Average Error: 0.2 → 0.2
Time: 4.7s
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 r32420 = x;
        double r32421 = 1.0;
        double r32422 = B;
        double r32423 = tan(r32422);
        double r32424 = r32421 / r32423;
        double r32425 = r32420 * r32424;
        double r32426 = -r32425;
        double r32427 = sin(r32422);
        double r32428 = r32421 / r32427;
        double r32429 = r32426 + r32428;
        return r32429;
}
↓
double f(double B, double x) {
        double r32430 = 1.0;
        double r32431 = 1.0;
        double r32432 = x;
        double r32433 = B;
        double r32434 = cos(r32433);
        double r32435 = r32432 * r32434;
        double r32436 = r32431 - r32435;
        double r32437 = sin(r32433);
        double r32438 = r32436 / r32437;
        double r32439 = r32430 * r32438;
        return r32439;
}

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 2020100 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))