Average Error: 0.2 → 0.2
Time: 23.1s
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 r545192 = x;
        double r545193 = 1.0;
        double r545194 = B;
        double r545195 = tan(r545194);
        double r545196 = r545193 / r545195;
        double r545197 = r545192 * r545196;
        double r545198 = -r545197;
        double r545199 = sin(r545194);
        double r545200 = r545193 / r545199;
        double r545201 = r545198 + r545200;
        return r545201;
}
↓
double f(double B, double x) {
        double r545202 = 1.0;
        double r545203 = B;
        double r545204 = cos(r545203);
        double r545205 = x;
        double r545206 = r545204 * r545205;
        double r545207 = r545202 - r545206;
        double r545208 = sin(r545203);
        double r545209 = r545207 / r545208;
        return r545209;
}

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