Average Error: 0.2 → 0.2
Time: 15.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \frac{1 - x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \frac{1 - x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r20036 = x;
        double r20037 = 1.0;
        double r20038 = B;
        double r20039 = tan(r20038);
        double r20040 = r20037 / r20039;
        double r20041 = r20036 * r20040;
        double r20042 = -r20041;
        double r20043 = sin(r20038);
        double r20044 = r20037 / r20043;
        double r20045 = r20042 + r20044;
        return r20045;
}
↓
double f(double B, double x) {
        double r20046 = 1.0;
        double r20047 = 1.0;
        double r20048 = x;
        double r20049 = B;
        double r20050 = cos(r20049);
        double r20051 = r20048 * r20050;
        double r20052 = r20047 - r20051;
        double r20053 = sin(r20049);
        double r20054 = r20052 / r20053;
        double r20055 = r20046 * r20054;
        return r20055;
}

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. Taylor expanded around inf 0.2

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

  3. Simplified0.2

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

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019305 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))