Average Error: 14.8 → 0.3
Time: 37.5s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r1133905 = r;
        double r1133906 = b;
        double r1133907 = sin(r1133906);
        double r1133908 = r1133905 * r1133907;
        double r1133909 = a;
        double r1133910 = r1133909 + r1133906;
        double r1133911 = cos(r1133910);
        double r1133912 = r1133908 / r1133911;
        return r1133912;
}
↓
double f(double r, double a, double b) {
        double r1133913 = r;
        double r1133914 = b;
        double r1133915 = sin(r1133914);
        double r1133916 = r1133913 * r1133915;
        double r1133917 = a;
        double r1133918 = cos(r1133917);
        double r1133919 = cos(r1133914);
        double r1133920 = r1133918 * r1133919;
        double r1133921 = sin(r1133917);
        double r1133922 = r1133921 * r1133915;
        double r1133923 = r1133920 - r1133922;
        double r1133924 = r1133916 / r1133923;
        return r1133924;
}

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 14.8

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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-cbrt-cube0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}}}\]

  6. Taylor expanded around -inf 0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))