Average Error: 0.2 → 0.2
Time: 25.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r24752 = x;
        double r24753 = 1.0;
        double r24754 = B;
        double r24755 = tan(r24754);
        double r24756 = r24753 / r24755;
        double r24757 = r24752 * r24756;
        double r24758 = -r24757;
        double r24759 = sin(r24754);
        double r24760 = r24753 / r24759;
        double r24761 = r24758 + r24760;
        return r24761;
}
↓
double f(double B, double x) {
        double r24762 = 1.0;
        double r24763 = x;
        double r24764 = B;
        double r24765 = sin(r24764);
        double r24766 = r24763 / r24765;
        double r24767 = r24762 * r24766;
        double r24768 = cos(r24764);
        double r24769 = r24767 * r24768;
        double r24770 = -r24769;
        double r24771 = r24762 / r24765;
        double r24772 = r24770 + r24771;
        return r24772;
}

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. Using strategy rm

  3. Applied tan-quot0.2

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

  4. Applied associate-/r/0.2

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

  5. Applied associate-*r*0.3

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019306 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))