Average Error: 0.2 → 0.2
Time: 6.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r44534 = x;
        double r44535 = 1.0;
        double r44536 = B;
        double r44537 = tan(r44536);
        double r44538 = r44535 / r44537;
        double r44539 = r44534 * r44538;
        double r44540 = -r44539;
        double r44541 = sin(r44536);
        double r44542 = r44535 / r44541;
        double r44543 = r44540 + r44542;
        return r44543;
}
↓
double f(double B, double x) {
        double r44544 = x;
        double r44545 = 1.0;
        double r44546 = r44544 * r44545;
        double r44547 = B;
        double r44548 = sin(r44547);
        double r44549 = r44546 / r44548;
        double r44550 = cos(r44547);
        double r44551 = r44549 * r44550;
        double r44552 = -r44551;
        double r44553 = r44545 / r44548;
        double r44554 = r44552 + r44553;
        return r44554;
}

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 associate-*r/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  4. Using strategy rm

  5. Applied tan-quot0.2

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

  6. Applied associate-/r/0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020035 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))