217 = x;
        double r1992218 = 1.0;
        double r1992219 = B;
        double r1992220 = tan(r1992219);
        double r1992221 = r1992218 / r1992220;
        double r1992222 = r1992217 * r1992221;
        double r1992223 = -r1992222;
        double r1992224 = sin(r1992219);
        double r1992225 = r1992218 / r1992224;
        double r1992226 = r1992223 + r1992225;
        return r1992226;
}
↓
double f(double B, double x) {
        double r1992227 = 1.0;
        double r1992228 = B;
        double r1992229 = cos(r1992228);
        double r1992230 = x;
        double r1992231 = r1992229 * r1992230;
        double r1992232 = r1992227 - r1992231;
        double r1992233 = sin(r1992228);
        double r1992234 = r1992232 / r1992233;
        return r1992234;
}

Error

Bits error versus B

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.2

    \[\leadsto \frac{1}{\sin B} - \frac{\color{blue}{1 \cdot x}}{\tan B}\]

  5. Applied associate-/l*0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{1}{\frac{\tan B}{x}}}\]

  6. Taylor expanded around inf 0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x \cdot \cos B}{\sin B}}\]
  7. Using strategy rm

  8. Applied sub-div0.2

    \[\leadsto \color{blue}{\frac{1 - x \cdot \cos B}{\sin B}}\]

  9. Final simplification0.2

    \[\leadsto \frac{1 - \cos B \cdot x}{\sin B}\]

Reproduce

herbie shell --seed 2019120 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))