Average Error: 0.2 → 0.2
Time: 7.6m
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r8063172 = x;
        double r8063173 = 1.0;
        double r8063174 = B;
        double r8063175 = tan(r8063174);
        double r8063176 = r8063173 / r8063175;
        double r8063177 = r8063172 * r8063176;
        double r8063178 = -r8063177;
        double r8063179 = sin(r8063174);
        double r8063180 = r8063173 / r8063179;
        double r8063181 = r8063178 + r8063180;
        return r8063181;
}
↓
double f(double B, double x) {
        double r8063182 = 1.0;
        double r8063183 = B;
        double r8063184 = cos(r8063183);
        double r8063185 = x;
        double r8063186 = r8063184 * r8063185;
        double r8063187 = r8063182 - r8063186;
        double r8063188 = sin(r8063183);
        double r8063189 = r8063187 / r8063188;
        return r8063189;
}

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. Using strategy rm

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))