Average Error: 0.2 → 0.3
Time: 20.0s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\frac{\sin B}{1 - \left(1 \cdot x\right) \cdot \cos B}}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\frac{\sin B}{1 - \left(1 \cdot x\right) \cdot \cos B}}
double f(double B, double x) {
        double r20280 = x;
        double r20281 = 1.0;
        double r20282 = B;
        double r20283 = tan(r20282);
        double r20284 = r20281 / r20283;
        double r20285 = r20280 * r20284;
        double r20286 = -r20285;
        double r20287 = sin(r20282);
        double r20288 = r20281 / r20287;
        double r20289 = r20286 + r20288;
        return r20289;
}
↓
double f(double B, double x) {
        double r20290 = 1.0;
        double r20291 = B;
        double r20292 = sin(r20291);
        double r20293 = 1.0;
        double r20294 = x;
        double r20295 = r20293 * r20294;
        double r20296 = cos(r20291);
        double r20297 = r20295 * r20296;
        double r20298 = r20293 - r20297;
        double r20299 = r20292 / r20298;
        double r20300 = r20290 / r20299;
        return r20300;
}

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 tan-quot0.3

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

  5. Applied associate-/r/0.3

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

  6. Applied associate-*r*0.3

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

  7. Simplified0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\left(1 \cdot \frac{x}{\sin B}\right)} \cdot \cos B\]
  8. Using strategy rm

  9. Applied associate-*r/0.2

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

  10. Applied associate-*l/0.2

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

  11. Applied sub-div0.2

    \[\leadsto \color{blue}{\frac{1 - \left(1 \cdot x\right) \cdot \cos B}{\sin B}}\]
  12. Using strategy rm

  13. Applied clear-num0.3

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

  14. Final simplification0.3

    \[\leadsto \frac{1}{\frac{\sin B}{1 - \left(1 \cdot x\right) \cdot \cos B}}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))