Average Error: 15.2 → 0.4
Time: 6.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r16941 = r;
        double r16942 = b;
        double r16943 = sin(r16942);
        double r16944 = a;
        double r16945 = r16944 + r16942;
        double r16946 = cos(r16945);
        double r16947 = r16943 / r16946;
        double r16948 = r16941 * r16947;
        return r16948;
}
↓
double f(double r, double a, double b) {
        double r16949 = r;
        double r16950 = b;
        double r16951 = sin(r16950);
        double r16952 = r16949 * r16951;
        double r16953 = a;
        double r16954 = cos(r16953);
        double r16955 = cos(r16950);
        double r16956 = r16954 * r16955;
        double r16957 = sin(r16953);
        double r16958 = r16957 * r16951;
        double r16959 = exp(r16958);
        double r16960 = log(r16959);
        double r16961 = r16956 - r16960;
        double r16962 = r16952 / r16961;
        return r16962;
}

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 15.2

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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-log-exp0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))