Average Error: 0.2 → 0.2
Time: 20.4s
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 r1000403 = x;
        double r1000404 = 1.0;
        double r1000405 = B;
        double r1000406 = tan(r1000405);
        double r1000407 = r1000404 / r1000406;
        double r1000408 = r1000403 * r1000407;
        double r1000409 = -r1000408;
        double r1000410 = sin(r1000405);
        double r1000411 = r1000404 / r1000410;
        double r1000412 = r1000409 + r1000411;
        return r1000412;
}
↓
double f(double B, double x) {
        double r1000413 = 1.0;
        double r1000414 = B;
        double r1000415 = cos(r1000414);
        double r1000416 = x;
        double r1000417 = r1000413 * r1000416;
        double r1000418 = r1000415 * r1000417;
        double r1000419 = r1000413 - r1000418;
        double r1000420 = sin(r1000414);
        double r1000421 = r1000419 / r1000420;
        return r1000421;
}

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

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{x \cdot 1}{\tan B}}\]

  3. Taylor expanded around inf 0.2

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

  4. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{\sin B} - \frac{1 \cdot x}{\sin B} \cdot \cos B}\]
  5. Using strategy rm

  6. Applied associate-*l/0.2

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

  7. Applied sub-div0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))