Average Error: 14.9 → 0.5
Time: 47.9s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\frac{r}{\cos b \cdot \cos a - \sin b \cdot \sin a}}{\frac{1}{\sin b}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\frac{r}{\cos b \cdot \cos a - \sin b \cdot \sin a}}{\frac{1}{\sin b}}
double f(double r, double a, double b) {
        double r1063197 = r;
        double r1063198 = b;
        double r1063199 = sin(r1063198);
        double r1063200 = r1063197 * r1063199;
        double r1063201 = a;
        double r1063202 = r1063201 + r1063198;
        double r1063203 = cos(r1063202);
        double r1063204 = r1063200 / r1063203;
        return r1063204;
}
↓
double f(double r, double a, double b) {
        double r1063205 = r;
        double r1063206 = b;
        double r1063207 = cos(r1063206);
        double r1063208 = a;
        double r1063209 = cos(r1063208);
        double r1063210 = r1063207 * r1063209;
        double r1063211 = sin(r1063206);
        double r1063212 = sin(r1063208);
        double r1063213 = r1063211 * r1063212;
        double r1063214 = r1063210 - r1063213;
        double r1063215 = r1063205 / r1063214;
        double r1063216 = 1.0;
        double r1063217 = r1063216 / r1063211;
        double r1063218 = r1063215 / r1063217;
        return r1063218;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.9

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

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

  8. Applied associate-/r*0.5

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

  9. Final simplification0.5

    \[\leadsto \frac{\frac{r}{\cos b \cdot \cos a - \sin b \cdot \sin a}}{\frac{1}{\sin b}}\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))