Average Error: 0.2 → 0.2
Time: 5.5s
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 r13946 = x;
        double r13947 = 1.0;
        double r13948 = B;
        double r13949 = tan(r13948);
        double r13950 = r13947 / r13949;
        double r13951 = r13946 * r13950;
        double r13952 = -r13951;
        double r13953 = sin(r13948);
        double r13954 = r13947 / r13953;
        double r13955 = r13952 + r13954;
        return r13955;
}
↓
double f(double B, double x) {
        double r13956 = x;
        double r13957 = 1.0;
        double r13958 = r13956 * r13957;
        double r13959 = B;
        double r13960 = sin(r13959);
        double r13961 = r13958 / r13960;
        double r13962 = cos(r13959);
        double r13963 = r13961 * r13962;
        double r13964 = -r13963;
        double r13965 = r13957 / r13960;
        double r13966 = r13964 + r13965;
        return r13966;
}

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))))