Average Error: 14.5 → 0.4
Time: 26.8s
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 r1124781 = r;
        double r1124782 = b;
        double r1124783 = sin(r1124782);
        double r1124784 = a;
        double r1124785 = r1124784 + r1124782;
        double r1124786 = cos(r1124785);
        double r1124787 = r1124783 / r1124786;
        double r1124788 = r1124781 * r1124787;
        return r1124788;
}
↓
double f(double r, double a, double b) {
        double r1124789 = r;
        double r1124790 = b;
        double r1124791 = sin(r1124790);
        double r1124792 = r1124789 * r1124791;
        double r1124793 = a;
        double r1124794 = cos(r1124793);
        double r1124795 = cos(r1124790);
        double r1124796 = r1124794 * r1124795;
        double r1124797 = sin(r1124793);
        double r1124798 = r1124797 * r1124791;
        double r1124799 = exp(r1124798);
        double r1124800 = log(r1124799);
        double r1124801 = r1124796 - r1124800;
        double r1124802 = r1124792 / r1124801;
        return r1124802;
}

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 14.5

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

  3. Applied +-commutative14.5

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

  4. Applied cos-sum0.3

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

  6. Applied div-inv0.4

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

  7. Applied associate-*r*0.4

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

  8. Taylor expanded around inf 0.3

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

  10. Applied add-log-exp0.4

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

  11. 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 2019158 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))