Average Error: 0.2 → 0.2
Time: 18.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-x \cdot \left(1 \cdot \frac{\cos B}{\sin B}\right)\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-x \cdot \left(1 \cdot \frac{\cos B}{\sin B}\right)\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r41279 = x;
        double r41280 = 1.0;
        double r41281 = B;
        double r41282 = tan(r41281);
        double r41283 = r41280 / r41282;
        double r41284 = r41279 * r41283;
        double r41285 = -r41284;
        double r41286 = sin(r41281);
        double r41287 = r41280 / r41286;
        double r41288 = r41285 + r41287;
        return r41288;
}
↓
double f(double B, double x) {
        double r41289 = x;
        double r41290 = 1.0;
        double r41291 = B;
        double r41292 = cos(r41291);
        double r41293 = sin(r41291);
        double r41294 = r41292 / r41293;
        double r41295 = r41290 * r41294;
        double r41296 = r41289 * r41295;
        double r41297 = -r41296;
        double r41298 = r41290 / r41293;
        double r41299 = r41297 + r41298;
        return r41299;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))