Average Error: 15.2 → 0.4
Time: 6.5s
Precision: binary64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left({\left(e^{\sin a}\right)}^{\sin b}\right)}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left({\left(e^{\sin a}\right)}^{\sin b}\right)}
(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))
↓
(FPCore (r a b)
 :precision binary64
 (/ (* r (sin b)) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
double code(double r, double a, double b) {
	return (r * sin(b)) / cos(a + b);
}
↓
double code(double r, double a, double b) {
	return (r * sin(b)) / ((cos(a) * cos(b)) - log(pow(exp(sin(a)), sin(b))));
}

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 15.2

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

  3. Applied cos-sum_binary64_5530.3

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

  5. Applied add-log-exp_binary64_4580.4

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

  7. Applied add-log-exp_binary64_4580.4

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020343 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))