Average Error: 0.2 → 0.2
Time: 11.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r18278 = x;
        double r18279 = 1.0;
        double r18280 = B;
        double r18281 = tan(r18280);
        double r18282 = r18279 / r18281;
        double r18283 = r18278 * r18282;
        double r18284 = -r18283;
        double r18285 = sin(r18280);
        double r18286 = r18279 / r18285;
        double r18287 = r18284 + r18286;
        return r18287;
}
↓
double f(double B, double x) {
        double r18288 = 1.0;
        double r18289 = B;
        double r18290 = sin(r18289);
        double r18291 = r18288 / r18290;
        double r18292 = x;
        double r18293 = cos(r18289);
        double r18294 = r18292 * r18293;
        double r18295 = r18294 / r18290;
        double r18296 = r18288 * r18295;
        double r18297 = r18291 - r18296;
        return r18297;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}}\]
  3. Using strategy rm

  4. Applied associate-*r/0.1

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

  5. Taylor expanded around inf 0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))