Average Error: 0.2 → 0.2
Time: 19.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \cos B \cdot \frac{x \cdot 1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \cos B \cdot \frac{x \cdot 1}{\sin B}
double f(double B, double x) {
        double r1815597 = x;
        double r1815598 = 1.0;
        double r1815599 = B;
        double r1815600 = tan(r1815599);
        double r1815601 = r1815598 / r1815600;
        double r1815602 = r1815597 * r1815601;
        double r1815603 = -r1815602;
        double r1815604 = sin(r1815599);
        double r1815605 = r1815598 / r1815604;
        double r1815606 = r1815603 + r1815605;
        return r1815606;
}
↓
double f(double B, double x) {
        double r1815607 = 1.0;
        double r1815608 = B;
        double r1815609 = sin(r1815608);
        double r1815610 = r1815607 / r1815609;
        double r1815611 = cos(r1815608);
        double r1815612 = x;
        double r1815613 = r1815612 * r1815607;
        double r1815614 = r1815613 / r1815609;
        double r1815615 = r1815611 * r1815614;
        double r1815616 = r1815610 - r1815615;
        return r1815616;
}

Error

Bits error versus B

Bits error versus x

Try it out

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x \cdot 1}{\tan B}}\]
  3. Using strategy rm

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))