Average Error: 15.1 → 0.3
Time: 26.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\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 r753018 = r;
        double r753019 = b;
        double r753020 = sin(r753019);
        double r753021 = a;
        double r753022 = r753021 + r753019;
        double r753023 = cos(r753022);
        double r753024 = r753020 / r753023;
        double r753025 = r753018 * r753024;
        return r753025;
}
↓
double f(double r, double a, double b) {
        double r753026 = r;
        double r753027 = b;
        double r753028 = sin(r753027);
        double r753029 = r753026 * r753028;
        double r753030 = a;
        double r753031 = cos(r753030);
        double r753032 = cos(r753027);
        double r753033 = r753031 * r753032;
        double r753034 = sin(r753030);
        double r753035 = r753034 * r753028;
        double r753036 = r753033 - r753035;
        double r753037 = r753029 / r753036;
        return r753037;
}

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

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

  3. Applied cos-sum0.3

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

  4. Taylor expanded around inf 0.3

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

  6. Applied *-un-lft-identity0.3

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

  7. Applied times-frac0.3

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

  8. Simplified0.3

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

  10. Applied associate-*r/0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019138 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))