Average Error: 0.2 → 0.2
Time: 26.6s
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 r815382 = x;
        double r815383 = 1.0;
        double r815384 = B;
        double r815385 = tan(r815384);
        double r815386 = r815383 / r815385;
        double r815387 = r815382 * r815386;
        double r815388 = -r815387;
        double r815389 = sin(r815384);
        double r815390 = r815383 / r815389;
        double r815391 = r815388 + r815390;
        return r815391;
}
↓
double f(double B, double x) {
        double r815392 = 1.0;
        double r815393 = B;
        double r815394 = sin(r815393);
        double r815395 = r815392 / r815394;
        double r815396 = x;
        double r815397 = r815396 / r815394;
        double r815398 = cos(r815393);
        double r815399 = r815397 * r815398;
        double r815400 = r815395 - r815399;
        return r815400;
}

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))))