Average Error: 0.2 → 0.2
Time: 18.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - 1 \cdot \left(x \cdot \cos B\right)}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - 1 \cdot \left(x \cdot \cos B\right)}{\sin B}
double f(double B, double x) {
        double r2815433 = x;
        double r2815434 = 1.0;
        double r2815435 = B;
        double r2815436 = tan(r2815435);
        double r2815437 = r2815434 / r2815436;
        double r2815438 = r2815433 * r2815437;
        double r2815439 = -r2815438;
        double r2815440 = sin(r2815435);
        double r2815441 = r2815434 / r2815440;
        double r2815442 = r2815439 + r2815441;
        return r2815442;
}
↓
double f(double B, double x) {
        double r2815443 = 1.0;
        double r2815444 = x;
        double r2815445 = B;
        double r2815446 = cos(r2815445);
        double r2815447 = r2815444 * r2815446;
        double r2815448 = r2815443 * r2815447;
        double r2815449 = r2815443 - r2815448;
        double r2815450 = sin(r2815445);
        double r2815451 = r2815449 / r2815450;
        return r2815451;
}

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. Taylor expanded around inf 0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{1 \cdot \frac{x \cdot \cos B}{\sin B}}\]
  4. Using strategy rm

  5. Applied associate-*r/0.2

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

  6. Applied sub-div0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))