Average Error: 0.2 → 0.2
Time: 23.2s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r1746492 = x;
        double r1746493 = 1.0;
        double r1746494 = B;
        double r1746495 = tan(r1746494);
        double r1746496 = r1746493 / r1746495;
        double r1746497 = r1746492 * r1746496;
        double r1746498 = -r1746497;
        double r1746499 = sin(r1746494);
        double r1746500 = r1746493 / r1746499;
        double r1746501 = r1746498 + r1746500;
        return r1746501;
}
↓
double f(double B, double x) {
        double r1746502 = 1.0;
        double r1746503 = B;
        double r1746504 = sin(r1746503);
        double r1746505 = r1746502 / r1746504;
        double r1746506 = x;
        double r1746507 = r1746506 / r1746504;
        double r1746508 = cos(r1746503);
        double r1746509 = r1746507 * r1746508;
        double r1746510 = r1746505 - r1746509;
        return r1746510;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x}{\tan B}}\]
  3. Using strategy rm

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019163 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))