Details

sample48.0ms

Algorithm

intervals

Results

14.0ms	51×	body	1280	valid
9.0ms	43×	body	640	valid
7.0ms	134×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify2.4s

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	1706	13
12	3584	13
done	5000	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ 1.0 x) (- x 1.0))
1.7b	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

rewrite160.0ms

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:

21.0ms	(/ x (+ x 1.0))
31.0ms	(/ (+ 1.0 x) (- x 1.0))
103.0ms	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

series269.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ x (+ x 1.0))
46.0ms	(/ (+ 1.0 x) (- x 1.0))
169.0ms	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

simplify1.1s

Counts

113 → 113

Iterations

Useful iterations: 2 (426.0ms)

Iter	Nodes	Cost
0	186	1584
1	448	1503
2	1902	1427
done	5000	1427

prune245.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- x 1.0))
0.2b	(cbrt (- x 1.0))
0.2b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
19.4b	(- (/ x (+ x 1.0)) (/ (/ (+ 1.0 x) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
42×	`cbrt-prod`
21×	`times-frac`
16×	`cbrt-div` `difference-of-squares`
14×	`add-cube-cbrt`
11×	`pow1` `distribute-lft-out--`
10×	`swap-sqr`
9×	`flip3--` `flip--`
8×	`pow1/3` `associate-r` `associate-l`
6×	`add-exp-log` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 112

Calls

4 calls:

4.0ms	(cbrt (- x 1.0))
4.0ms	(cbrt (- x 1.0))
40.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
224.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ 1.0 x) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (- x 1.0))
125.0ms	(cbrt (- x 1.0))
184.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
235.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ 1.0 x) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify1.3s

Counts

124 → 124

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	240	2491
1	573	2339
2	2109	1940
done	5000	1933

prune418.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3.0 x) 1.0)
0.0b	(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`sum-log`
2×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
1×	`associate-+r+`

Counts

2 → 24

Calls

2 calls:

12.0ms	(+ (* 3.0 x) 1.0)
39.0ms	(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

series89.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(+ (* 3.0 x) 1.0)
32.0ms	(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

simplify2.6s

Counts

30 → 30

Iterations

Useful iterations: 3 (861.0ms)

Iter	Nodes	Cost
0	50	397
1	167	375
2	675	345
3	3985	311
done	5002	311

prune60.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.5b	(/ 3.0 (pow x 3))
0.9b	(/ 1.0 (* x x))
10.3b	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
38×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp` `frac-add`
4×	`pow1` `cube-mult` `unpow3` `sum-log` `distribute-lft-out` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+`
2×	`+-commutative` `frac-2neg` `clear-num` `div-inv`
1×	`pow-to-exp` `associate-+l+` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

27.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
9.0ms	(/ 3.0 (pow x 3))
8.0ms	(/ 1.0 (* x x))
163.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
58.0ms	(/ 3.0 (pow x 3))
34.0ms	(/ 1.0 (* x x))
33.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify2.5s

Counts

129 → 129

Iterations

Useful iterations: 2 (880.0ms)

Iter	Nodes	Cost
0	194	1725
1	520	1505
2	3854	1414
done	5000	1414

prune313.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes41.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch134.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	7503.829948731607
10	-911936.9907706906	-4.3470241882695893e-07	-11192.062083074488

simplify10.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	64
1	35	49
2	42	49
3	45	49
done	45	49

end0.0ms

sample1.5s

Algorithm

intervals

Results

702.0ms	1707×	body	1280	valid
318.0ms	1227×	body	640	valid
172.0ms	4136×	body	80	valid
107.0ms	613×	body	320	valid
24.0ms	317×	body	160	valid