Average Error: 14.9 → 0.4
Time: 6.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r17129 = r;
        double r17130 = b;
        double r17131 = sin(r17130);
        double r17132 = a;
        double r17133 = r17132 + r17130;
        double r17134 = cos(r17133);
        double r17135 = r17131 / r17134;
        double r17136 = r17129 * r17135;
        return r17136;
}
↓
double f(double r, double a, double b) {
        double r17137 = r;
        double r17138 = b;
        double r17139 = sin(r17138);
        double r17140 = r17137 * r17139;
        double r17141 = 1.0;
        double r17142 = a;
        double r17143 = cos(r17142);
        double r17144 = cos(r17138);
        double r17145 = r17143 * r17144;
        double r17146 = sin(r17142);
        double r17147 = r17146 * r17139;
        double r17148 = r17145 - r17147;
        double r17149 = r17141 / r17148;
        double r17150 = r17140 * r17149;
        return r17150;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.9

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied div-inv0.4

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right)}\]

  6. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  7. Final simplification0.4

    \[\leadsto \left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]

Reproduce

herbie shell --seed 2019353 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))