Average Error: 15.0 → 0.3
Time: 30.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r761982 = r;
        double r761983 = b;
        double r761984 = sin(r761983);
        double r761985 = a;
        double r761986 = r761985 + r761983;
        double r761987 = cos(r761986);
        double r761988 = r761984 / r761987;
        double r761989 = r761982 * r761988;
        return r761989;
}
↓
double f(double r, double a, double b) {
        double r761990 = r;
        double r761991 = b;
        double r761992 = sin(r761991);
        double r761993 = r761990 * r761992;
        double r761994 = a;
        double r761995 = cos(r761994);
        double r761996 = cos(r761991);
        double r761997 = r761995 * r761996;
        double r761998 = sin(r761994);
        double r761999 = r761992 * r761998;
        double r762000 = r761997 - r761999;
        double r762001 = r761993 / r762000;
        return r762001;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

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

  5. Applied associate-*r/0.3

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

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

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

  8. Applied associate-*r*0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

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