Details

sample29.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	163
1	17	163
2	27	163
3	39	163
4	50	163
5	65	163
6	118	163
7	199	163
8	302	163
9	445	163
10	550	163
11	680	163
12	792	163
13	926	163
14	1036	163
15	1176	163
16	1292	163
17	1434	163
18	1549	163
19	1689	163
20	1805	163
21	1947	163
22	2062	163
23	2202	163
24	2318	163
25	2460	163
26	2575	163
27	2715	163
28	2831	163
29	2973	163
30	3088	163
31	3228	163
32	3344	163
33	3486	163
34	3601	163
35	3741	163
36	3857	163
37	3999	163
38	4114	163
39	4254	163
40	4370	163
41	4512	163
42	4627	163
43	4767	163
44	4883	163
done	5000	163

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (- x y) (- 2.0 (+ x y)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
30×	`times-frac`
19×	`distribute-lft-out--`
14×	`add-cube-cbrt`
13×	`difference-of-squares`
6×	`associate-/r*` `distribute-lft-out`
5×	`associate-/l*`
3×	`add-cbrt-cube` `add-exp-log`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 60

Calls

1 calls:

68.0ms

(/ (- x y) (- 2.0 (+ x y)))

series71.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

(/ (- x y) (- 2.0 (+ x y)))

simplify2.4s

Counts

63 → 63

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	114	21096
1	289	19250
2	791	19110
3	3410	18990
done	5009	18990

prune270.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
0.0b	(/ x (- 2.0 (+ x y)))
0.0b	(/ y (- 2.0 (+ x y)))

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

1352×	`*-un-lft-identity`
946×	`times-frac`
843×	`add-sqr-sqrt`
576×	`prod-diff`
517×	`add-cube-cbrt`
335×	`distribute-lft-out--`
161×	`distribute-lft-out` `difference-of-squares`
106×	`associate-/r/`
54×	`flip3--` `flip--`
53×	`div-inv`
24×	`fma-neg`
12×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `distribute-rgt-out--` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `diff-log` `frac-sub` `sub-div`

Counts

3 → 722

Calls

3 calls:

390.0ms	(- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
35.0ms	(/ x (- 2.0 (+ x y)))
30.0ms	(/ y (- 2.0 (+ x y)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))
64.0ms	(/ x (- 2.0 (+ x y)))
58.0ms	(/ y (- 2.0 (+ x y)))

simplify3.3s

Counts

731 → 731

Iterations

Useful iterations: 2 (1.8s)

Iter	Nodes	Cost
0	580	609027
1	1339	535964
2	3295	478177
done	5000	478177

prune2.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (- 2.0 (+ x y)))
0.0b	(- (/ x (- 2.0 (+ x y))) (/ 1 (/ (- 2.0 (+ x y)) y)))
0.0b	(/ (- 2.0 (+ x y)) y)
0.2b	(/ 1 (/ (- 2.0 (+ x y)) y))

rewrite829.0ms

Algorithm

rewrite-expression-head

Rules

4373×	`times-frac`
4363×	`*-un-lft-identity`
3018×	`add-sqr-sqrt`
2081×	`add-cube-cbrt`
1704×	`prod-diff`
911×	`distribute-lft-out--`
462×	`difference-of-squares`
453×	`distribute-lft-out`
176×	`div-inv`
171×	`associate-/r/`
75×	`flip3--` `flip--`
31×	`associate-/r*`
24×	`fma-neg`
19×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`associate-/l*`
9×	`div-exp`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `1-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `frac-sub` `pow-flip` `inv-pow`

Counts

4 → 1959

Calls

4 calls:

24.0ms	(/ x (- 2.0 (+ x y)))
346.0ms	(- (/ x (- 2.0 (+ x y))) (/ 1 (/ (- 2.0 (+ x y)) y)))
52.0ms	(/ (- 2.0 (+ x y)) y)
46.0ms	(/ 1 (/ (- 2.0 (+ x y)) y))

series294.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ x (- 2.0 (+ x y)))
82.0ms	(- (/ x (- 2.0 (+ x y))) (/ 1 (/ (- 2.0 (+ x y)) y)))
45.0ms	(/ (- 2.0 (+ x y)) y)
96.0ms	(/ 1 (/ (- 2.0 (+ x y)) y))

simplify5.7s

Counts

1971 → 1971

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	1456	2102234
1	3402	1588984
done	5002	1495059

prune9.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- 2.0 (+ x y)) y))
0.2b	(/ 1 (/ (- 2.0 (+ x y)) y))
0.2b	(/ 1 (/ (- 2.0 (+ x y)) y))
4.3b	(/ (- (* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))) (* (/ 1 (/ (- 2.0 (+ x y)) y)) (/ 1 (/ (- 2.0 (+ x y)) y)))) (+ (/ x (- 2.0 (+ x y))) (/ 1 (/ (- 2.0 (+ x y)) y))))

rewrite694.0ms

Algorithm

rewrite-expression-head

Rules

477×	`*-un-lft-identity`
476×	`times-frac`
279×	`add-sqr-sqrt`
207×	`add-cube-cbrt`
82×	`distribute-lft-out--`
74×	`associate-/r*`
66×	`distribute-lft-out`
45×	`difference-of-squares`
39×	`add-exp-log`
22×	`div-exp`
21×	`add-cbrt-cube` `div-inv`
14×	`associate-/l/`
13×	`associate-/l*`
12×	`frac-sub`
10×	`cbrt-undiv`
7×	`frac-times` `pow1` `associate-l/` `associate-r/`
6×	`rec-exp` `1-exp` `associate-/r/`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv` `pow-flip` `inv-pow`
1×	`flip3-+` `flip3--` `div-sub` `frac-add` `flip-+` `flip--`

Counts

4 → 418

Calls

4 calls:

46.0ms	(/ 1 (/ (- 2.0 (+ x y)) y))
33.0ms	(/ 1 (/ (- 2.0 (+ x y)) y))
34.0ms	(/ 1 (/ (- 2.0 (+ x y)) y))
551.0ms	(/ (- (* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))) (* (/ 1 (/ (- 2.0 (+ x y)) y)) (/ 1 (/ (- 2.0 (+ x y)) y)))) (+ (/ x (- 2.0 (+ x y))) (/ 1 (/ (- 2.0 (+ x y)) y))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ 1 (/ (- 2.0 (+ x y)) y))
75.0ms	(/ 1 (/ (- 2.0 (+ x y)) y))
73.0ms	(/ 1 (/ (- 2.0 (+ x y)) y))
231.0ms	(/ (- (* (/ x (- 2.0 (+ x y))) (/ x (- 2.0 (+ x y)))) (* (/ 1 (/ (- 2.0 (+ x y)) y)) (/ 1 (/ (- 2.0 (+ x y)) y)))) (+ (/ x (- 2.0 (+ x y))) (/ 1 (/ (- 2.0 (+ x y)) y))))

simplify351.0ms

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	285	182576