Average Error: 15.5 → 0.4
Time: 20.8s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)} \cdot r
double f(double r, double a, double b) {
        double r1005163 = r;
        double r1005164 = b;
        double r1005165 = sin(r1005164);
        double r1005166 = r1005163 * r1005165;
        double r1005167 = a;
        double r1005168 = r1005167 + r1005164;
        double r1005169 = cos(r1005168);
        double r1005170 = r1005166 / r1005169;
        return r1005170;
}
↓
double f(double r, double a, double b) {
        double r1005171 = b;
        double r1005172 = sin(r1005171);
        double r1005173 = a;
        double r1005174 = cos(r1005173);
        double r1005175 = cos(r1005171);
        double r1005176 = r1005174 * r1005175;
        double r1005177 = sin(r1005173);
        double r1005178 = r1005177 * r1005172;
        double r1005179 = exp(r1005178);
        double r1005180 = log(r1005179);
        double r1005181 = r1005176 - r1005180;
        double r1005182 = r1005172 / r1005181;
        double r1005183 = r;
        double r1005184 = r1005182 * r1005183;
        return r1005184;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 add-log-exp0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))