Average Error: 15.1 → 0.4
Time: 6.2s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b \cdot \cos a - \sin a \cdot \sin b}{\sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos b \cdot \cos a - \sin a \cdot \sin b}{\sin b}}
double f(double r, double a, double b) {
        double r16104 = r;
        double r16105 = b;
        double r16106 = sin(r16105);
        double r16107 = a;
        double r16108 = r16107 + r16105;
        double r16109 = cos(r16108);
        double r16110 = r16106 / r16109;
        double r16111 = r16104 * r16110;
        return r16111;
}
↓
double f(double r, double a, double b) {
        double r16112 = r;
        double r16113 = b;
        double r16114 = cos(r16113);
        double r16115 = a;
        double r16116 = cos(r16115);
        double r16117 = r16114 * r16116;
        double r16118 = sin(r16115);
        double r16119 = sin(r16113);
        double r16120 = r16118 * r16119;
        double r16121 = r16117 - r16120;
        double r16122 = r16121 / r16119;
        double r16123 = r16112 / r16122;
        return r16123;
}

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 15.1

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 add-cbrt-cube0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{\sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}}\]

  8. Applied add-cbrt-cube0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\sin a \cdot \sin a\right) \cdot \sin a}} \cdot \sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}\]

  9. Applied cbrt-unprod0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin a\right) \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin b\right) \cdot \sin b\right)}}}\]

  10. Simplified0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\color{blue}{{\left(\sin a \cdot \sin b\right)}^{3}}}}\]
  11. Using strategy rm

  12. Applied associate-/l*0.4

    \[\leadsto \color{blue}{\frac{r}{\frac{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}{\sin b}}}\]

  13. Simplified0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2020020 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))