Average Error: 0.2 → 0.2
Time: 4.1s
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 r56407 = x;
        double r56408 = 1.0;
        double r56409 = B;
        double r56410 = tan(r56409);
        double r56411 = r56408 / r56410;
        double r56412 = r56407 * r56411;
        double r56413 = -r56412;
        double r56414 = sin(r56409);
        double r56415 = r56408 / r56414;
        double r56416 = r56413 + r56415;
        return r56416;
}
↓
double f(double B, double x) {
        double r56417 = x;
        double r56418 = 1.0;
        double r56419 = r56417 * r56418;
        double r56420 = B;
        double r56421 = sin(r56420);
        double r56422 = r56419 / r56421;
        double r56423 = cos(r56420);
        double r56424 = r56422 * r56423;
        double r56425 = -r56424;
        double r56426 = r56418 / r56421;
        double r56427 = r56425 + r56426;
        return r56427;
}

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 2020062 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))