Average Error: 0.2 → 0.2
Time: 21.5s
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 r2430430 = x;
        double r2430431 = 1.0;
        double r2430432 = B;
        double r2430433 = tan(r2430432);
        double r2430434 = r2430431 / r2430433;
        double r2430435 = r2430430 * r2430434;
        double r2430436 = -r2430435;
        double r2430437 = sin(r2430432);
        double r2430438 = r2430431 / r2430437;
        double r2430439 = r2430436 + r2430438;
        return r2430439;
}
↓
double f(double B, double x) {
        double r2430440 = 1.0;
        double r2430441 = B;
        double r2430442 = sin(r2430441);
        double r2430443 = r2430440 / r2430442;
        double r2430444 = x;
        double r2430445 = r2430444 / r2430442;
        double r2430446 = cos(r2430441);
        double r2430447 = r2430445 * r2430446;
        double r2430448 = r2430443 - r2430447;
        return r2430448;
}

Error

Bits error versus B

Bits error versus x

Try it out

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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 2019164 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))