Average Error: 14.5 → 0.3
Time: 2.5min
Precision: binary64
Cost: 32704
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
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

Alternatives

Alternative 1
Error0.3
Cost32704
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
Alternative 2
Error0.4
Cost26304
\[r \cdot \frac{1}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}\]
Alternative 3
Error0.4
Cost26176
\[\frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}\]
Alternative 4
Error14.5
Cost13248
\[r \cdot \frac{\sin b}{\cos \left(b + a\right)}\]
Alternative 5
Error16.0
Cost13762
\[\begin{array}{l} \mathbf{if}\;b \leq -6447650229.15258:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{elif}\;b \leq 1.1400914348472507 \cdot 10^{+52}:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\frac{r \cdot \sin b}{\cos b}\\ \end{array}\]
Alternative 6
Error15.0
Cost13762
\[\begin{array}{l} \mathbf{if}\;b \leq -1253051527.059556:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{elif}\;b \leq 658.9103230507245:\\ \;\;\;\;r \cdot \frac{b}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\frac{r \cdot \sin b}{\cos b}\\ \end{array}\]
Alternative 7
Error15.0
Cost13448
\[\begin{array}{l} \mathbf{if}\;b \leq -1253051527.059556 \lor \neg \left(b \leq 658.9103230507245\right):\\ \;\;\;\;\frac{r \cdot \sin b}{\cos b}\\ \mathbf{else}:\\ \;\;\;\;r \cdot \frac{b}{\cos a}\\ \end{array}\]
Alternative 8
Error31.1
Cost6720
\[r \cdot \frac{b}{\cos a}\]
Alternative 9
Error41.6
Cost192
\[r \cdot b\]
Alternative 10
Error54.0
Cost64
\[0\]
Alternative 11
Error61.7
Cost64
\[-1\]

Error

Derivation

  1. Initial program 14.5

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

  3. Applied cos-sum_binary64_2120.3

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

  4. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2021014 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))