Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	53×	body	1280	valid
3.0ms	40×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	12×	body	160	valid

simplify116.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

10.0ms	(/ x (+ x 1.0))
25.0ms	(/ (+ x 1.0) (- x 1.0))
85.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series192.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ x (+ x 1.0))
36.0ms	(/ (+ x 1.0) (- x 1.0))
124.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	176	1584
1	390	1503
2	1022	1427
3	2388	1414
done	5000	1412

prune199.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (+ 3.0 (* 1.0 x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
2×	`associate-*r/`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp` `unswap-sqr`

Counts

1 → 22

Calls

1 calls:

15.0ms

(* x (+ 3.0 (* 1.0 x)))

series65.0ms

Counts

1 → 3

Calls

1 calls:

65.0ms

(* x (+ 3.0 (* 1.0 x)))

simplify1.3s

Counts

25 → 25

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	50	253
1	143	244
2	479	216
3	1693	216
done	5000	216

prune40.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ 3.0 (pow x 3))
0.3b	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
6.2b	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
13×	`add-exp-log` `associate-l`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
10×	`add-cbrt-cube`
5×	`pow1` `frac-sub` `add-log-exp`
4×	`cube-mult` `frac-times` `flip3-+` `unpow3` `associate-r/` `div-exp` `associate-r*` `flip-+` `sqr-pow`
3×	`associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `associate-*l/` `prod-exp` `associate--l+` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `*-commutative` `flip--` `distribute-lft-out`

Counts

3 → 123

Calls

3 calls:

8.0ms	(/ 3.0 (pow x 3))
55.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
33.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ 3.0 (pow x 3))
73.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
32.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

simplify1.1s

Counts

132 → 132

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	229	1884
1	624	1631
2	2207	1511
done	5001	1507

prune224.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (+ 3.0 (/ 1.0 x)) x)
0.3b	(/ 3.0 (pow x 3))
6.2b	(- (* -1 (/ (+ 3.0 (/ 1.0 x)) x)) (/ 3.0 (pow x 3)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
45×	`*-un-lft-identity`
37×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
10×	`add-exp-log`
7×	`add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`cube-mult` `unpow3` `div-exp` `distribute-lft-out` `sqr-pow`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*r/` `pow-exp` `frac-sub` `flip--` `flip-+`

Counts

3 → 111

Calls

3 calls:

35.0ms	(/ (+ 3.0 (/ 1.0 x)) x)
8.0ms	(/ 3.0 (pow x 3))
28.0ms	(- (* -1 (/ (+ 3.0 (/ 1.0 x)) x)) (/ 3.0 (pow x 3)))

series138.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ (+ 3.0 (/ 1.0 x)) x)
36.0ms	(/ 3.0 (pow x 3))
32.0ms	(- (* -1 (/ (+ 3.0 (/ 1.0 x)) x)) (/ 3.0 (pow x 3)))

simplify741.0ms

Counts

120 → 120

Iterations

Useful iterations: done (738.0ms)

Iter	Nodes	Cost
0	184	1571
1	401	1368
2	1219	1272
done	5000	1267

prune199.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 31.6b

bsearch79.0ms

Steps

Iters	Range		Point
11	6.1632953816490534e-12	2923699147.8271213	0.9975580681503712
10	-21283307590.397102	-3.152803306627408e-07	-0.9868159492179903

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	47
1	32	32
2	34	32
3	38	32
4	40	32
done	40	32

end0.0ms

sample548.0ms

Algorithm

intervals

Results

167.0ms	1669×	body	1280	valid
101.0ms	4129×	body	80	valid
96.0ms	1239×	body	640	valid
38.0ms	644×	body	320	valid
14.0ms	319×	body	160	valid