Average Error: 0.2 → 0.2
Time: 5.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - 1 \cdot \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r41436 = x;
        double r41437 = 1.0;
        double r41438 = B;
        double r41439 = tan(r41438);
        double r41440 = r41437 / r41439;
        double r41441 = r41436 * r41440;
        double r41442 = -r41441;
        double r41443 = sin(r41438);
        double r41444 = r41437 / r41443;
        double r41445 = r41442 + r41444;
        return r41445;
}
↓
double f(double B, double x) {
        double r41446 = 1.0;
        double r41447 = B;
        double r41448 = sin(r41447);
        double r41449 = r41446 / r41448;
        double r41450 = x;
        double r41451 = cos(r41447);
        double r41452 = r41450 * r41451;
        double r41453 = r41452 / r41448;
        double r41454 = r41446 * r41453;
        double r41455 = r41449 - r41454;
        return r41455;
}

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. Simplified0.2

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

  3. Taylor expanded around inf 0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))