Average Error: 0.2 → 0.2
Time: 56.9s
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 r412453 = x;
        double r412454 = 1.0;
        double r412455 = B;
        double r412456 = tan(r412455);
        double r412457 = r412454 / r412456;
        double r412458 = r412453 * r412457;
        double r412459 = -r412458;
        double r412460 = sin(r412455);
        double r412461 = r412454 / r412460;
        double r412462 = r412459 + r412461;
        return r412462;
}
↓
double f(double B, double x) {
        double r412463 = 1.0;
        double r412464 = B;
        double r412465 = sin(r412464);
        double r412466 = r412463 / r412465;
        double r412467 = x;
        double r412468 = r412467 / r412465;
        double r412469 = cos(r412464);
        double r412470 = r412468 * r412469;
        double r412471 = r412466 - r412470;
        return r412471;
}

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 2019152 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))