Average Error: 0.2 → 0.2
Time: 4.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r9558 = x;
        double r9559 = 1.0;
        double r9560 = B;
        double r9561 = tan(r9560);
        double r9562 = r9559 / r9561;
        double r9563 = r9558 * r9562;
        double r9564 = -r9563;
        double r9565 = sin(r9560);
        double r9566 = r9559 / r9565;
        double r9567 = r9564 + r9566;
        return r9567;
}
↓
double f(double B, double x) {
        double r9568 = 1.0;
        double r9569 = B;
        double r9570 = sin(r9569);
        double r9571 = r9568 / r9570;
        double r9572 = x;
        double r9573 = cos(r9569);
        double r9574 = r9572 * r9573;
        double r9575 = r9574 / r9570;
        double r9576 = r9568 * r9575;
        double r9577 = r9571 - r9576;
        return r9577;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020059 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))