Average Error: 0.2 → 0.2
Time: 29.4s
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 r312198 = x;
        double r312199 = 1.0;
        double r312200 = B;
        double r312201 = tan(r312200);
        double r312202 = r312199 / r312201;
        double r312203 = r312198 * r312202;
        double r312204 = -r312203;
        double r312205 = sin(r312200);
        double r312206 = r312199 / r312205;
        double r312207 = r312204 + r312206;
        return r312207;
}
↓
double f(double B, double x) {
        double r312208 = 1.0;
        double r312209 = B;
        double r312210 = sin(r312209);
        double r312211 = r312208 / r312210;
        double r312212 = x;
        double r312213 = cos(r312209);
        double r312214 = r312212 * r312213;
        double r312215 = r312214 / r312210;
        double r312216 = r312211 - r312215;
        return r312216;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))