Average Error: 0.2 → 0.2
Time: 4.1m
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 r691558 = x;
        double r691559 = 1.0;
        double r691560 = B;
        double r691561 = tan(r691560);
        double r691562 = r691559 / r691561;
        double r691563 = r691558 * r691562;
        double r691564 = -r691563;
        double r691565 = sin(r691560);
        double r691566 = r691559 / r691565;
        double r691567 = r691564 + r691566;
        return r691567;
}
↓
double f(double B, double x) {
        double r691568 = 1.0;
        double r691569 = B;
        double r691570 = cos(r691569);
        double r691571 = x;
        double r691572 = r691570 * r691571;
        double r691573 = r691568 - r691572;
        double r691574 = sin(r691569);
        double r691575 = r691573 / r691574;
        return r691575;
}

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. Simplified0.1

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

  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 2019144 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))