Average Error: 14.4 → 0.3
Time: 14.7s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)} \]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a} \]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}

(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)) (* (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 r * (sin(b) / ((cos(a) * cos(b)) - (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 14.4

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

  2. Applied cos-sum_binary640.3

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

  3. Applied *-un-lft-identity_binary640.3

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

  4. Applied *-un-lft-identity_binary640.3

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

  5. Applied times-frac_binary640.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2022081 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))