Average Error: 0.2 → 0.2
Time: 5.2m
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 r1442236 = x;
        double r1442237 = 1.0;
        double r1442238 = B;
        double r1442239 = tan(r1442238);
        double r1442240 = r1442237 / r1442239;
        double r1442241 = r1442236 * r1442240;
        double r1442242 = -r1442241;
        double r1442243 = sin(r1442238);
        double r1442244 = r1442237 / r1442243;
        double r1442245 = r1442242 + r1442244;
        return r1442245;
}
↓
double f(double B, double x) {
        double r1442246 = 1.0;
        double r1442247 = B;
        double r1442248 = sin(r1442247);
        double r1442249 = r1442246 / r1442248;
        double r1442250 = x;
        double r1442251 = r1442250 / r1442248;
        double r1442252 = cos(r1442247);
        double r1442253 = r1442251 * r1442252;
        double r1442254 = r1442249 - r1442253;
        return r1442254;
}

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 2019149 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))