Average Error: 0.2 → 0.2
Time: 7.7m
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 r9213168 = x;
        double r9213169 = 1.0;
        double r9213170 = B;
        double r9213171 = tan(r9213170);
        double r9213172 = r9213169 / r9213171;
        double r9213173 = r9213168 * r9213172;
        double r9213174 = -r9213173;
        double r9213175 = sin(r9213170);
        double r9213176 = r9213169 / r9213175;
        double r9213177 = r9213174 + r9213176;
        return r9213177;
}
↓
double f(double B, double x) {
        double r9213178 = 1.0;
        double r9213179 = B;
        double r9213180 = cos(r9213179);
        double r9213181 = x;
        double r9213182 = r9213180 * r9213181;
        double r9213183 = r9213178 - r9213182;
        double r9213184 = sin(r9213179);
        double r9213185 = r9213183 / r9213184;
        return r9213185;
}

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

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