Average Error: 0.2 → 0.2
Time: 5.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \left(x \cdot 1\right) \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \left(x \cdot 1\right) \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r12175 = x;
        double r12176 = 1.0;
        double r12177 = B;
        double r12178 = tan(r12177);
        double r12179 = r12176 / r12178;
        double r12180 = r12175 * r12179;
        double r12181 = -r12180;
        double r12182 = sin(r12177);
        double r12183 = r12176 / r12182;
        double r12184 = r12181 + r12183;
        return r12184;
}
↓
double f(double B, double x) {
        double r12185 = 1.0;
        double r12186 = x;
        double r12187 = r12186 * r12185;
        double r12188 = B;
        double r12189 = cos(r12188);
        double r12190 = r12187 * r12189;
        double r12191 = r12185 - r12190;
        double r12192 = sin(r12188);
        double r12193 = r12191 / r12192;
        return r12193;
}

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

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

  4. Applied associate-*r/0.2

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

  6. Applied tan-quot0.2

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

  7. Applied associate-/r/0.2

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

  9. Applied associate-*l/0.2

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

  10. Applied sub-div0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020035 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))