Average Error: 0.2 → 0.2
Time: 16.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}
double f(double B, double x) {
        double r29504 = x;
        double r29505 = 1.0;
        double r29506 = B;
        double r29507 = tan(r29506);
        double r29508 = r29505 / r29507;
        double r29509 = r29504 * r29508;
        double r29510 = -r29509;
        double r29511 = sin(r29506);
        double r29512 = r29505 / r29511;
        double r29513 = r29510 + r29512;
        return r29513;
}
↓
double f(double B, double x) {
        double r29514 = 1.0;
        double r29515 = B;
        double r29516 = cos(r29515);
        double r29517 = x;
        double r29518 = r29514 * r29517;
        double r29519 = r29516 * r29518;
        double r29520 = r29514 - r29519;
        double r29521 = sin(r29515);
        double r29522 = r29520 / r29521;
        return r29522;
}

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

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

  3. Taylor expanded around inf 0.2

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

  5. Applied associate-*r/0.2

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

  6. Applied sub-div0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))