Average Error: 15.4 → 0.3
Time: 12.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{1 \cdot \left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{1 \cdot \left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)}
double f(double r, double a, double b) {
        double r64 = r;
        double r65 = b;
        double r66 = sin(r65);
        double r67 = a;
        double r68 = r67 + r65;
        double r69 = cos(r68);
        double r70 = r66 / r69;
        double r71 = r64 * r70;
        return r71;
}
↓
double f(double r, double a, double b) {
        double r72 = r;
        double r73 = b;
        double r74 = sin(r73);
        double r75 = r72 * r74;
        double r76 = 1.0;
        double r77 = a;
        double r78 = cos(r77);
        double r79 = cos(r73);
        double r80 = r78 * r79;
        double r81 = sin(r77);
        double r82 = r81 * r74;
        double r83 = r80 - r82;
        double r84 = r76 * r83;
        double r85 = r75 / r84;
        return r85;
}

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 15.4

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020025 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))