Average Error: 0.2 → 0.2
Time: 17.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{1 \cdot \left(\cos B \cdot x\right)}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{1 \cdot \left(\cos B \cdot x\right)}{\sin B}
double f(double B, double x) {
        double r2488238 = x;
        double r2488239 = 1.0;
        double r2488240 = B;
        double r2488241 = tan(r2488240);
        double r2488242 = r2488239 / r2488241;
        double r2488243 = r2488238 * r2488242;
        double r2488244 = -r2488243;
        double r2488245 = sin(r2488240);
        double r2488246 = r2488239 / r2488245;
        double r2488247 = r2488244 + r2488246;
        return r2488247;
}
↓
double f(double B, double x) {
        double r2488248 = 1.0;
        double r2488249 = B;
        double r2488250 = sin(r2488249);
        double r2488251 = r2488248 / r2488250;
        double r2488252 = cos(r2488249);
        double r2488253 = x;
        double r2488254 = r2488252 * r2488253;
        double r2488255 = r2488248 * r2488254;
        double r2488256 = r2488255 / r2488250;
        double r2488257 = r2488251 - r2488256;
        return r2488257;
}

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. Simplified0.2

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

  4. Applied *-un-lft-identity0.2

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

  5. Applied times-frac0.2

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

  6. Simplified0.2

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

  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

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019170 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))