Average Error: 14.7 → 0.3
Time: 19.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[-\frac{r \cdot \sin b}{\sin a \cdot \sin b - \cos b \cdot \cos a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
-\frac{r \cdot \sin b}{\sin a \cdot \sin b - \cos b \cdot \cos a}
double f(double r, double a, double b) {
        double r28500 = r;
        double r28501 = b;
        double r28502 = sin(r28501);
        double r28503 = a;
        double r28504 = r28503 + r28501;
        double r28505 = cos(r28504);
        double r28506 = r28502 / r28505;
        double r28507 = r28500 * r28506;
        return r28507;
}
↓
double f(double r, double a, double b) {
        double r28508 = r;
        double r28509 = b;
        double r28510 = sin(r28509);
        double r28511 = r28508 * r28510;
        double r28512 = a;
        double r28513 = sin(r28512);
        double r28514 = r28513 * r28510;
        double r28515 = cos(r28509);
        double r28516 = cos(r28512);
        double r28517 = r28515 * r28516;
        double r28518 = r28514 - r28517;
        double r28519 = r28511 / r28518;
        double r28520 = -r28519;
        return r28520;
}

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 14.7

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Simplified0.3

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sin b \cdot \sin a}}\]
  5. Using strategy rm

  6. Applied frac-2neg0.3

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

  7. Taylor expanded around inf 0.3

    \[\leadsto \color{blue}{-1 \cdot \frac{r \cdot \sin b}{\sin a \cdot \sin b - \cos b \cdot \cos a}}\]

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019235 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))