Average Error: 0.2 → 0.2
Time: 36.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r22234 = x;
        double r22235 = 1.0;
        double r22236 = B;
        double r22237 = tan(r22236);
        double r22238 = r22235 / r22237;
        double r22239 = r22234 * r22238;
        double r22240 = -r22239;
        double r22241 = sin(r22236);
        double r22242 = r22235 / r22241;
        double r22243 = r22240 + r22242;
        return r22243;
}
↓
double f(double B, double x) {
        double r22244 = x;
        double r22245 = 1.0;
        double r22246 = r22244 * r22245;
        double r22247 = B;
        double r22248 = sin(r22247);
        double r22249 = r22246 / r22248;
        double r22250 = cos(r22247);
        double r22251 = r22249 * r22250;
        double r22252 = -r22251;
        double r22253 = r22245 / r22248;
        double r22254 = r22252 + r22253;
        return r22254;
}

Error

Bits error versus B

Bits error versus x

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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 associate-*r/0.1

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

  5. Applied tan-quot0.2

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

  6. Applied associate-/r/0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))