Average Error: 0.2 → 0.2
Time: 16.8s
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 r804257 = x;
        double r804258 = 1.0;
        double r804259 = B;
        double r804260 = tan(r804259);
        double r804261 = r804258 / r804260;
        double r804262 = r804257 * r804261;
        double r804263 = -r804262;
        double r804264 = sin(r804259);
        double r804265 = r804258 / r804264;
        double r804266 = r804263 + r804265;
        return r804266;
}
↓
double f(double B, double x) {
        double r804267 = 1.0;
        double r804268 = B;
        double r804269 = sin(r804268);
        double r804270 = r804267 / r804269;
        double r804271 = x;
        double r804272 = r804271 / r804269;
        double r804273 = cos(r804268);
        double r804274 = r804272 * r804273;
        double r804275 = r804270 - r804274;
        return r804275;
}

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 2019156 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))