Average Error: 15.5 → 0.4
Time: 17.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin b \cdot \sin a}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin b \cdot \sin a}\right)}
double f(double r, double a, double b) {
        double r25397 = r;
        double r25398 = b;
        double r25399 = sin(r25398);
        double r25400 = a;
        double r25401 = r25400 + r25398;
        double r25402 = cos(r25401);
        double r25403 = r25399 / r25402;
        double r25404 = r25397 * r25403;
        return r25404;
}
↓
double f(double r, double a, double b) {
        double r25405 = r;
        double r25406 = b;
        double r25407 = sin(r25406);
        double r25408 = r25405 * r25407;
        double r25409 = a;
        double r25410 = cos(r25409);
        double r25411 = cos(r25406);
        double r25412 = r25410 * r25411;
        double r25413 = sin(r25409);
        double r25414 = r25407 * r25413;
        double r25415 = exp(r25414);
        double r25416 = log(r25415);
        double r25417 = r25412 - r25416;
        double r25418 = r25408 / r25417;
        return r25418;
}

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 15.5

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

  8. Applied add-log-exp0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019209 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))