Average Error: 0.2 → 0.2
Time: 28.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r435993 = x;
        double r435994 = 1.0;
        double r435995 = B;
        double r435996 = tan(r435995);
        double r435997 = r435994 / r435996;
        double r435998 = r435993 * r435997;
        double r435999 = -r435998;
        double r436000 = sin(r435995);
        double r436001 = r435994 / r436000;
        double r436002 = r435999 + r436001;
        return r436002;
}
↓
double f(double B, double x) {
        double r436003 = 1.0;
        double r436004 = B;
        double r436005 = cos(r436004);
        double r436006 = x;
        double r436007 = r436005 * r436006;
        double r436008 = r436003 - r436007;
        double r436009 = sin(r436004);
        double r436010 = r436008 / r436009;
        return r436010;
}

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

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

  7. Applied associate-*l/0.2

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

  8. Applied sub-div0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))