Average Error: 0.2 → 0.2
Time: 4.6s
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 r10271 = x;
        double r10272 = 1.0;
        double r10273 = B;
        double r10274 = tan(r10273);
        double r10275 = r10272 / r10274;
        double r10276 = r10271 * r10275;
        double r10277 = -r10276;
        double r10278 = sin(r10273);
        double r10279 = r10272 / r10278;
        double r10280 = r10277 + r10279;
        return r10280;
}
↓
double f(double B, double x) {
        double r10281 = 1.0;
        double r10282 = x;
        double r10283 = B;
        double r10284 = cos(r10283);
        double r10285 = r10282 * r10284;
        double r10286 = sin(r10283);
        double r10287 = r10285 / r10286;
        double r10288 = r10281 * r10287;
        double r10289 = -r10288;
        double r10290 = r10281 / r10286;
        double r10291 = r10289 + r10290;
        return r10291;
}

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 2020059 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))