Average Error: 0.2 → 0.2
Time: 23.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r747614 = x;
        double r747615 = 1.0;
        double r747616 = B;
        double r747617 = tan(r747616);
        double r747618 = r747615 / r747617;
        double r747619 = r747614 * r747618;
        double r747620 = -r747619;
        double r747621 = sin(r747616);
        double r747622 = r747615 / r747621;
        double r747623 = r747620 + r747622;
        return r747623;
}
↓
double f(double B, double x) {
        double r747624 = 1.0;
        double r747625 = B;
        double r747626 = sin(r747625);
        double r747627 = r747624 / r747626;
        double r747628 = x;
        double r747629 = r747628 / r747626;
        double r747630 = cos(r747625);
        double r747631 = r747629 * r747630;
        double r747632 = r747627 - r747631;
        return r747632;
}

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. Simplified0.1

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

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019164 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))