Average Error: 0.2 → 0.2
Time: 17.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r46629 = x;
        double r46630 = 1.0;
        double r46631 = B;
        double r46632 = tan(r46631);
        double r46633 = r46630 / r46632;
        double r46634 = r46629 * r46633;
        double r46635 = -r46634;
        double r46636 = sin(r46631);
        double r46637 = r46630 / r46636;
        double r46638 = r46635 + r46637;
        return r46638;
}
↓
double f(double B, double x) {
        double r46639 = 1.0;
        double r46640 = 1.0;
        double r46641 = B;
        double r46642 = sin(r46641);
        double r46643 = r46640 / r46642;
        double r46644 = x;
        double r46645 = cos(r46641);
        double r46646 = r46644 * r46645;
        double r46647 = r46646 / r46642;
        double r46648 = r46643 - r46647;
        double r46649 = r46639 * r46648;
        return r46649;
}

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

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))