Average Error: 0.2 → 0.3
Time: 19.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-x \cdot \left(\frac{1}{\sin B} \cdot \cos B\right)\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r23360 = x;
        double r23361 = 1.0;
        double r23362 = B;
        double r23363 = tan(r23362);
        double r23364 = r23361 / r23363;
        double r23365 = r23360 * r23364;
        double r23366 = -r23365;
        double r23367 = sin(r23362);
        double r23368 = r23361 / r23367;
        double r23369 = r23366 + r23368;
        return r23369;
}
↓
double f(double B, double x) {
        double r23370 = x;
        double r23371 = 1.0;
        double r23372 = B;
        double r23373 = sin(r23372);
        double r23374 = r23371 / r23373;
        double r23375 = cos(r23372);
        double r23376 = r23374 * r23375;
        double r23377 = r23370 * r23376;
        double r23378 = -r23377;
        double r23379 = r23378 + r23374;
        return r23379;
}

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. Using strategy rm

  3. Applied tan-quot0.3

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

  4. Applied associate-/r/0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019325 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))