Average Error: 14.9 → 0.4
Time: 36.6s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\frac{\sin b}{\sin a \cdot \sin b + \cos b \cdot \cos a} \cdot r}{\cos b \cdot \cos a - \sin a \cdot \sin b} \cdot \left(\sin a \cdot \sin b + \cos b \cdot \cos a\right)\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\frac{\sin b}{\sin a \cdot \sin b + \cos b \cdot \cos a} \cdot r}{\cos b \cdot \cos a - \sin a \cdot \sin b} \cdot \left(\sin a \cdot \sin b + \cos b \cdot \cos a\right)
double f(double r, double a, double b) {
        double r1197218 = r;
        double r1197219 = b;
        double r1197220 = sin(r1197219);
        double r1197221 = r1197218 * r1197220;
        double r1197222 = a;
        double r1197223 = r1197222 + r1197219;
        double r1197224 = cos(r1197223);
        double r1197225 = r1197221 / r1197224;
        return r1197225;
}
↓
double f(double r, double a, double b) {
        double r1197226 = b;
        double r1197227 = sin(r1197226);
        double r1197228 = a;
        double r1197229 = sin(r1197228);
        double r1197230 = r1197229 * r1197227;
        double r1197231 = cos(r1197226);
        double r1197232 = cos(r1197228);
        double r1197233 = r1197231 * r1197232;
        double r1197234 = r1197230 + r1197233;
        double r1197235 = r1197227 / r1197234;
        double r1197236 = r;
        double r1197237 = r1197235 * r1197236;
        double r1197238 = r1197233 - r1197230;
        double r1197239 = r1197237 / r1197238;
        double r1197240 = r1197239 * r1197234;
        return r1197240;
}

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 flip--0.4

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

  6. Applied associate-/r/0.4

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019200 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))