Average Error: 0.2 → 0.2
Time: 23.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r22294 = x;
        double r22295 = 1.0;
        double r22296 = B;
        double r22297 = tan(r22296);
        double r22298 = r22295 / r22297;
        double r22299 = r22294 * r22298;
        double r22300 = -r22299;
        double r22301 = sin(r22296);
        double r22302 = r22295 / r22301;
        double r22303 = r22300 + r22302;
        return r22303;
}
↓
double f(double B, double x) {
        double r22304 = 1.0;
        double r22305 = x;
        double r22306 = B;
        double r22307 = cos(r22306);
        double r22308 = r22305 * r22307;
        double r22309 = sin(r22306);
        double r22310 = r22308 / r22309;
        double r22311 = r22304 * r22310;
        double r22312 = -r22311;
        double r22313 = r22304 / r22309;
        double r22314 = r22312 + r22313;
        return r22314;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))