Average Error: 15.0 → 0.3
Time: 6.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r17145 = r;
        double r17146 = b;
        double r17147 = sin(r17146);
        double r17148 = a;
        double r17149 = r17148 + r17146;
        double r17150 = cos(r17149);
        double r17151 = r17147 / r17150;
        double r17152 = r17145 * r17151;
        return r17152;
}
↓
double f(double r, double a, double b) {
        double r17153 = r;
        double r17154 = b;
        double r17155 = sin(r17154);
        double r17156 = r17153 * r17155;
        double r17157 = a;
        double r17158 = cos(r17157);
        double r17159 = cos(r17154);
        double r17160 = r17158 * r17159;
        double r17161 = sin(r17157);
        double r17162 = r17161 * r17155;
        double r17163 = r17160 - r17162;
        double r17164 = r17156 / r17163;
        return r17164;
}

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 15.0

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 associate-*r/0.3

    \[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  6. Final simplification0.3

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))