Average Error: 0.2 → 0.2
Time: 22.0s
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 r2411275 = x;
        double r2411276 = 1.0;
        double r2411277 = B;
        double r2411278 = tan(r2411277);
        double r2411279 = r2411276 / r2411278;
        double r2411280 = r2411275 * r2411279;
        double r2411281 = -r2411280;
        double r2411282 = sin(r2411277);
        double r2411283 = r2411276 / r2411282;
        double r2411284 = r2411281 + r2411283;
        return r2411284;
}
↓
double f(double B, double x) {
        double r2411285 = 1.0;
        double r2411286 = B;
        double r2411287 = cos(r2411286);
        double r2411288 = x;
        double r2411289 = r2411287 * r2411288;
        double r2411290 = r2411285 - r2411289;
        double r2411291 = sin(r2411286);
        double r2411292 = r2411290 / r2411291;
        return r2411292;
}

Error

Bits error versus B

Bits error versus x

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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 2019162 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))