Average Error: 0.2 → 0.2
Time: 20.2s
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 r337164 = x;
        double r337165 = 1.0;
        double r337166 = B;
        double r337167 = tan(r337166);
        double r337168 = r337165 / r337167;
        double r337169 = r337164 * r337168;
        double r337170 = -r337169;
        double r337171 = sin(r337166);
        double r337172 = r337165 / r337171;
        double r337173 = r337170 + r337172;
        return r337173;
}
↓
double f(double B, double x) {
        double r337174 = 1.0;
        double r337175 = B;
        double r337176 = sin(r337175);
        double r337177 = r337174 / r337176;
        double r337178 = x;
        double r337179 = cos(r337175);
        double r337180 = r337178 * r337179;
        double r337181 = r337180 / r337176;
        double r337182 = r337177 - r337181;
        return r337182;
}

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))))