Average Error: 0.2 → 0.2
Time: 5.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r13957 = x;
        double r13958 = 1.0;
        double r13959 = B;
        double r13960 = tan(r13959);
        double r13961 = r13958 / r13960;
        double r13962 = r13957 * r13961;
        double r13963 = -r13962;
        double r13964 = sin(r13959);
        double r13965 = r13958 / r13964;
        double r13966 = r13963 + r13965;
        return r13966;
}
↓
double f(double B, double x) {
        double r13967 = x;
        double r13968 = 1.0;
        double r13969 = r13967 * r13968;
        double r13970 = B;
        double r13971 = sin(r13970);
        double r13972 = r13969 / r13971;
        double r13973 = cos(r13970);
        double r13974 = r13972 * r13973;
        double r13975 = -r13974;
        double r13976 = r13968 / r13971;
        double r13977 = r13975 + r13976;
        return r13977;
}

Error

Bits error versus B

Bits error versus x

Try it out

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. Using strategy rm

  3. Applied associate-*r/0.2

    \[\leadsto \left(-\color{blue}{\frac{x \cdot 1}{\tan B}}\right) + \frac{1}{\sin B}\]
  4. Using strategy rm

  5. Applied tan-quot0.2

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

  6. Applied associate-/r/0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020056 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))