Average Error: 0.2 → 0.2
Time: 5.7s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - x \cdot \frac{\cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - x \cdot \frac{\cos B}{\sin B}\right)
double f(double B, double x) {
        double r43402 = x;
        double r43403 = 1.0;
        double r43404 = B;
        double r43405 = tan(r43404);
        double r43406 = r43403 / r43405;
        double r43407 = r43402 * r43406;
        double r43408 = -r43407;
        double r43409 = sin(r43404);
        double r43410 = r43403 / r43409;
        double r43411 = r43408 + r43410;
        return r43411;
}
↓
double f(double B, double x) {
        double r43412 = 1.0;
        double r43413 = 1.0;
        double r43414 = B;
        double r43415 = sin(r43414);
        double r43416 = r43413 / r43415;
        double r43417 = x;
        double r43418 = cos(r43414);
        double r43419 = r43418 / r43415;
        double r43420 = r43417 * r43419;
        double r43421 = r43416 - r43420;
        double r43422 = r43412 * r43421;
        return r43422;
}

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

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

  4. Simplified0.2

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

  6. Applied *-un-lft-identity0.2

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

  7. Applied times-frac0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020020 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))