Average Error: 0.2 → 0.2
Time: 20.1s
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 r1793610 = x;
        double r1793611 = 1.0;
        double r1793612 = B;
        double r1793613 = tan(r1793612);
        double r1793614 = r1793611 / r1793613;
        double r1793615 = r1793610 * r1793614;
        double r1793616 = -r1793615;
        double r1793617 = sin(r1793612);
        double r1793618 = r1793611 / r1793617;
        double r1793619 = r1793616 + r1793618;
        return r1793619;
}
↓
double f(double B, double x) {
        double r1793620 = 1.0;
        double r1793621 = B;
        double r1793622 = sin(r1793621);
        double r1793623 = r1793620 / r1793622;
        double r1793624 = x;
        double r1793625 = r1793624 / r1793622;
        double r1793626 = cos(r1793621);
        double r1793627 = r1793625 * r1793626;
        double r1793628 = r1793623 - r1793627;
        return r1793628;
}

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 2019135 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))