Average Error: 0.2 → 0.2
Time: 21.5s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}
↓
\frac{1}{\sin B} - \frac{x}{\sin B} \cdot \cos B
double f(double B, double x) {
        double r1676120 = x;
        double r1676121 = 1.0;
        double r1676122 = B;
        double r1676123 = tan(r1676122);
        double r1676124 = r1676121 / r1676123;
        double r1676125 = r1676120 * r1676124;
        double r1676126 = -r1676125;
        double r1676127 = sin(r1676122);
        double r1676128 = r1676121 / r1676127;
        double r1676129 = r1676126 + r1676128;
        return r1676129;
}
↓
double f(double B, double x) {
        double r1676130 = 1.0;
        double r1676131 = B;
        double r1676132 = sin(r1676131);
        double r1676133 = r1676130 / r1676132;
        double r1676134 = x;
        double r1676135 = r1676134 / r1676132;
        double r1676136 = cos(r1676131);
        double r1676137 = r1676135 * r1676136;
        double r1676138 = r1676133 - r1676137;
        return r1676138;
}

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

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

  4. Applied tan-quot0.2

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

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))