Average Error: 15.0 → 0.4
Time: 11.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r18857 = r;
        double r18858 = b;
        double r18859 = sin(r18858);
        double r18860 = a;
        double r18861 = r18860 + r18858;
        double r18862 = cos(r18861);
        double r18863 = r18859 / r18862;
        double r18864 = r18857 * r18863;
        return r18864;
}
↓
double f(double r, double a, double b) {
        double r18865 = r;
        double r18866 = b;
        double r18867 = sin(r18866);
        double r18868 = a;
        double r18869 = cos(r18868);
        double r18870 = cos(r18866);
        double r18871 = r18869 * r18870;
        double r18872 = sin(r18868);
        double r18873 = r18872 * r18867;
        double r18874 = exp(r18873);
        double r18875 = log(r18874);
        double r18876 = r18871 - r18875;
        double r18877 = r18867 / r18876;
        double r18878 = r18865 * r18877;
        return r18878;
}

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 15.0

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 add-log-exp0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))