Average Error: 0.2 → 0.2
Time: 22.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{\cos B}{\sin B} \cdot x\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{\cos B}{\sin B} \cdot x
double f(double B, double x) {
        double r2242830 = x;
        double r2242831 = 1.0;
        double r2242832 = B;
        double r2242833 = tan(r2242832);
        double r2242834 = r2242831 / r2242833;
        double r2242835 = r2242830 * r2242834;
        double r2242836 = -r2242835;
        double r2242837 = sin(r2242832);
        double r2242838 = r2242831 / r2242837;
        double r2242839 = r2242836 + r2242838;
        return r2242839;
}
↓
double f(double B, double x) {
        double r2242840 = 1.0;
        double r2242841 = B;
        double r2242842 = sin(r2242841);
        double r2242843 = r2242840 / r2242842;
        double r2242844 = cos(r2242841);
        double r2242845 = r2242844 / r2242842;
        double r2242846 = x;
        double r2242847 = r2242845 * r2242846;
        double r2242848 = r2242843 - r2242847;
        return r2242848;
}

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. Taylor expanded around inf 0.2

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

  5. Applied *-un-lft-identity0.2

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

  6. Applied times-frac0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))