Average Error: 15.3 → 0.4
Time: 26.7s
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 r25819 = r;
        double r25820 = b;
        double r25821 = sin(r25820);
        double r25822 = a;
        double r25823 = r25822 + r25820;
        double r25824 = cos(r25823);
        double r25825 = r25821 / r25824;
        double r25826 = r25819 * r25825;
        return r25826;
}
↓
double f(double r, double a, double b) {
        double r25827 = r;
        double r25828 = b;
        double r25829 = sin(r25828);
        double r25830 = a;
        double r25831 = cos(r25830);
        double r25832 = cos(r25828);
        double r25833 = r25831 * r25832;
        double r25834 = sin(r25830);
        double r25835 = r25834 * r25829;
        double r25836 = exp(r25835);
        double r25837 = log(r25836);
        double r25838 = r25833 - r25837;
        double r25839 = r25829 / r25838;
        double r25840 = r25827 * r25839;
        return r25840;
}

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)))))