Average Error: 0.2 → 0.2
Time: 1.7m
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r1511860 = x;
        double r1511861 = 1.0;
        double r1511862 = B;
        double r1511863 = tan(r1511862);
        double r1511864 = r1511861 / r1511863;
        double r1511865 = r1511860 * r1511864;
        double r1511866 = -r1511865;
        double r1511867 = sin(r1511862);
        double r1511868 = r1511861 / r1511867;
        double r1511869 = r1511866 + r1511868;
        return r1511869;
}
↓
double f(double B, double x) {
        double r1511870 = 1.0;
        double r1511871 = B;
        double r1511872 = sin(r1511871);
        double r1511873 = r1511870 / r1511872;
        double r1511874 = x;
        double r1511875 = r1511874 / r1511872;
        double r1511876 = cos(r1511871);
        double r1511877 = r1511875 * r1511876;
        double r1511878 = r1511873 - r1511877;
        return r1511878;
}

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. Simplified0.2

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

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019143 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))