Average Error: 0.2 → 0.2
Time: 23.6s
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 r897601 = x;
        double r897602 = 1.0;
        double r897603 = B;
        double r897604 = tan(r897603);
        double r897605 = r897602 / r897604;
        double r897606 = r897601 * r897605;
        double r897607 = -r897606;
        double r897608 = sin(r897603);
        double r897609 = r897602 / r897608;
        double r897610 = r897607 + r897609;
        return r897610;
}
↓
double f(double B, double x) {
        double r897611 = 1.0;
        double r897612 = B;
        double r897613 = sin(r897612);
        double r897614 = r897611 / r897613;
        double r897615 = x;
        double r897616 = r897615 / r897613;
        double r897617 = cos(r897612);
        double r897618 = r897616 * r897617;
        double r897619 = r897614 - r897618;
        return r897619;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  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. Final simplification0.2

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

Reproduce

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