Average Error: 0.2 → 0.2
Time: 19.4s
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 r37559 = x;
        double r37560 = 1.0;
        double r37561 = B;
        double r37562 = tan(r37561);
        double r37563 = r37560 / r37562;
        double r37564 = r37559 * r37563;
        double r37565 = -r37564;
        double r37566 = sin(r37561);
        double r37567 = r37560 / r37566;
        double r37568 = r37565 + r37567;
        return r37568;
}
↓
double f(double B, double x) {
        double r37569 = 1.0;
        double r37570 = x;
        double r37571 = r37569 * r37570;
        double r37572 = B;
        double r37573 = cos(r37572);
        double r37574 = r37571 * r37573;
        double r37575 = r37569 - r37574;
        double r37576 = sin(r37572);
        double r37577 = r37575 / r37576;
        return r37577;
}

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 2019303 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))