Average Error: 0.2 → 0.2
Time: 31.0s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r1909969 = x;
        double r1909970 = 1.0;
        double r1909971 = B;
        double r1909972 = tan(r1909971);
        double r1909973 = r1909970 / r1909972;
        double r1909974 = r1909969 * r1909973;
        double r1909975 = -r1909974;
        double r1909976 = sin(r1909971);
        double r1909977 = r1909970 / r1909976;
        double r1909978 = r1909975 + r1909977;
        return r1909978;
}
↓
double f(double B, double x) {
        double r1909979 = 1.0;
        double r1909980 = B;
        double r1909981 = cos(r1909980);
        double r1909982 = x;
        double r1909983 = r1909981 * r1909982;
        double r1909984 = r1909979 - r1909983;
        double r1909985 = sin(r1909980);
        double r1909986 = r1909984 / r1909985;
        return r1909986;
}

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. Simplified0.1

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

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  7. Applied *-un-lft-identity0.2

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

  8. Applied associate-/r*0.2

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

  9. Applied associate-*l/0.2

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

  10. Applied sub-div0.2

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))