Average Error: 0.2 → 0.2
Time: 4.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot 1}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r56501 = x;
        double r56502 = 1.0;
        double r56503 = B;
        double r56504 = tan(r56503);
        double r56505 = r56502 / r56504;
        double r56506 = r56501 * r56505;
        double r56507 = -r56506;
        double r56508 = sin(r56503);
        double r56509 = r56502 / r56508;
        double r56510 = r56507 + r56509;
        return r56510;
}
↓
double f(double B, double x) {
        double r56511 = 1.0;
        double r56512 = B;
        double r56513 = sin(r56512);
        double r56514 = r56511 / r56513;
        double r56515 = x;
        double r56516 = r56515 * r56511;
        double r56517 = r56516 / r56513;
        double r56518 = cos(r56512);
        double r56519 = r56517 * r56518;
        double r56520 = r56514 - r56519;
        return r56520;
}

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. Using strategy rm

  4. Applied associate-*r/0.2

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

  6. Applied tan-quot0.2

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

  7. Applied associate-/r/0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))