Average Error: 15.0 → 0.4
Time: 6.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b - {\left(\sin a \cdot \sin b\right)}^{1}}{\sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b - {\left(\sin a \cdot \sin b\right)}^{1}}{\sin b}}
double f(double r, double a, double b) {
        double r17928 = r;
        double r17929 = b;
        double r17930 = sin(r17929);
        double r17931 = a;
        double r17932 = r17931 + r17929;
        double r17933 = cos(r17932);
        double r17934 = r17930 / r17933;
        double r17935 = r17928 * r17934;
        return r17935;
}
↓
double f(double r, double a, double b) {
        double r17936 = r;
        double r17937 = a;
        double r17938 = cos(r17937);
        double r17939 = b;
        double r17940 = cos(r17939);
        double r17941 = r17938 * r17940;
        double r17942 = sin(r17937);
        double r17943 = sin(r17939);
        double r17944 = r17942 * r17943;
        double r17945 = 1.0;
        double r17946 = pow(r17944, r17945);
        double r17947 = r17941 - r17946;
        double r17948 = r17947 / r17943;
        double r17949 = r17936 / r17948;
        return r17949;
}

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 15.0

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

  5. Applied associate-*r/0.3

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

  7. Applied associate-/l*0.4

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

  9. Applied pow10.4

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

  10. Applied pow10.4

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

  11. Applied pow-prod-down0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))