Average Error: 14.6 → 0.4
Time: 6.0s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \log \left(e^{\sin a \cdot \sin b}\right)}\]
\frac{r \cdot \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 r15646 = r;
        double r15647 = b;
        double r15648 = sin(r15647);
        double r15649 = r15646 * r15648;
        double r15650 = a;
        double r15651 = r15650 + r15647;
        double r15652 = cos(r15651);
        double r15653 = r15649 / r15652;
        return r15653;
}
↓
double f(double r, double a, double b) {
        double r15654 = r;
        double r15655 = b;
        double r15656 = sin(r15655);
        double r15657 = cos(r15655);
        double r15658 = a;
        double r15659 = cos(r15658);
        double r15660 = r15657 * r15659;
        double r15661 = sin(r15658);
        double r15662 = r15661 * r15656;
        double r15663 = exp(r15662);
        double r15664 = log(r15663);
        double r15665 = r15660 - r15664;
        double r15666 = r15656 / r15665;
        double r15667 = r15654 * r15666;
        return r15667;
}

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 14.6

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

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

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Simplified0.3

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

  10. Applied add-log-exp0.4

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

  11. 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 2020062 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))