Average Error: 0.2 → 0.2
Time: 19.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - 1 \cdot \left(x \cdot \cos B\right)}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - 1 \cdot \left(x \cdot \cos B\right)}{\sin B}
double f(double B, double x) {
        double r1385412 = x;
        double r1385413 = 1.0;
        double r1385414 = B;
        double r1385415 = tan(r1385414);
        double r1385416 = r1385413 / r1385415;
        double r1385417 = r1385412 * r1385416;
        double r1385418 = -r1385417;
        double r1385419 = sin(r1385414);
        double r1385420 = r1385413 / r1385419;
        double r1385421 = r1385418 + r1385420;
        return r1385421;
}
↓
double f(double B, double x) {
        double r1385422 = 1.0;
        double r1385423 = x;
        double r1385424 = B;
        double r1385425 = cos(r1385424);
        double r1385426 = r1385423 * r1385425;
        double r1385427 = r1385422 * r1385426;
        double r1385428 = r1385422 - r1385427;
        double r1385429 = sin(r1385424);
        double r1385430 = r1385428 / r1385429;
        return r1385430;
}

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. Using strategy rm

  5. Applied associate-*r/0.2

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

  6. Applied sub-div0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))