Average Error: 0.2 → 0.2
Time: 17.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r711226 = x;
        double r711227 = 1.0;
        double r711228 = B;
        double r711229 = tan(r711228);
        double r711230 = r711227 / r711229;
        double r711231 = r711226 * r711230;
        double r711232 = -r711231;
        double r711233 = sin(r711228);
        double r711234 = r711227 / r711233;
        double r711235 = r711232 + r711234;
        return r711235;
}
↓
double f(double B, double x) {
        double r711236 = 1.0;
        double r711237 = B;
        double r711238 = cos(r711237);
        double r711239 = x;
        double r711240 = r711238 * r711239;
        double r711241 = r711236 - r711240;
        double r711242 = sin(r711237);
        double r711243 = r711241 / r711242;
        return r711243;
}

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

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

  3. Taylor expanded around inf 0.2

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

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019154 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))