Average Error: 0.2 → 0.2
Time: 16.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r60547 = x;
        double r60548 = 1.0;
        double r60549 = B;
        double r60550 = tan(r60549);
        double r60551 = r60548 / r60550;
        double r60552 = r60547 * r60551;
        double r60553 = -r60552;
        double r60554 = sin(r60549);
        double r60555 = r60548 / r60554;
        double r60556 = r60553 + r60555;
        return r60556;
}
↓
double f(double B, double x) {
        double r60557 = 1.0;
        double r60558 = 1.0;
        double r60559 = B;
        double r60560 = sin(r60559);
        double r60561 = r60558 / r60560;
        double r60562 = x;
        double r60563 = cos(r60559);
        double r60564 = r60562 * r60563;
        double r60565 = r60564 / r60560;
        double r60566 = r60561 - r60565;
        double r60567 = r60557 * r60566;
        return r60567;
}

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. Taylor expanded around inf 0.2

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))