Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	54×	body	1280	valid
4.0ms	49×	body	640	valid
3.0ms	123×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	3×	body	160	valid

simplify121.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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	60	13
8	78	13
9	99	13
10	147	13
11	190	13
12	205	13
done	205	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite77.0ms

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:

7.0ms	(/ x (+ x 1.0))
11.0ms	(/ (+ x 1.0) (- x 1.0))
55.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
123.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify486.0ms

Counts

113 → 113

Iterations

Useful iterations: done (483.0ms)

Iter	Nodes	Cost
0	176	1584
1	399	1503
2	1294	1427
done	5000	1425

prune196.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
0.2b	(/ (- 1.0) (* x x))
0.3b	(/ 3.0 (pow x 3))
6.4b	(- (/ (- 1.0) (* x x)) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

61×	`times-frac`
58×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r` `associate-/l`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
9×	`unpow3`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `distribute-lft-out`
5×	`div-exp`
4×	`pow1` `cube-mult` `distribute-rgt-out` `div-inv` `sqr-pow`
3×	`cbrt-undiv` `frac-sub`
2×	`neg-sub0` `neg-mul-1` `frac-2neg` `flip3-+` `diff-log` `div-sub` `frac-add` `clear-num` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft1-in` `distribute-frac-neg` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `associate--r+`

Counts

4 → 146

Calls

4 calls:

40.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
5.0ms	(/ (- 1.0) (* x x))
4.0ms	(/ 3.0 (pow x 3))
122.0ms	(- (/ (- 1.0) (* x x)) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
24.0ms	(/ (- 1.0) (* x x))
37.0ms	(/ 3.0 (pow x 3))
31.0ms	(- (/ (- 1.0) (* x x)) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

simplify1.1s

Counts

158 → 158

Iterations

Useful iterations: 2 (226.0ms)

Iter	Nodes	Cost
0	236	2098
1	582	1830
2	3091	1732
done	5000	1732

prune281.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
1.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 329

Calls

4 calls:

48.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
31.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
113.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
41.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
350.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
199.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify417.0ms

Counts

341 → 341

Iterations

Useful iterations: done (403.0ms)

Iter	Nodes	Cost
0	410	10805
1	1285	9795
done	5000	9701

prune482.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- x 1.0))
0.3b	(cbrt (- x 1.0))
0.3b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
21.4b	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite166.0ms

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:

2.0ms	(cbrt (- x 1.0))
2.0ms	(cbrt (- x 1.0))
21.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
137.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (- x 1.0))
96.0ms	(cbrt (- x 1.0))
126.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
172.0ms	(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify602.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (172.0ms)

Iter	Nodes	Cost
0	238	2491
1	545	2351
2	1781	1940
done	5000	1940

prune267.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch87.0ms

Steps

Iters	Range		Point
11	0.08347146558812443	3.320253512051989e+22	12679.85899306799
8	-14583263.309321204	-1162.6651869185068	-11931.41196902016

simplify10.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	97
1	42	82
done	42	82

end0.0ms

sample526.0ms

Algorithm

intervals

Results

185.0ms	1731×	body	1280	valid
105.0ms	1265×	body	640	valid
92.0ms	4084×	body	80	valid
38.0ms	618×	body	320	valid
13.0ms	302×	body	160	valid