Average Error: 0.2 → 0.3
Time: 5.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r13510 = x;
        double r13511 = 1.0;
        double r13512 = B;
        double r13513 = tan(r13512);
        double r13514 = r13511 / r13513;
        double r13515 = r13510 * r13514;
        double r13516 = -r13515;
        double r13517 = sin(r13512);
        double r13518 = r13511 / r13517;
        double r13519 = r13516 + r13518;
        return r13519;
}
↓
double f(double B, double x) {
        double r13520 = x;
        double r13521 = 1.0;
        double r13522 = B;
        double r13523 = sin(r13522);
        double r13524 = r13521 / r13523;
        double r13525 = r13520 * r13524;
        double r13526 = cos(r13522);
        double r13527 = r13525 * r13526;
        double r13528 = -r13527;
        double r13529 = r13528 + r13524;
        return r13529;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019347 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))