Average Error: 0.2 → 0.2
Time: 5.9s
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 r13983 = x;
        double r13984 = 1.0;
        double r13985 = B;
        double r13986 = tan(r13985);
        double r13987 = r13984 / r13986;
        double r13988 = r13983 * r13987;
        double r13989 = -r13988;
        double r13990 = sin(r13985);
        double r13991 = r13984 / r13990;
        double r13992 = r13989 + r13991;
        return r13992;
}
↓
double f(double B, double x) {
        double r13993 = x;
        double r13994 = 1.0;
        double r13995 = r13993 * r13994;
        double r13996 = B;
        double r13997 = sin(r13996);
        double r13998 = r13995 / r13997;
        double r13999 = cos(r13996);
        double r14000 = r13998 * r13999;
        double r14001 = -r14000;
        double r14002 = r13994 / r13997;
        double r14003 = r14001 + r14002;
        return r14003;
}

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/0.1

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  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 2019362 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))