Average Error: 0.2 → 0.2
Time: 22.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r29025 = x;
        double r29026 = 1.0;
        double r29027 = B;
        double r29028 = tan(r29027);
        double r29029 = r29026 / r29028;
        double r29030 = r29025 * r29029;
        double r29031 = -r29030;
        double r29032 = sin(r29027);
        double r29033 = r29026 / r29032;
        double r29034 = r29031 + r29033;
        return r29034;
}
↓
double f(double B, double x) {
        double r29035 = 1.0;
        double r29036 = 1.0;
        double r29037 = B;
        double r29038 = sin(r29037);
        double r29039 = r29036 / r29038;
        double r29040 = x;
        double r29041 = cos(r29037);
        double r29042 = r29040 * r29041;
        double r29043 = r29042 / r29038;
        double r29044 = r29039 - r29043;
        double r29045 = r29035 * r29044;
        return r29045;
}

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. Taylor expanded around inf 0.2

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019304 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))