Average Error: 14.9 → 0.3
Time: 13.7s
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 r16939 = r;
        double r16940 = b;
        double r16941 = sin(r16940);
        double r16942 = a;
        double r16943 = r16942 + r16940;
        double r16944 = cos(r16943);
        double r16945 = r16941 / r16944;
        double r16946 = r16939 * r16945;
        return r16946;
}
↓
double f(double r, double a, double b) {
        double r16947 = r;
        double r16948 = b;
        double r16949 = sin(r16948);
        double r16950 = r16947 * r16949;
        double r16951 = a;
        double r16952 = cos(r16951);
        double r16953 = cos(r16948);
        double r16954 = r16952 * r16953;
        double r16955 = sin(r16951);
        double r16956 = r16955 * r16949;
        double r16957 = r16954 - r16956;
        double r16958 = r16950 / r16957;
        return r16958;
}

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 14.9

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))