Average Error: 0.2 → 0.2
Time: 4.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r9383 = x;
        double r9384 = 1.0;
        double r9385 = B;
        double r9386 = tan(r9385);
        double r9387 = r9384 / r9386;
        double r9388 = r9383 * r9387;
        double r9389 = -r9388;
        double r9390 = sin(r9385);
        double r9391 = r9384 / r9390;
        double r9392 = r9389 + r9391;
        return r9392;
}
↓
double f(double B, double x) {
        double r9393 = 1.0;
        double r9394 = B;
        double r9395 = sin(r9394);
        double r9396 = r9393 / r9395;
        double r9397 = x;
        double r9398 = r9397 * r9393;
        double r9399 = r9398 / r9395;
        double r9400 = cos(r9394);
        double r9401 = r9399 * r9400;
        double r9402 = r9396 - r9401;
        return r9402;
}

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. Simplified0.2

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

  4. Applied associate-*r/0.2

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

  6. Applied tan-quot0.2

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

  7. Applied associate-/r/0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))