Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	63×	body	1280	valid
5.0ms	45×	body	640	valid
4.0ms	117×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify160.0ms

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: 32.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite149.0ms

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:

12.0ms	(/ x (+ x 1.0))
29.0ms	(/ (+ x 1.0) (- x 1.0))
100.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series253.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ x (+ x 1.0))
59.0ms	(/ (+ x 1.0) (- x 1.0))
146.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: done (1.8s)

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

prune267.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 3.0 (pow x 3))
0.3b	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
4.4b	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

rewrite177.0ms

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:

14.0ms	(/ 3.0 (pow x 3))
88.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
65.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ 3.0 (pow x 3))
129.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
42.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

simplify1.7s

Counts

132 → 132

Iterations

Useful iterations: done (1.7s)

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

prune336.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (+ (/ 1.0 x) 3.0)) x)
0.2b	(/ 3.0 (pow x 3))
4.4b	(- (/ (- (+ (/ 1.0 x) 3.0)) x) (/ 3.0 (pow x 3)))

rewrite570.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac`
84×	`add-sqr-sqrt` `*-un-lft-identity`
53×	`add-cube-cbrt`
18×	`distribute-rgt-neg-in`
16×	`distribute-lft-neg-in`
15×	`associate-/r` `associate-/l`
14×	`unpow-prod-down` `cube-prod`
10×	`add-exp-log` `difference-of-squares`
9×	`distribute-lft-out`
7×	`add-cbrt-cube`
6×	`sqr-pow`
5×	`add-log-exp`
4×	`cube-mult` `neg-mul-1` `unpow3` `div-exp` `distribute-lft-out--`
3×	`pow1`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `div-inv` `associate-/l/` `distribute-neg-frac`
1×	`associate--l-` `pow-to-exp` `sub-neg` `flip3--` `flip3-+` `diff-log` `distribute-frac-neg` `pow-exp` `frac-sub` `flip--` `flip-+`

Counts

3 → 160

Calls

3 calls:

107.0ms	(/ (- (+ (/ 1.0 x) 3.0)) x)
14.0ms	(/ 3.0 (pow x 3))
442.0ms	(- (/ (- (+ (/ 1.0 x) 3.0)) x) (/ 3.0 (pow x 3)))

series538.0ms

Counts

3 → 9

Calls

3 calls:

449.0ms	(/ (- (+ (/ 1.0 x) 3.0)) x)
54.0ms	(/ 3.0 (pow x 3))
35.0ms	(- (/ (- (+ (/ 1.0 x) 3.0)) x) (/ 3.0 (pow x 3)))

simplify1.2s

Counts

169 → 169

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	244	2529
1	495	2295
2	1366	2213
done	5001	2194

prune513.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (- x 1.0))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
6.6b	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
44×	`times-frac`
33×	`add-cube-cbrt`
21×	`associate-l`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `frac-sub` `flip-+` `distribute-lft-out`
4×	`frac-times` `associate-r/` `associate-r*` `prod-exp`
3×	`cbrt-undiv` `flip3--` `flip--` `div-inv` `unswap-sqr`
2×	`distribute-rgt-in` `rec-exp` `frac-2neg` `distribute-lft-in` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod` `associate--r+`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

12.0ms	(/ x (+ x 1.0))
14.0ms	(/ 1 (- x 1.0))
64.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
109.0ms	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ x (+ x 1.0))
33.0ms	(/ 1 (- x 1.0))
53.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
177.0ms	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

simplify1.5s

Counts

155 → 155

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	241	2054
1	683	1761
2	2032	1617
done	5002	1600

prune288.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes39.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch112.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	11917.97074271185
7	-41918.349557210015	-1608.0958488538781	-10439.152056359573

simplify10.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	32	77
1	49	64
2	52	64
done	52	64

end0.0ms

sample1.3s

Algorithm

intervals

Results

479.0ms	1770×	body	1280	valid
325.0ms	1220×	body	640	valid
178.0ms	4059×	body	80	valid
109.0ms	660×	body	320	valid
23.0ms	291×	body	160	valid