Average Error: 0.2 → 0.2
Time: 18.3s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r781327 = x;
        double r781328 = 1.0;
        double r781329 = B;
        double r781330 = tan(r781329);
        double r781331 = r781328 / r781330;
        double r781332 = r781327 * r781331;
        double r781333 = -r781332;
        double r781334 = sin(r781329);
        double r781335 = r781328 / r781334;
        double r781336 = r781333 + r781335;
        return r781336;
}
↓
double f(double B, double x) {
        double r781337 = 1.0;
        double r781338 = B;
        double r781339 = sin(r781338);
        double r781340 = r781337 / r781339;
        double r781341 = x;
        double r781342 = cos(r781338);
        double r781343 = r781341 * r781342;
        double r781344 = r781343 / r781339;
        double r781345 = r781340 - r781344;
        return r781345;
}

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

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

  3. Taylor expanded around inf 0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))