Average Error: 0.2 → 0.2
Time: 21.0s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1 - \left(1 \cdot x\right) \cdot \cos B}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1 - \left(1 \cdot x\right) \cdot \cos B}{\sin B}
double f(double B, double x) {
        double r20533 = x;
        double r20534 = 1.0;
        double r20535 = B;
        double r20536 = tan(r20535);
        double r20537 = r20534 / r20536;
        double r20538 = r20533 * r20537;
        double r20539 = -r20538;
        double r20540 = sin(r20535);
        double r20541 = r20534 / r20540;
        double r20542 = r20539 + r20541;
        return r20542;
}
↓
double f(double B, double x) {
        double r20543 = 1.0;
        double r20544 = x;
        double r20545 = r20543 * r20544;
        double r20546 = B;
        double r20547 = cos(r20546);
        double r20548 = r20545 * r20547;
        double r20549 = r20543 - r20548;
        double r20550 = sin(r20546);
        double r20551 = r20549 / r20550;
        return r20551;
}

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

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

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Applied associate-*r*0.2

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

  7. Simplified0.2

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

  9. Applied associate-*r/0.2

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

  10. Applied associate-*l/0.2

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

  11. Applied sub-div0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))