Average Error: 14.5 → 0.3
Time: 1.4min
Precision: binary64
Cost: 32704
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \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 b) (cos a)) (* (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(b) * cos(a)) - (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
Error0.4
Cost26304
\[r \cdot \frac{1}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}\]
Alternative 2
Error0.3
Cost26176
\[\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}\]
Alternative 3
Error14.5
Cost13248
\[r \cdot \frac{\sin b}{\cos \left(b + a\right)}\]
Alternative 4
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 5
Error16.0
Cost13448
\[\begin{array}{l} \mathbf{if}\;b \leq -6447650229.15258 \lor \neg \left(b \leq 1.1400914348472507 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{r \cdot \sin b}{\cos b}\\ \mathbf{else}:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos a}\\ \end{array}\]
Alternative 6
Error28.5
Cost13120
\[r \cdot \frac{\sin b}{\cos a}\]
Alternative 7
Error28.4
Cost7048
\[\begin{array}{l} \mathbf{if}\;b \leq -10.923607995985302 \lor \neg \left(b \leq 582574895630.2306\right):\\ \;\;\;\;r \cdot \sin b\\ \mathbf{else}:\\ \;\;\;\;r \cdot \frac{b}{\cos a}\\ \end{array}\]
Alternative 8
Error38.8
Cost6592
\[r \cdot \sin b\]
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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity_binary64_4190.3

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

  6. Applied times-frac_binary64_4250.3

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

  7. Simplified0.3

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

  8. Simplified0.3

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

  10. Applied *-un-lft-identity_binary64_4190.3

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

  12. Applied pow1_binary64_4800.3

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

  13. Simplified0.3

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

  14. Final simplification0.3

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

Reproduce

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