Average Error: 0.2 → 0.2
Time: 8.4m
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 r17742904 = x;
        double r17742905 = 1.0;
        double r17742906 = B;
        double r17742907 = tan(r17742906);
        double r17742908 = r17742905 / r17742907;
        double r17742909 = r17742904 * r17742908;
        double r17742910 = -r17742909;
        double r17742911 = sin(r17742906);
        double r17742912 = r17742905 / r17742911;
        double r17742913 = r17742910 + r17742912;
        return r17742913;
}
↓
double f(double B, double x) {
        double r17742914 = 1.0;
        double r17742915 = B;
        double r17742916 = sin(r17742915);
        double r17742917 = r17742914 / r17742916;
        double r17742918 = x;
        double r17742919 = cos(r17742915);
        double r17742920 = r17742918 * r17742919;
        double r17742921 = r17742920 / r17742916;
        double r17742922 = r17742917 - r17742921;
        return r17742922;
}

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. Simplified0.1

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

  3. Taylor expanded around -inf 0.2

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

  4. Taylor expanded around -inf 0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))