Average Error: 0.2 → 0.2
Time: 18.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \left(x \cdot 1\right) \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \left(x \cdot 1\right) \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r39945 = x;
        double r39946 = 1.0;
        double r39947 = B;
        double r39948 = tan(r39947);
        double r39949 = r39946 / r39948;
        double r39950 = r39945 * r39949;
        double r39951 = -r39950;
        double r39952 = sin(r39947);
        double r39953 = r39946 / r39952;
        double r39954 = r39951 + r39953;
        return r39954;
}
↓
double f(double B, double x) {
        double r39955 = 1.0;
        double r39956 = x;
        double r39957 = r39956 * r39955;
        double r39958 = B;
        double r39959 = cos(r39958);
        double r39960 = r39957 * r39959;
        double r39961 = r39955 - r39960;
        double r39962 = sin(r39958);
        double r39963 = r39961 / r39962;
        return r39963;
}

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 associate-*r/0.1

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

  6. Applied tan-quot0.2

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

  7. Applied associate-/r/0.2

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

  9. Applied associate-*l/0.2

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

  10. Applied sub-div0.2

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

  11. Final simplification0.2

    \[\leadsto \frac{1 - \left(x \cdot 1\right) \cdot \cos B}{\sin B}\]

Reproduce

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