Average Error: 0.2 → 0.1
Time: 16.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} + \frac{-x \cdot 1}{\tan B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} + \frac{-x \cdot 1}{\tan B}
double f(double B, double x) {
        double r22256 = x;
        double r22257 = 1.0;
        double r22258 = B;
        double r22259 = tan(r22258);
        double r22260 = r22257 / r22259;
        double r22261 = r22256 * r22260;
        double r22262 = -r22261;
        double r22263 = sin(r22258);
        double r22264 = r22257 / r22263;
        double r22265 = r22262 + r22264;
        return r22265;
}
↓
double f(double B, double x) {
        double r22266 = 1.0;
        double r22267 = B;
        double r22268 = sin(r22267);
        double r22269 = r22266 / r22268;
        double r22270 = x;
        double r22271 = r22270 * r22266;
        double r22272 = -r22271;
        double r22273 = tan(r22267);
        double r22274 = r22272 / r22273;
        double r22275 = r22269 + r22274;
        return r22275;
}

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. Using strategy rm

  3. Applied associate-*r/0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))