Average Error: 0.2 → 0.2
Time: 6.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r19323 = x;
        double r19324 = 1.0;
        double r19325 = B;
        double r19326 = tan(r19325);
        double r19327 = r19324 / r19326;
        double r19328 = r19323 * r19327;
        double r19329 = -r19328;
        double r19330 = sin(r19325);
        double r19331 = r19324 / r19330;
        double r19332 = r19329 + r19331;
        return r19332;
}
↓
double f(double B, double x) {
        double r19333 = x;
        double r19334 = 1.0;
        double r19335 = r19333 * r19334;
        double r19336 = B;
        double r19337 = sin(r19336);
        double r19338 = r19335 / r19337;
        double r19339 = cos(r19336);
        double r19340 = r19338 * r19339;
        double r19341 = -r19340;
        double r19342 = r19334 / r19337;
        double r19343 = r19341 + r19342;
        return r19343;
}

Error

Bits error versus B

Bits error versus x

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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. Using strategy rm

  3. Applied associate-*r/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  4. Using strategy rm

  5. Applied tan-quot0.2

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

  6. Applied associate-/r/0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020049 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))