Average Error: 0.2 → 0.2
Time: 3.9m
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 r1838874 = x;
        double r1838875 = 1.0;
        double r1838876 = B;
        double r1838877 = tan(r1838876);
        double r1838878 = r1838875 / r1838877;
        double r1838879 = r1838874 * r1838878;
        double r1838880 = -r1838879;
        double r1838881 = sin(r1838876);
        double r1838882 = r1838875 / r1838881;
        double r1838883 = r1838880 + r1838882;
        return r1838883;
}
↓
double f(double B, double x) {
        double r1838884 = 1.0;
        double r1838885 = B;
        double r1838886 = cos(r1838885);
        double r1838887 = x;
        double r1838888 = r1838886 * r1838887;
        double r1838889 = r1838884 - r1838888;
        double r1838890 = sin(r1838885);
        double r1838891 = r1838889 / r1838890;
        return r1838891;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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 associate-*l/0.2

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

  8. Applied sub-div0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019151 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))