Average Error: 0.2 → 0.2
Time: 5.8s
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 r13414 = x;
        double r13415 = 1.0;
        double r13416 = B;
        double r13417 = tan(r13416);
        double r13418 = r13415 / r13417;
        double r13419 = r13414 * r13418;
        double r13420 = -r13419;
        double r13421 = sin(r13416);
        double r13422 = r13415 / r13421;
        double r13423 = r13420 + r13422;
        return r13423;
}
↓
double f(double B, double x) {
        double r13424 = 1.0;
        double r13425 = 1.0;
        double r13426 = B;
        double r13427 = sin(r13426);
        double r13428 = r13425 / r13427;
        double r13429 = x;
        double r13430 = cos(r13426);
        double r13431 = r13429 * r13430;
        double r13432 = r13431 / r13427;
        double r13433 = r13428 - r13432;
        double r13434 = r13424 * r13433;
        return r13434;
}

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 2020001 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))