Average Error: 0.2 → 0.2
Time: 19.1s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot x}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot x}{\sin B}
double f(double B, double x) {
        double r327319 = x;
        double r327320 = 1.0;
        double r327321 = B;
        double r327322 = tan(r327321);
        double r327323 = r327320 / r327322;
        double r327324 = r327319 * r327323;
        double r327325 = -r327324;
        double r327326 = sin(r327321);
        double r327327 = r327320 / r327326;
        double r327328 = r327325 + r327327;
        return r327328;
}
↓
double f(double B, double x) {
        double r327329 = 1.0;
        double r327330 = B;
        double r327331 = cos(r327330);
        double r327332 = x;
        double r327333 = r327331 * r327332;
        double r327334 = r327329 - r327333;
        double r327335 = sin(r327330);
        double r327336 = r327334 / r327335;
        return r327336;
}

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

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

  3. Taylor expanded around inf 0.2

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

  5. Applied sub-div0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019154 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))