Average Error: 14.8 → 0.3
Time: 18.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\sin b \cdot \frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\sin b \cdot \frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r26422 = r;
        double r26423 = b;
        double r26424 = sin(r26423);
        double r26425 = a;
        double r26426 = r26425 + r26423;
        double r26427 = cos(r26426);
        double r26428 = r26424 / r26427;
        double r26429 = r26422 * r26428;
        return r26429;
}
↓
double f(double r, double a, double b) {
        double r26430 = b;
        double r26431 = sin(r26430);
        double r26432 = r;
        double r26433 = a;
        double r26434 = cos(r26433);
        double r26435 = cos(r26430);
        double r26436 = r26434 * r26435;
        double r26437 = sin(r26433);
        double r26438 = r26431 * r26437;
        double r26439 = r26436 - r26438;
        double r26440 = r26432 / r26439;
        double r26441 = r26431 * r26440;
        return r26441;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Results

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Derivation

  1. Initial program 14.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

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

  4. Simplified0.3

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sin b \cdot \sin a}}\]
  5. Using strategy rm

  6. Applied associate-*r/0.3

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

  7. Simplified0.3

    \[\leadsto \frac{\color{blue}{\sin b \cdot r}}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity0.3

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

  10. Applied times-frac0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019195 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))