Average Error: 0.2 → 0.2
Time: 15.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{\cos B \cdot x}{\sin B} \cdot 1\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{\cos B \cdot x}{\sin B} \cdot 1
double f(double B, double x) {
        double r54258 = x;
        double r54259 = 1.0;
        double r54260 = B;
        double r54261 = tan(r54260);
        double r54262 = r54259 / r54261;
        double r54263 = r54258 * r54262;
        double r54264 = -r54263;
        double r54265 = sin(r54260);
        double r54266 = r54259 / r54265;
        double r54267 = r54264 + r54266;
        return r54267;
}
↓
double f(double B, double x) {
        double r54268 = 1.0;
        double r54269 = B;
        double r54270 = sin(r54269);
        double r54271 = r54268 / r54270;
        double r54272 = cos(r54269);
        double r54273 = x;
        double r54274 = r54272 * r54273;
        double r54275 = r54274 / r54270;
        double r54276 = r54275 * r54268;
        double r54277 = r54271 - r54276;
        return r54277;
}

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 tan-quot0.2

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

  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. Applied associate-*r*0.3

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

  6. Simplified0.2

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

  7. Taylor expanded around inf 0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

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