Average Error: 14.9 → 0.4
Time: 40.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)
double f(double r, double a, double b) {
        double r1424871 = r;
        double r1424872 = b;
        double r1424873 = sin(r1424872);
        double r1424874 = a;
        double r1424875 = r1424874 + r1424872;
        double r1424876 = cos(r1424875);
        double r1424877 = r1424873 / r1424876;
        double r1424878 = r1424871 * r1424877;
        return r1424878;
}
↓
double f(double r, double a, double b) {
        double r1424879 = 1.0;
        double r1424880 = b;
        double r1424881 = cos(r1424880);
        double r1424882 = a;
        double r1424883 = cos(r1424882);
        double r1424884 = r1424881 * r1424883;
        double r1424885 = sin(r1424880);
        double r1424886 = sin(r1424882);
        double r1424887 = r1424885 * r1424886;
        double r1424888 = r1424884 - r1424887;
        double r1424889 = r1424879 / r1424888;
        double r1424890 = r;
        double r1424891 = r1424890 * r1424885;
        double r1424892 = r1424889 * r1424891;
        return r1424892;
}

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 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. Using strategy rm

  5. Applied div-inv0.4

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

  6. Applied associate-*r*0.4

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

  7. Taylor expanded around inf 0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019107 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))