Average Error: 0.2 → 0.2
Time: 6.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r48500 = x;
        double r48501 = 1.0;
        double r48502 = B;
        double r48503 = tan(r48502);
        double r48504 = r48501 / r48503;
        double r48505 = r48500 * r48504;
        double r48506 = -r48505;
        double r48507 = sin(r48502);
        double r48508 = r48501 / r48507;
        double r48509 = r48506 + r48508;
        return r48509;
}
↓
double f(double B, double x) {
        double r48510 = x;
        double r48511 = 1.0;
        double r48512 = B;
        double r48513 = sin(r48512);
        double r48514 = r48511 / r48513;
        double r48515 = cos(r48512);
        double r48516 = r48514 * r48515;
        double r48517 = r48510 * r48516;
        double r48518 = -r48517;
        double r48519 = r48518 + r48514;
        return r48519;
}

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-quot0.2

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

  4. Applied associate-/r/0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020083 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))