Average Error: 0.2 → 0.2
Time: 7.5s
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 r41316 = x;
        double r41317 = 1.0;
        double r41318 = B;
        double r41319 = tan(r41318);
        double r41320 = r41317 / r41319;
        double r41321 = r41316 * r41320;
        double r41322 = -r41321;
        double r41323 = sin(r41318);
        double r41324 = r41317 / r41323;
        double r41325 = r41322 + r41324;
        return r41325;
}
↓
double f(double B, double x) {
        double r41326 = 1.0;
        double r41327 = 1.0;
        double r41328 = x;
        double r41329 = B;
        double r41330 = cos(r41329);
        double r41331 = r41328 * r41330;
        double r41332 = r41327 - r41331;
        double r41333 = sin(r41329);
        double r41334 = r41332 / r41333;
        double r41335 = r41326 * r41334;
        return r41335;
}

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. Using strategy rm

  6. Applied sub-div0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019322 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))