Average Error: 0.2 → 0.2
Time: 6.2s
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 r57524 = x;
        double r57525 = 1.0;
        double r57526 = B;
        double r57527 = tan(r57526);
        double r57528 = r57525 / r57527;
        double r57529 = r57524 * r57528;
        double r57530 = -r57529;
        double r57531 = sin(r57526);
        double r57532 = r57525 / r57531;
        double r57533 = r57530 + r57532;
        return r57533;
}
↓
double f(double B, double x) {
        double r57534 = 1.0;
        double r57535 = x;
        double r57536 = B;
        double r57537 = cos(r57536);
        double r57538 = r57535 * r57537;
        double r57539 = sin(r57536);
        double r57540 = r57538 / r57539;
        double r57541 = r57534 * r57540;
        double r57542 = -r57541;
        double r57543 = r57534 / r57539;
        double r57544 = r57542 + r57543;
        return r57544;
}

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 2020027 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))