Average Error: 0.2 → 0.2
Time: 24.5s
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 r815385 = x;
        double r815386 = 1.0;
        double r815387 = B;
        double r815388 = tan(r815387);
        double r815389 = r815386 / r815388;
        double r815390 = r815385 * r815389;
        double r815391 = -r815390;
        double r815392 = sin(r815387);
        double r815393 = r815386 / r815392;
        double r815394 = r815391 + r815393;
        return r815394;
}
↓
double f(double B, double x) {
        double r815395 = 1.0;
        double r815396 = B;
        double r815397 = sin(r815396);
        double r815398 = r815395 / r815397;
        double r815399 = x;
        double r815400 = r815399 / r815397;
        double r815401 = cos(r815396);
        double r815402 = r815400 * r815401;
        double r815403 = r815398 - r815402;
        return r815403;
}

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 2019163 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))