Average Error: 0.2 → 0.2
Time: 20.2s
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 r64617 = x;
        double r64618 = 1.0;
        double r64619 = B;
        double r64620 = tan(r64619);
        double r64621 = r64618 / r64620;
        double r64622 = r64617 * r64621;
        double r64623 = -r64622;
        double r64624 = sin(r64619);
        double r64625 = r64618 / r64624;
        double r64626 = r64623 + r64625;
        return r64626;
}
↓
double f(double B, double x) {
        double r64627 = 1.0;
        double r64628 = B;
        double r64629 = sin(r64628);
        double r64630 = r64627 / r64629;
        double r64631 = x;
        double r64632 = r64631 * r64627;
        double r64633 = r64632 / r64629;
        double r64634 = cos(r64628);
        double r64635 = r64633 * r64634;
        double r64636 = r64630 - r64635;
        return r64636;
}

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/0.1

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{x \cdot 1}{\tan B}}\]
  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 2019323 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))