Average Error: 0.2 → 0.2
Time: 18.4s
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 r313928 = x;
        double r313929 = 1.0;
        double r313930 = B;
        double r313931 = tan(r313930);
        double r313932 = r313929 / r313931;
        double r313933 = r313928 * r313932;
        double r313934 = -r313933;
        double r313935 = sin(r313930);
        double r313936 = r313929 / r313935;
        double r313937 = r313934 + r313936;
        return r313937;
}
↓
double f(double B, double x) {
        double r313938 = 1.0;
        double r313939 = B;
        double r313940 = sin(r313939);
        double r313941 = r313938 / r313940;
        double r313942 = x;
        double r313943 = r313942 / r313940;
        double r313944 = cos(r313939);
        double r313945 = r313943 * r313944;
        double r313946 = r313941 - r313945;
        return r313946;
}

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 2019156 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))