Average Error: 0.2 → 0.2
Time: 11.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \left(1 \cdot x\right) \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \left(1 \cdot x\right) \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r12440 = x;
        double r12441 = 1.0;
        double r12442 = B;
        double r12443 = tan(r12442);
        double r12444 = r12441 / r12443;
        double r12445 = r12440 * r12444;
        double r12446 = -r12445;
        double r12447 = sin(r12442);
        double r12448 = r12441 / r12447;
        double r12449 = r12446 + r12448;
        return r12449;
}
↓
double f(double B, double x) {
        double r12450 = 1.0;
        double r12451 = x;
        double r12452 = r12450 * r12451;
        double r12453 = B;
        double r12454 = cos(r12453);
        double r12455 = r12452 * r12454;
        double r12456 = r12450 - r12455;
        double r12457 = sin(r12453);
        double r12458 = r12456 / r12457;
        return r12458;
}

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

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

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Applied associate-*r*0.2

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019350 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))