Average Error: 0.2 → 0.2
Time: 58.2s
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 r545576 = x;
        double r545577 = 1.0;
        double r545578 = B;
        double r545579 = tan(r545578);
        double r545580 = r545577 / r545579;
        double r545581 = r545576 * r545580;
        double r545582 = -r545581;
        double r545583 = sin(r545578);
        double r545584 = r545577 / r545583;
        double r545585 = r545582 + r545584;
        return r545585;
}
↓
double f(double B, double x) {
        double r545586 = 1.0;
        double r545587 = B;
        double r545588 = sin(r545587);
        double r545589 = r545586 / r545588;
        double r545590 = x;
        double r545591 = r545590 / r545588;
        double r545592 = cos(r545587);
        double r545593 = r545591 * r545592;
        double r545594 = r545589 - r545593;
        return r545594;
}

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 2019142 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))