Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	63×	body	1280	valid
6.0ms	45×	body	640	valid
4.0ms	117×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify573.0ms

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

localize12.0ms

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)))

rewrite184.0ms

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))
32.0ms	(/ (+ x 1.0) (- x 1.0))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series287.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ x (+ x 1.0))
63.0ms	(/ (+ x 1.0) (- x 1.0))
160.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.0s

Counts

113 → 113

Iterations

Useful iterations: done (2.0s)

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

prune357.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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)))

rewrite176.0ms

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:

9.0ms	(/ 3.0 (pow x 3))
119.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
43.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ 3.0 (pow x 3))
111.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
38.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

simplify1.8s

Counts

132 → 132

Iterations

Useful iterations: done (1.8s)

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

prune458.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

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	(- (pow (/ (- (+ (/ 1.0 x) 3.0)) x) 1) (/ 3.0 (pow x 3)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 165

Calls

3 calls:

105.0ms	(/ (- (+ (/ 1.0 x) 3.0)) x)
18.0ms	(/ 3.0 (pow x 3))
881.0ms	(- (pow (/ (- (+ (/ 1.0 x) 3.0)) x) 1) (/ 3.0 (pow x 3)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(/ (- (+ (/ 1.0 x) 3.0)) x)
78.0ms	(/ 3.0 (pow x 3))
51.0ms	(- (pow (/ (- (+ (/ 1.0 x) 3.0)) x) 1) (/ 3.0 (pow x 3)))

simplify1.3s

Counts

174 → 174

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	263	2923
1	522	2549
2	1389	2463
done	5001	2449

prune457.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

21.0ms	(/ x (+ x 1.0))
14.0ms	(/ 1 (- x 1.0))
49.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
108.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ x (+ x 1.0))
34.0ms	(/ 1 (- x 1.0))
63.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
171.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify1.7s

Counts

153 → 153

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	235	2040
1	564	1722
2	1782	1586
done	5000	1553

prune307.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes42.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch124.0ms

Steps

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

simplify12.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	34	81
1	53	64
2	56	64
done	56	64

end0.0ms

sample1.2s

Algorithm

intervals

Results

482.0ms	1770×	body	1280	valid
208.0ms	1220×	body	640	valid
161.0ms	4059×	body	80	valid
152.0ms	660×	body	320	valid
22.0ms	291×	body	160	valid