Average Error: 0.2 → 0.2
Time: 20.6s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r767541 = x;
        double r767542 = 1.0;
        double r767543 = B;
        double r767544 = tan(r767543);
        double r767545 = r767542 / r767544;
        double r767546 = r767541 * r767545;
        double r767547 = -r767546;
        double r767548 = sin(r767543);
        double r767549 = r767542 / r767548;
        double r767550 = r767547 + r767549;
        return r767550;
}
↓
double f(double B, double x) {
        double r767551 = 1.0;
        double r767552 = B;
        double r767553 = cos(r767552);
        double r767554 = x;
        double r767555 = r767553 * r767554;
        double r767556 = r767551 - r767555;
        double r767557 = sin(r767552);
        double r767558 = r767556 / r767557;
        return r767558;
}

Error

Bits error versus B

Bits error versus x

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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

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

  3. Taylor expanded around -inf 0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}}\]
  4. Using strategy rm

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019153 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))