Average Error: 0.2 → 0.2
Time: 14.8s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
1 \cdot \left(\frac{1}{\sin B} - \frac{x \cdot \cos B}{\sin B}\right)
double f(double B, double x) {
        double r16378 = x;
        double r16379 = 1.0;
        double r16380 = B;
        double r16381 = tan(r16380);
        double r16382 = r16379 / r16381;
        double r16383 = r16378 * r16382;
        double r16384 = -r16383;
        double r16385 = sin(r16380);
        double r16386 = r16379 / r16385;
        double r16387 = r16384 + r16386;
        return r16387;
}
↓
double f(double B, double x) {
        double r16388 = 1.0;
        double r16389 = 1.0;
        double r16390 = B;
        double r16391 = sin(r16390);
        double r16392 = r16389 / r16391;
        double r16393 = x;
        double r16394 = cos(r16390);
        double r16395 = r16393 * r16394;
        double r16396 = r16395 / r16391;
        double r16397 = r16392 - r16396;
        double r16398 = r16388 * r16397;
        return r16398;
}

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. Using strategy rm

  3. Applied associate-*r/0.2

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

  4. Applied distribute-neg-frac0.2

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

  5. Applied frac-add11.0

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

  6. Simplified11.0

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

  7. Taylor expanded around inf 0.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))