Average Error: 14.8 → 0.3
Time: 20.4s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r1058187 = r;
        double r1058188 = b;
        double r1058189 = sin(r1058188);
        double r1058190 = r1058187 * r1058189;
        double r1058191 = a;
        double r1058192 = r1058191 + r1058188;
        double r1058193 = cos(r1058192);
        double r1058194 = r1058190 / r1058193;
        return r1058194;
}
↓
double f(double r, double a, double b) {
        double r1058195 = r;
        double r1058196 = b;
        double r1058197 = sin(r1058196);
        double r1058198 = a;
        double r1058199 = cos(r1058198);
        double r1058200 = cos(r1058196);
        double r1058201 = r1058199 * r1058200;
        double r1058202 = sin(r1058198);
        double r1058203 = r1058202 * r1058197;
        double r1058204 = r1058201 - r1058203;
        double r1058205 = r1058197 / r1058204;
        double r1058206 = r1058195 * r1058205;
        return r1058206;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))