Average Error: 0.2 → 0.2
Time: 16.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-1 \cdot \frac{x \cdot \cos B}{\sin B}\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r22445 = x;
        double r22446 = 1.0;
        double r22447 = B;
        double r22448 = tan(r22447);
        double r22449 = r22446 / r22448;
        double r22450 = r22445 * r22449;
        double r22451 = -r22450;
        double r22452 = sin(r22447);
        double r22453 = r22446 / r22452;
        double r22454 = r22451 + r22453;
        return r22454;
}
↓
double f(double B, double x) {
        double r22455 = 1.0;
        double r22456 = x;
        double r22457 = B;
        double r22458 = cos(r22457);
        double r22459 = r22456 * r22458;
        double r22460 = sin(r22457);
        double r22461 = r22459 / r22460;
        double r22462 = r22455 * r22461;
        double r22463 = -r22462;
        double r22464 = r22455 / r22460;
        double r22465 = r22463 + r22464;
        return r22465;
}

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. Taylor expanded around inf 0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))