Average Error: 0.2 → 0.3
Time: 24.0s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} \cdot \left(1 - \cos B \cdot x\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} \cdot \left(1 - \cos B \cdot x\right)
double f(double B, double x) {
        double r774695 = x;
        double r774696 = 1.0;
        double r774697 = B;
        double r774698 = tan(r774697);
        double r774699 = r774696 / r774698;
        double r774700 = r774695 * r774699;
        double r774701 = -r774700;
        double r774702 = sin(r774697);
        double r774703 = r774696 / r774702;
        double r774704 = r774701 + r774703;
        return r774704;
}
↓
double f(double B, double x) {
        double r774705 = 1.0;
        double r774706 = B;
        double r774707 = sin(r774706);
        double r774708 = r774705 / r774707;
        double r774709 = cos(r774706);
        double r774710 = x;
        double r774711 = r774709 * r774710;
        double r774712 = r774705 - r774711;
        double r774713 = r774708 * r774712;
        return r774713;
}

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 div-inv0.3

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

  6. Applied *-un-lft-identity0.3

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

  7. Applied *-un-lft-identity0.3

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

  8. Applied times-frac0.3

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

  9. Applied distribute-rgt-out--0.3

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))