Average Error: 15.0 → 0.3
Time: 17.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r26054 = r;
        double r26055 = b;
        double r26056 = sin(r26055);
        double r26057 = a;
        double r26058 = r26057 + r26055;
        double r26059 = cos(r26058);
        double r26060 = r26056 / r26059;
        double r26061 = r26054 * r26060;
        return r26061;
}
↓
double f(double r, double a, double b) {
        double r26062 = r;
        double r26063 = b;
        double r26064 = sin(r26063);
        double r26065 = r26062 * r26064;
        double r26066 = a;
        double r26067 = cos(r26066);
        double r26068 = cos(r26063);
        double r26069 = r26067 * r26068;
        double r26070 = sin(r26066);
        double r26071 = r26070 * r26064;
        double r26072 = r26069 - r26071;
        double r26073 = r26065 / r26072;
        return r26073;
}

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 clear-num0.7

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))