Average Error: 15.0 → 0.4
Time: 30.5s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)} \cdot r
double f(double r, double a, double b) {
        double r728141 = r;
        double r728142 = b;
        double r728143 = sin(r728142);
        double r728144 = r728141 * r728143;
        double r728145 = a;
        double r728146 = r728145 + r728142;
        double r728147 = cos(r728146);
        double r728148 = r728144 / r728147;
        return r728148;
}
↓
double f(double r, double a, double b) {
        double r728149 = b;
        double r728150 = sin(r728149);
        double r728151 = a;
        double r728152 = cos(r728151);
        double r728153 = cos(r728149);
        double r728154 = r728152 * r728153;
        double r728155 = sin(r728151);
        double r728156 = r728155 * r728150;
        double r728157 = exp(r728156);
        double r728158 = log(r728157);
        double r728159 = r728154 - r728158;
        double r728160 = r728150 / r728159;
        double r728161 = r;
        double r728162 = r728160 * r728161;
        return r728162;
}

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

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

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  9. Applied add-log-exp0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019142 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))