Average Error: 15.0 → 0.3
Time: 13.5s
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 r16261 = r;
        double r16262 = b;
        double r16263 = sin(r16262);
        double r16264 = r16261 * r16263;
        double r16265 = a;
        double r16266 = r16265 + r16262;
        double r16267 = cos(r16266);
        double r16268 = r16264 / r16267;
        return r16268;
}
↓
double f(double r, double a, double b) {
        double r16269 = r;
        double r16270 = b;
        double r16271 = sin(r16270);
        double r16272 = a;
        double r16273 = cos(r16272);
        double r16274 = cos(r16270);
        double r16275 = r16273 * r16274;
        double r16276 = sin(r16272);
        double r16277 = r16276 * r16271;
        double r16278 = r16275 - r16277;
        double r16279 = r16271 / r16278;
        double r16280 = r16269 * r16279;
        return r16280;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

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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. 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 2019351 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))