Average Error: 15.1 → 0.4
Time: 12.4s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]
\frac{r \cdot \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 r16229 = r;
        double r16230 = b;
        double r16231 = sin(r16230);
        double r16232 = r16229 * r16231;
        double r16233 = a;
        double r16234 = r16233 + r16230;
        double r16235 = cos(r16234);
        double r16236 = r16232 / r16235;
        return r16236;
}
↓
double f(double r, double a, double b) {
        double r16237 = r;
        double r16238 = b;
        double r16239 = sin(r16238);
        double r16240 = r16237 * r16239;
        double r16241 = a;
        double r16242 = cos(r16241);
        double r16243 = cos(r16238);
        double r16244 = r16242 * r16243;
        double r16245 = sin(r16241);
        double r16246 = r16245 * r16239;
        double r16247 = exp(r16246);
        double r16248 = log(r16247);
        double r16249 = r16244 - r16248;
        double r16250 = r16240 / r16249;
        return r16250;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.4

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

  6. 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 2020045 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))