Average Error: 14.7 → 0.3
Time: 13.1s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b
double f(double r, double a, double b) {
        double r26046 = r;
        double r26047 = b;
        double r26048 = sin(r26047);
        double r26049 = r26046 * r26048;
        double r26050 = a;
        double r26051 = r26050 + r26047;
        double r26052 = cos(r26051);
        double r26053 = r26049 / r26052;
        return r26053;
}
↓
double f(double r, double a, double b) {
        double r26054 = r;
        double r26055 = a;
        double r26056 = cos(r26055);
        double r26057 = b;
        double r26058 = cos(r26057);
        double r26059 = r26056 * r26058;
        double r26060 = sin(r26055);
        double r26061 = sin(r26057);
        double r26062 = r26060 * r26061;
        double r26063 = r26059 - r26062;
        double r26064 = r26054 / r26063;
        double r26065 = r26064 * r26061;
        return r26065;
}

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 14.7

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

  3. Applied cos-sum0.3

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

  5. Applied associate-/l*0.4

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

  7. Applied associate-/r/0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019304 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))