Average Error: 0.2 → 0.2
Time: 5.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x}{\frac{\sin B}{\cos B}}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x}{\frac{\sin B}{\cos B}}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r18233 = x;
        double r18234 = 1.0;
        double r18235 = B;
        double r18236 = tan(r18235);
        double r18237 = r18234 / r18236;
        double r18238 = r18233 * r18237;
        double r18239 = -r18238;
        double r18240 = sin(r18235);
        double r18241 = r18234 / r18240;
        double r18242 = r18239 + r18241;
        return r18242;
}
↓
double f(double B, double x) {
        double r18243 = 1.0;
        double r18244 = x;
        double r18245 = B;
        double r18246 = sin(r18245);
        double r18247 = cos(r18245);
        double r18248 = r18246 / r18247;
        double r18249 = r18244 / r18248;
        double r18250 = r18243 * r18249;
        double r18251 = -r18250;
        double r18252 = r18243 / r18246;
        double r18253 = r18251 + r18252;
        return r18253;
}

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. Using strategy rm

  4. Applied associate-/l*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020065 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))