Average Error: 14.9 → 0.3
Time: 52.1s
Precision: binary64
Cost: 32704
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
\frac{r \cdot \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
Cost26176
\[\frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}\]
Alternative 3
Error14.8
Cost13248
\[r \cdot \frac{\sin b}{\cos \left(b + a\right)}\]
Alternative 4
Error14.9
Cost13248
\[\frac{r \cdot \sin b}{\cos \left(b + a\right)}\]
Alternative 5
Error15.2
Cost13762
\[\begin{array}{l} \mathbf{if}\;a \leq -1.4900711756188913 \cdot 10^{-06}:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos a}\\ \mathbf{elif}\;a \leq 6170342723.028669:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{else}:\\ \;\;\;\;\frac{r \cdot \sin b}{\cos a}\\ \end{array}\]
Alternative 6
Error15.2
Cost13448
\[\begin{array}{l} \mathbf{if}\;a \leq -0.00016507842525845492 \lor \neg \left(a \leq 6170342723.028669\right):\\ \;\;\;\;\frac{r \cdot \sin b}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \end{array}\]
Alternative 7
Error15.2
Cost13448
\[\begin{array}{l} \mathbf{if}\;b \leq -70789682870.41708 \lor \neg \left(b \leq 6.033058917648657 \cdot 10^{-05}\right):\\ \;\;\;\;r \cdot \frac{\sin b}{\cos b}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \end{array}\]
Alternative 8
Error15.2
Cost13448
\[\begin{array}{l} \mathbf{if}\;b \leq -70789682870.41708 \lor \neg \left(b \leq 0.00011667278309408788\right):\\ \;\;\;\;\frac{r \cdot \sin b}{\cos b}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{r}{\cos a}\\ \end{array}\]
Alternative 9
Error31.4
Cost6848
\[\frac{r \cdot b}{\cos \left(b + a\right)}\]
Alternative 10
Error31.4
Cost6720
\[b \cdot \frac{r}{\cos a}\]
Alternative 11
Error31.4
Cost6720
\[r \cdot \frac{b}{\cos a}\]
Alternative 12
Error41.9
Cost192
\[r \cdot b\]
Alternative 13
Error54.0
Cost64
\[0\]
Alternative 14
Error61.7
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 14.9

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

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

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2021065 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))