Average Error: 0.2 → 0.3
Time: 18.0s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r28522 = x;
        double r28523 = 1.0;
        double r28524 = B;
        double r28525 = tan(r28524);
        double r28526 = r28523 / r28525;
        double r28527 = r28522 * r28526;
        double r28528 = -r28527;
        double r28529 = sin(r28524);
        double r28530 = r28523 / r28529;
        double r28531 = r28528 + r28530;
        return r28531;
}
↓
double f(double B, double x) {
        double r28532 = x;
        double r28533 = 1.0;
        double r28534 = B;
        double r28535 = sin(r28534);
        double r28536 = r28533 / r28535;
        double r28537 = r28532 * r28536;
        double r28538 = cos(r28534);
        double r28539 = r28537 * r28538;
        double r28540 = -r28539;
        double r28541 = r28540 + r28536;
        return r28541;
}

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. Using strategy rm

  3. Applied tan-quot0.3

    \[\leadsto \left(-x \cdot \frac{1}{\color{blue}{\frac{\sin B}{\cos B}}}\right) + \frac{1}{\sin B}\]

  4. Applied associate-/r/0.3

    \[\leadsto \left(-x \cdot \color{blue}{\left(\frac{1}{\sin B} \cdot \cos B\right)}\right) + \frac{1}{\sin B}\]

  5. Applied associate-*r*0.3

    \[\leadsto \left(-\color{blue}{\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B}\right) + \frac{1}{\sin B}\]

  6. Final simplification0.3

    \[\leadsto \left(-\left(x \cdot \frac{1}{\sin B}\right) \cdot \cos B\right) + \frac{1}{\sin B}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))