Average Error: 15.0 → 0.4
Time: 32.5s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \frac{\cos b}{\sin b} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \frac{\cos b}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r1055315 = r;
        double r1055316 = b;
        double r1055317 = sin(r1055316);
        double r1055318 = r1055315 * r1055317;
        double r1055319 = a;
        double r1055320 = r1055319 + r1055316;
        double r1055321 = cos(r1055320);
        double r1055322 = r1055318 / r1055321;
        return r1055322;
}
↓
double f(double r, double a, double b) {
        double r1055323 = r;
        double r1055324 = a;
        double r1055325 = cos(r1055324);
        double r1055326 = b;
        double r1055327 = cos(r1055326);
        double r1055328 = sin(r1055326);
        double r1055329 = r1055327 / r1055328;
        double r1055330 = r1055325 * r1055329;
        double r1055331 = sin(r1055324);
        double r1055332 = r1055330 - r1055331;
        double r1055333 = r1055323 / r1055332;
        return r1055333;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around -inf 0.3

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019119 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))