Average Error: 0.2 → 0.3
Time: 21.8s
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 r1718730 = x;
        double r1718731 = 1.0;
        double r1718732 = B;
        double r1718733 = tan(r1718732);
        double r1718734 = r1718731 / r1718733;
        double r1718735 = r1718730 * r1718734;
        double r1718736 = -r1718735;
        double r1718737 = sin(r1718732);
        double r1718738 = r1718731 / r1718737;
        double r1718739 = r1718736 + r1718738;
        return r1718739;
}
↓
double f(double B, double x) {
        double r1718740 = 1.0;
        double r1718741 = B;
        double r1718742 = sin(r1718741);
        double r1718743 = r1718740 / r1718742;
        double r1718744 = cos(r1718741);
        double r1718745 = x;
        double r1718746 = r1718744 * r1718745;
        double r1718747 = r1718740 - r1718746;
        double r1718748 = r1718743 * r1718747;
        return r1718748;
}

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))))