Average Error: 0.2 → 0.2
Time: 25.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B
double f(double B, double x) {
        double r26687 = x;
        double r26688 = 1.0;
        double r26689 = B;
        double r26690 = tan(r26689);
        double r26691 = r26688 / r26690;
        double r26692 = r26687 * r26691;
        double r26693 = -r26692;
        double r26694 = sin(r26689);
        double r26695 = r26688 / r26694;
        double r26696 = r26693 + r26695;
        return r26696;
}
↓
double f(double B, double x) {
        double r26697 = 1.0;
        double r26698 = B;
        double r26699 = sin(r26698);
        double r26700 = r26697 / r26699;
        double r26701 = x;
        double r26702 = r26701 * r26700;
        double r26703 = cos(r26698);
        double r26704 = r26702 * r26703;
        double r26705 = r26700 - r26704;
        return r26705;
}

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 tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Applied associate-*r*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))