Average Error: 0.2 → 0.2
Time: 15.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \cos B \cdot \left(1 \cdot x\right)}{\sin B}
double f(double B, double x) {
        double r20200 = x;
        double r20201 = 1.0;
        double r20202 = B;
        double r20203 = tan(r20202);
        double r20204 = r20201 / r20203;
        double r20205 = r20200 * r20204;
        double r20206 = -r20205;
        double r20207 = sin(r20202);
        double r20208 = r20201 / r20207;
        double r20209 = r20206 + r20208;
        return r20209;
}
↓
double f(double B, double x) {
        double r20210 = 1.0;
        double r20211 = B;
        double r20212 = cos(r20211);
        double r20213 = x;
        double r20214 = r20210 * r20213;
        double r20215 = r20212 * r20214;
        double r20216 = r20210 - r20215;
        double r20217 = sin(r20211);
        double r20218 = r20216 / r20217;
        return r20218;
}

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. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019194 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))