Average Error: 0.2 → 0.2
Time: 22.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B
double f(double B, double x) {
        double r21952 = x;
        double r21953 = 1.0;
        double r21954 = B;
        double r21955 = tan(r21954);
        double r21956 = r21953 / r21955;
        double r21957 = r21952 * r21956;
        double r21958 = -r21957;
        double r21959 = sin(r21954);
        double r21960 = r21953 / r21959;
        double r21961 = r21958 + r21960;
        return r21961;
}
↓
double f(double B, double x) {
        double r21962 = 1.0;
        double r21963 = B;
        double r21964 = sin(r21963);
        double r21965 = r21962 / r21964;
        double r21966 = x;
        double r21967 = r21966 / r21964;
        double r21968 = r21962 * r21967;
        double r21969 = cos(r21963);
        double r21970 = r21968 * r21969;
        double r21971 = r21965 - r21970;
        return r21971;
}

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 tan-quot0.2

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

  5. Applied associate-/r/0.3

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

  6. Applied associate-*r*0.3

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))