Average Error: 0.2 → 0.2
Time: 18.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \left(\cos B \cdot x\right) \cdot 1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \left(\cos B \cdot x\right) \cdot 1}{\sin B}
double f(double B, double x) {
        double r853007 = x;
        double r853008 = 1.0;
        double r853009 = B;
        double r853010 = tan(r853009);
        double r853011 = r853008 / r853010;
        double r853012 = r853007 * r853011;
        double r853013 = -r853012;
        double r853014 = sin(r853009);
        double r853015 = r853008 / r853014;
        double r853016 = r853013 + r853015;
        return r853016;
}
↓
double f(double B, double x) {
        double r853017 = 1.0;
        double r853018 = B;
        double r853019 = cos(r853018);
        double r853020 = x;
        double r853021 = r853019 * r853020;
        double r853022 = r853021 * r853017;
        double r853023 = r853017 - r853022;
        double r853024 = sin(r853018);
        double r853025 = r853023 / r853024;
        return r853025;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))