Average Error: 14.9 → 0.4
Time: 37.5s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\left(\frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\right) \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\left(\frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\right) \cdot r
double f(double r, double a, double b) {
        double r1260044 = r;
        double r1260045 = b;
        double r1260046 = sin(r1260045);
        double r1260047 = r1260044 * r1260046;
        double r1260048 = a;
        double r1260049 = r1260048 + r1260045;
        double r1260050 = cos(r1260049);
        double r1260051 = r1260047 / r1260050;
        return r1260051;
}
↓
double f(double r, double a, double b) {
        double r1260052 = 1.0;
        double r1260053 = a;
        double r1260054 = cos(r1260053);
        double r1260055 = b;
        double r1260056 = cos(r1260055);
        double r1260057 = r1260054 * r1260056;
        double r1260058 = sin(r1260055);
        double r1260059 = sin(r1260053);
        double r1260060 = r1260058 * r1260059;
        double r1260061 = r1260057 - r1260060;
        double r1260062 = r1260052 / r1260061;
        double r1260063 = r1260062 * r1260058;
        double r1260064 = r;
        double r1260065 = r1260063 * r1260064;
        return r1260065;
}

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 14.9

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

  9. Applied div-inv0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019121 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))