Average Error: 14.9 → 0.4
Time: 36.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r1028110 = r;
        double r1028111 = b;
        double r1028112 = sin(r1028111);
        double r1028113 = a;
        double r1028114 = r1028113 + r1028111;
        double r1028115 = cos(r1028114);
        double r1028116 = r1028112 / r1028115;
        double r1028117 = r1028110 * r1028116;
        return r1028117;
}
↓
double f(double r, double a, double b) {
        double r1028118 = r;
        double r1028119 = b;
        double r1028120 = sin(r1028119);
        double r1028121 = cos(r1028119);
        double r1028122 = a;
        double r1028123 = cos(r1028122);
        double r1028124 = r1028121 * r1028123;
        double r1028125 = sin(r1028122);
        double r1028126 = r1028125 * r1028120;
        double r1028127 = exp(r1028126);
        double r1028128 = log(r1028127);
        double r1028129 = r1028124 - r1028128;
        double r1028130 = r1028120 / r1028129;
        double r1028131 = r1028118 * r1028130;
        return r1028131;
}

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. 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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))