Average Error: 0.2 → 0.2
Time: 4.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\left(-\frac{x \cdot 1}{\sin B} \cdot \cos B\right) + \frac{1}{\sin B}
double f(double B, double x) {
        double r58305 = x;
        double r58306 = 1.0;
        double r58307 = B;
        double r58308 = tan(r58307);
        double r58309 = r58306 / r58308;
        double r58310 = r58305 * r58309;
        double r58311 = -r58310;
        double r58312 = sin(r58307);
        double r58313 = r58306 / r58312;
        double r58314 = r58311 + r58313;
        return r58314;
}
↓
double f(double B, double x) {
        double r58315 = x;
        double r58316 = 1.0;
        double r58317 = r58315 * r58316;
        double r58318 = B;
        double r58319 = sin(r58318);
        double r58320 = r58317 / r58319;
        double r58321 = cos(r58318);
        double r58322 = r58320 * r58321;
        double r58323 = -r58322;
        double r58324 = r58316 / r58319;
        double r58325 = r58323 + r58324;
        return r58325;
}

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. Using strategy rm

  5. Applied tan-quot0.2

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

  6. Applied associate-/r/0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))