Average Error: 0.2 → 0.2
Time: 6.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r16435 = x;
        double r16436 = 1.0;
        double r16437 = B;
        double r16438 = tan(r16437);
        double r16439 = r16436 / r16438;
        double r16440 = r16435 * r16439;
        double r16441 = -r16440;
        double r16442 = sin(r16437);
        double r16443 = r16436 / r16442;
        double r16444 = r16441 + r16443;
        return r16444;
}
↓
double f(double B, double x) {
        double r16445 = 1.0;
        double r16446 = x;
        double r16447 = B;
        double r16448 = cos(r16447);
        double r16449 = r16446 * r16448;
        double r16450 = sin(r16447);
        double r16451 = r16449 / r16450;
        double r16452 = r16445 * r16451;
        double r16453 = -r16452;
        double r16454 = r16445 / r16450;
        double r16455 = r16453 + r16454;
        return r16455;
}

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. Taylor expanded around inf 0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))