Average Error: 0.2 → 0.2
Time: 19.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r317412 = x;
        double r317413 = 1.0;
        double r317414 = B;
        double r317415 = tan(r317414);
        double r317416 = r317413 / r317415;
        double r317417 = r317412 * r317416;
        double r317418 = -r317417;
        double r317419 = sin(r317414);
        double r317420 = r317413 / r317419;
        double r317421 = r317418 + r317420;
        return r317421;
}
↓
double f(double B, double x) {
        double r317422 = 1.0;
        double r317423 = B;
        double r317424 = cos(r317423);
        double r317425 = x;
        double r317426 = r317424 * r317425;
        double r317427 = r317422 - r317426;
        double r317428 = sin(r317423);
        double r317429 = r317427 / r317428;
        return r317429;
}

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. Taylor expanded around inf 0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x \cdot \cos B}{\sin B}}\]
  4. Using strategy rm

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019153 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))