Average Error: 14.7 → 0.3
Time: 17.4s
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 r25353 = r;
        double r25354 = b;
        double r25355 = sin(r25354);
        double r25356 = r25353 * r25355;
        double r25357 = a;
        double r25358 = r25357 + r25354;
        double r25359 = cos(r25358);
        double r25360 = r25356 / r25359;
        return r25360;
}
↓
double f(double r, double a, double b) {
        double r25361 = r;
        double r25362 = b;
        double r25363 = sin(r25362);
        double r25364 = a;
        double r25365 = cos(r25364);
        double r25366 = cos(r25362);
        double r25367 = r25365 * r25366;
        double r25368 = sin(r25364);
        double r25369 = r25368 * r25363;
        double r25370 = r25367 - r25369;
        double r25371 = r25363 / r25370;
        double r25372 = r25361 * r25371;
        return r25372;
}

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 14.7

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 2019235 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))