Average Error: 15.3 → 0.4
Time: 26.2s
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 r25826 = r;
        double r25827 = b;
        double r25828 = sin(r25827);
        double r25829 = a;
        double r25830 = r25829 + r25827;
        double r25831 = cos(r25830);
        double r25832 = r25828 / r25831;
        double r25833 = r25826 * r25832;
        return r25833;
}
↓
double f(double r, double a, double b) {
        double r25834 = r;
        double r25835 = b;
        double r25836 = sin(r25835);
        double r25837 = a;
        double r25838 = cos(r25837);
        double r25839 = cos(r25835);
        double r25840 = r25838 * r25839;
        double r25841 = sin(r25837);
        double r25842 = r25841 * r25836;
        double r25843 = exp(r25842);
        double r25844 = log(r25843);
        double r25845 = r25840 - r25844;
        double r25846 = r25836 / r25845;
        double r25847 = r25834 * r25846;
        return r25847;
}

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 15.3

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 2019326 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))