Average Error: 14.9 → 0.4
Time: 17.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{1}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{1}{\frac{\cos a \cdot \cos b}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r25953 = r;
        double r25954 = b;
        double r25955 = sin(r25954);
        double r25956 = a;
        double r25957 = r25956 + r25954;
        double r25958 = cos(r25957);
        double r25959 = r25955 / r25958;
        double r25960 = r25953 * r25959;
        return r25960;
}
↓
double f(double r, double a, double b) {
        double r25961 = r;
        double r25962 = 1.0;
        double r25963 = a;
        double r25964 = cos(r25963);
        double r25965 = b;
        double r25966 = cos(r25965);
        double r25967 = r25964 * r25966;
        double r25968 = sin(r25965);
        double r25969 = r25967 / r25968;
        double r25970 = sin(r25963);
        double r25971 = r25969 - r25970;
        double r25972 = r25962 / r25971;
        double r25973 = r25961 * r25972;
        return r25973;
}

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 14.9

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Simplified0.3

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

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

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

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

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

  8. Applied times-frac0.3

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

  9. Simplified0.3

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019212 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))