Average Error: 15.3 → 0.4
Time: 13.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r15966 = r;
        double r15967 = b;
        double r15968 = sin(r15967);
        double r15969 = a;
        double r15970 = r15969 + r15967;
        double r15971 = cos(r15970);
        double r15972 = r15968 / r15971;
        double r15973 = r15966 * r15972;
        return r15973;
}
↓
double f(double r, double a, double b) {
        double r15974 = r;
        double r15975 = a;
        double r15976 = cos(r15975);
        double r15977 = b;
        double r15978 = cos(r15977);
        double r15979 = r15976 * r15978;
        double r15980 = sin(r15977);
        double r15981 = r15979 / r15980;
        double r15982 = sin(r15975);
        double r15983 = r15981 - r15982;
        double r15984 = r15974 / r15983;
        return r15984;
}

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 15.3

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 pow10.3

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

  6. Applied pow10.3

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

  7. Applied pow-prod-down0.3

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020042 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))