Details

sample60.0ms

Algorithm

intervals

Results

21.0ms	54×	body	1280	valid
10.0ms	44×	body	640	valid
8.0ms	132×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	7×	body	160	valid

simplify2.8s

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	79	13
9	183	13
10	535	13
11	1745	13
12	4085	13
done	5000	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite182.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

18.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
115.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series279.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ x (+ x 1.0))
68.0ms	(/ (+ x 1.0) (- x 1.0))
172.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify900.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (313.0ms)

Iter	Nodes	Cost
0	176	1584
1	408	1507
2	1794	1427
done	5002	1427

prune426.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
2.6b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

342×	`*-un-lft-identity`
208×	`times-frac`
152×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
73×	`distribute-lft-out`
72×	`swap-sqr`
44×	`associate-r` `associate-l`
36×	`distribute-lft-out--`
28×	`add-cbrt-cube` `add-exp-log`
21×	`difference-of-squares`
18×	`pow1`
16×	`associate-/r/`
9×	`frac-sub`
8×	`frac-times` `cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
5×	`flip3-+` `flip3--` `flip-+` `flip--`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log` `frac-add`

Counts

4 → 259

Calls

4 calls:

97.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
111.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
78.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
32.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
68.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
54.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
303.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify684.0ms

Counts

271 → 271

Iterations

Useful iterations: done (675.0ms)

Iter	Nodes	Cost
0	361	6049
1	1257	5349
done	5001	4953

prune857.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(cbrt (pow (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) 3))
0.1b	(pow (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) 3)
2.6b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
64×	`times-frac`
58×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
27×	`frac-sub`
24×	`swap-sqr`
22×	`cube-div`
19×	`frac-times` `associate-l/` `associate-r/`
18×	`associate-r` `associate-l` `distribute-lft-out`
17×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-prod`
12×	`pow1`
11×	`cbrt-div`
8×	`unpow-prod-down` `cube-prod` `associate-/r/`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow2` `pow-to-exp` `sub-neg` `pow-pow` `pow-plus` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 180

Calls

4 calls:

52.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
60.0ms	(cbrt (pow (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) 3))
36.0ms	(pow (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) 3)
25.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series979.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
295.0ms	(cbrt (pow (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) 3))
345.0ms	(pow (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) 3)
283.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify601.0ms

Counts

192 → 192

Iterations

Useful iterations: done (586.0ms)

Iter	Nodes	Cost
0	306	6064
1	1066	5427
done	5001	4635

prune791.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite892.0ms

Algorithm

rewrite-expression-head

Rules

236×	`*-un-lft-identity`
88×	`times-frac`
67×	`distribute-lft-out`
38×	`distribute-lft-out--`
32×	`add-sqr-sqrt`
16×	`associate-r`
12×	`associate-l`
10×	`add-log-exp`
9×	`frac-times`
8×	`difference-of-squares`
6×	`pow1` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `add-cube-cbrt` `flip-+`
5×	`flip3--` `frac-sub` `flip--`
3×	`sub-neg` `associate-l/` `associate-r/`
2×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 127

Calls

4 calls:

593.0ms	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
97.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
85.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
108.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

437.0ms	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
189.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
158.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
221.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.8s

Counts

139 → 139

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	153	3757
1	465	3645
2	2679	3421
done	5001	3419

prune405.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.7b

bsearch160.0ms

Steps

Iters	Range		Point
9	2205.5689030668646	4825064884.677679	12811.273113389769
10	-185496355225.45163	-22.8286883066892	-13946.27375560417

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	34	86
1	44	71
done	44	71

end0.0ms

sample1.3s

Algorithm

intervals

Results

436.0ms	1659×	body	1280	valid
317.0ms	4183×	body	80	valid
255.0ms	1242×	body	640	valid
107.0ms	629×	body	320	valid
25.0ms	287×	body	160	valid