Average Error: 0.2 → 0.2
Time: 19.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \left(1 \cdot \frac{x}{\sin B}\right) \cdot \cos B
double f(double B, double x) {
        double r39622 = x;
        double r39623 = 1.0;
        double r39624 = B;
        double r39625 = tan(r39624);
        double r39626 = r39623 / r39625;
        double r39627 = r39622 * r39626;
        double r39628 = -r39627;
        double r39629 = sin(r39624);
        double r39630 = r39623 / r39629;
        double r39631 = r39628 + r39630;
        return r39631;
}
↓
double f(double B, double x) {
        double r39632 = 1.0;
        double r39633 = B;
        double r39634 = sin(r39633);
        double r39635 = r39632 / r39634;
        double r39636 = x;
        double r39637 = r39636 / r39634;
        double r39638 = r39632 * r39637;
        double r39639 = cos(r39633);
        double r39640 = r39638 * r39639;
        double r39641 = r39635 - r39640;
        return r39641;
}

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/0.3

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

  6. Applied associate-*r*0.3

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))