Average Error: 15.0 → 0.3
Time: 6.0s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r17083 = r;
        double r17084 = b;
        double r17085 = sin(r17084);
        double r17086 = r17083 * r17085;
        double r17087 = a;
        double r17088 = r17087 + r17084;
        double r17089 = cos(r17088);
        double r17090 = r17086 / r17089;
        return r17090;
}
↓
double f(double r, double a, double b) {
        double r17091 = r;
        double r17092 = b;
        double r17093 = sin(r17092);
        double r17094 = cos(r17092);
        double r17095 = a;
        double r17096 = cos(r17095);
        double r17097 = r17094 * r17096;
        double r17098 = sin(r17095);
        double r17099 = r17098 * r17093;
        double r17100 = r17097 - r17099;
        double r17101 = r17093 / r17100;
        double r17102 = r17091 * r17101;
        return r17102;
}

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 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. Using strategy rm

  7. Applied *-un-lft-identity0.4

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

  8. Applied times-frac0.4

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

  9. Simplified0.4

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))