Average Error: 0.2 → 0.2
Time: 33.8s
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 r589658 = x;
        double r589659 = 1.0;
        double r589660 = B;
        double r589661 = tan(r589660);
        double r589662 = r589659 / r589661;
        double r589663 = r589658 * r589662;
        double r589664 = -r589663;
        double r589665 = sin(r589660);
        double r589666 = r589659 / r589665;
        double r589667 = r589664 + r589666;
        return r589667;
}
↓
double f(double B, double x) {
        double r589668 = 1.0;
        double r589669 = B;
        double r589670 = cos(r589669);
        double r589671 = x;
        double r589672 = r589670 * r589671;
        double r589673 = r589668 - r589672;
        double r589674 = sin(r589669);
        double r589675 = r589673 / r589674;
        return r589675;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}}\]
  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 2019132 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))