Average Error: 0.2 → 0.2
Time: 32.0s
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 r1623194 = x;
        double r1623195 = 1.0;
        double r1623196 = B;
        double r1623197 = tan(r1623196);
        double r1623198 = r1623195 / r1623197;
        double r1623199 = r1623194 * r1623198;
        double r1623200 = -r1623199;
        double r1623201 = sin(r1623196);
        double r1623202 = r1623195 / r1623201;
        double r1623203 = r1623200 + r1623202;
        return r1623203;
}
↓
double f(double B, double x) {
        double r1623204 = 1.0;
        double r1623205 = B;
        double r1623206 = cos(r1623205);
        double r1623207 = x;
        double r1623208 = r1623206 * r1623207;
        double r1623209 = r1623204 - r1623208;
        double r1623210 = sin(r1623205);
        double r1623211 = r1623209 / r1623210;
        return r1623211;
}

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 2019132 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))