Average Error: 0.2 → 0.2
Time: 40.7s
Precision: 64
\[\left(-x \cdot \frac{1.0}{\tan B}\right) + \frac{1.0}{\sin B}\]
↓
\[\frac{1.0}{\sin B} - \cos B \cdot \frac{x \cdot 1.0}{\sin B}\]
\left(-x \cdot \frac{1.0}{\tan B}\right) + \frac{1.0}{\sin B}
↓
\frac{1.0}{\sin B} - \cos B \cdot \frac{x \cdot 1.0}{\sin B}
double f(double B, double x) {
        double r1953234 = x;
        double r1953235 = 1.0;
        double r1953236 = B;
        double r1953237 = tan(r1953236);
        double r1953238 = r1953235 / r1953237;
        double r1953239 = r1953234 * r1953238;
        double r1953240 = -r1953239;
        double r1953241 = sin(r1953236);
        double r1953242 = r1953235 / r1953241;
        double r1953243 = r1953240 + r1953242;
        return r1953243;
}
↓
double f(double B, double x) {
        double r1953244 = 1.0;
        double r1953245 = B;
        double r1953246 = sin(r1953245);
        double r1953247 = r1953244 / r1953246;
        double r1953248 = cos(r1953245);
        double r1953249 = x;
        double r1953250 = r1953249 * r1953244;
        double r1953251 = r1953250 / r1953246;
        double r1953252 = r1953248 * r1953251;
        double r1953253 = r1953247 - r1953252;
        return r1953253;
}

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

    \[\left(-x \cdot \frac{1.0}{\tan B}\right) + \frac{1.0}{\sin B}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{1.0}{\sin B} - \frac{x \cdot 1.0}{\tan B}}\]
  3. Using strategy rm

  4. Applied tan-quot0.2

    \[\leadsto \frac{1.0}{\sin B} - \frac{x \cdot 1.0}{\color{blue}{\frac{\sin B}{\cos B}}}\]

  5. Applied associate-/r/0.2

    \[\leadsto \frac{1.0}{\sin B} - \color{blue}{\frac{x \cdot 1.0}{\sin B} \cdot \cos B}\]

  6. Final simplification0.2

    \[\leadsto \frac{1.0}{\sin B} - \cos B \cdot \frac{x \cdot 1.0}{\sin B}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))