Average Error: 14.6 → 0.4
Time: 7.9s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b \cdot r}{\cos a \cdot \cos b - \log \left(e^{\sin b \cdot \sin a}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b \cdot r}{\cos a \cdot \cos b - \log \left(e^{\sin b \cdot \sin a}\right)}
(FPCore (r a b) :precision binary64 (* r (/ (sin b) (cos (+ a b)))))
↓
(FPCore (r a b)
 :precision binary64
 (/ (* (sin b) r) (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a)))))))
double code(double r, double a, double b) {
	return r * (sin(b) / cos(a + b));
}
↓
double code(double r, double a, double b) {
	return (sin(b) * r) / ((cos(a) * cos(b)) - log(exp(sin(b) * sin(a))));
}

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

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

  3. Applied cos-sum_binary640.3

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

  5. Applied associate-*r/_binary640.3

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

  6. Simplified0.3

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

  8. Applied add-log-exp_binary640.4

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2020253 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))