Average Error: 0.2 → 0.2
Time: 5.3m
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r735974 = x;
        double r735975 = 1.0;
        double r735976 = B;
        double r735977 = tan(r735976);
        double r735978 = r735975 / r735977;
        double r735979 = r735974 * r735978;
        double r735980 = -r735979;
        double r735981 = sin(r735976);
        double r735982 = r735975 / r735981;
        double r735983 = r735980 + r735982;
        return r735983;
}
↓
double f(double B, double x) {
        double r735984 = 1.0;
        double r735985 = B;
        double r735986 = sin(r735985);
        double r735987 = r735984 / r735986;
        double r735988 = x;
        double r735989 = r735988 / r735986;
        double r735990 = cos(r735985);
        double r735991 = r735989 * r735990;
        double r735992 = r735987 - r735991;
        return r735992;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019149 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))