Average Error: 0.2 → 0.2
Time: 21.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B
double f(double B, double x) {
        double r22297 = x;
        double r22298 = 1.0;
        double r22299 = B;
        double r22300 = tan(r22299);
        double r22301 = r22298 / r22300;
        double r22302 = r22297 * r22301;
        double r22303 = -r22302;
        double r22304 = sin(r22299);
        double r22305 = r22298 / r22304;
        double r22306 = r22303 + r22305;
        return r22306;
}
↓
double f(double B, double x) {
        double r22307 = 1.0;
        double r22308 = B;
        double r22309 = sin(r22308);
        double r22310 = r22307 / r22309;
        double r22311 = x;
        double r22312 = r22311 / r22309;
        double r22313 = r22307 * r22312;
        double r22314 = cos(r22308);
        double r22315 = r22313 * r22314;
        double r22316 = r22310 - r22315;
        return r22316;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}}\]
  3. Using strategy rm

  4. Applied tan-quot0.2

    \[\leadsto \frac{1}{\sin B} - x \cdot \frac{1}{\color{blue}{\frac{\sin B}{\cos B}}}\]

  5. Applied associate-/r/0.3

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

  6. Applied associate-*r*0.3

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))