Average Error: 0.2 → 0.2
Time: 13.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r46585 = x;
        double r46586 = 1.0;
        double r46587 = B;
        double r46588 = tan(r46587);
        double r46589 = r46586 / r46588;
        double r46590 = r46585 * r46589;
        double r46591 = -r46590;
        double r46592 = sin(r46587);
        double r46593 = r46586 / r46592;
        double r46594 = r46591 + r46593;
        return r46594;
}
↓
double f(double B, double x) {
        double r46595 = x;
        double r46596 = 1.0;
        double r46597 = r46595 * r46596;
        double r46598 = B;
        double r46599 = sin(r46598);
        double r46600 = r46597 / r46599;
        double r46601 = cos(r46598);
        double r46602 = r46600 * r46601;
        double r46603 = -r46602;
        double r46604 = r46596 / r46599;
        double r46605 = r46603 + r46604;
        return r46605;
}

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. Using strategy rm

  3. Applied associate-*r/0.1

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  4. Using strategy rm

  5. Applied tan-quot0.2

    \[\leadsto \left(-\frac{x \cdot 1}{\color{blue}{\frac{\sin B}{\cos B}}}\right) + \frac{1}{\sin B}\]

  6. Applied associate-/r/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\sin B} \cdot \cos B}\right) + \frac{1}{\sin B}\]

  7. Final simplification0.2

    \[\leadsto \left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))