Average Error: 14.8 → 0.3
Time: 6.4s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r16799 = r;
        double r16800 = b;
        double r16801 = sin(r16800);
        double r16802 = a;
        double r16803 = r16802 + r16800;
        double r16804 = cos(r16803);
        double r16805 = r16801 / r16804;
        double r16806 = r16799 * r16805;
        return r16806;
}
↓
double f(double r, double a, double b) {
        double r16807 = r;
        double r16808 = b;
        double r16809 = sin(r16808);
        double r16810 = cos(r16808);
        double r16811 = a;
        double r16812 = cos(r16811);
        double r16813 = r16810 * r16812;
        double r16814 = sin(r16811);
        double r16815 = r16814 * r16809;
        double r16816 = r16813 - r16815;
        double r16817 = r16809 / r16816;
        double r16818 = r16807 * r16817;
        return r16818;
}

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 14.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.3

    \[\leadsto r \cdot \color{blue}{\frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}}\]

  7. Final simplification0.3

    \[\leadsto r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))