Average Error: 0.2 → 0.2
Time: 1.7m
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r1325008 = x;
        double r1325009 = 1.0;
        double r1325010 = B;
        double r1325011 = tan(r1325010);
        double r1325012 = r1325009 / r1325011;
        double r1325013 = r1325008 * r1325012;
        double r1325014 = -r1325013;
        double r1325015 = sin(r1325010);
        double r1325016 = r1325009 / r1325015;
        double r1325017 = r1325014 + r1325016;
        return r1325017;
}
↓
double f(double B, double x) {
        double r1325018 = 1.0;
        double r1325019 = B;
        double r1325020 = sin(r1325019);
        double r1325021 = r1325018 / r1325020;
        double r1325022 = x;
        double r1325023 = cos(r1325019);
        double r1325024 = r1325022 * r1325023;
        double r1325025 = r1325024 / r1325020;
        double r1325026 = r1325021 - r1325025;
        return r1325026;
}

Error

Bits error versus B

Bits error versus x

Try it out

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. Final simplification0.2

    \[\leadsto \frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\]

Reproduce

herbie shell --seed 2019142 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))