Average Error: 0.2 → 0.2
Time: 5.5s
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 r12940 = x;
        double r12941 = 1.0;
        double r12942 = B;
        double r12943 = tan(r12942);
        double r12944 = r12941 / r12943;
        double r12945 = r12940 * r12944;
        double r12946 = -r12945;
        double r12947 = sin(r12942);
        double r12948 = r12941 / r12947;
        double r12949 = r12946 + r12948;
        return r12949;
}
↓
double f(double B, double x) {
        double r12950 = 1.0;
        double r12951 = x;
        double r12952 = r12951 * r12950;
        double r12953 = B;
        double r12954 = cos(r12953);
        double r12955 = r12952 * r12954;
        double r12956 = r12950 - r12955;
        double r12957 = sin(r12953);
        double r12958 = r12956 / r12957;
        return r12958;
}

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. Simplified0.2

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

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.3

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

  6. Applied associate-*r*0.2

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

  8. Applied associate-*r/0.2

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

  10. Applied associate-*l/0.2

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

  11. Applied sub-div0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020060 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))