Details

sample42.0ms

Algorithm

intervals

Results

11.0ms	49×	body	1280	valid
9.0ms	49×	body	640	valid
6.0ms	119×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid

simplify165.0ms

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: 32.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite151.0ms

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:

11.0ms	(/ x (+ x 1.0))
25.0ms	(/ (+ x 1.0) (- x 1.0))
110.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series300.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ x (+ x 1.0))
45.0ms	(/ (+ x 1.0) (- x 1.0))
190.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.7s

Counts

113 → 113

Iterations

Useful iterations: done (1.7s)

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

prune262.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
0.4b	(/ 3.0 (pow x 3))
5.6b	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

rewrite121.0ms

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:

65.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
9.0ms	(/ 3.0 (pow x 3))
42.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

series161.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
43.0ms	(/ 3.0 (pow x 3))
34.0ms	(- (* (/ -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	2201	1511
done	5001	1507

prune326.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ (/ 1.0 x) x)) (/ (- 3.0) x))
0.1b	(/ (/ 1.0 x) x)
0.4b	(/ 3.0 (pow x 3))
5.6b	(- (+ (- (/ (/ 1.0 x) x)) (/ (- 3.0) x)) (/ 3.0 (pow x 3)))

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
112×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
16×	`associate-/l*` `add-log-exp`
15×	`associate-/r*`
14×	`add-exp-log` `distribute-rgt-neg-in`
13×	`unpow-prod-down` `cube-prod`
12×	`distribute-lft-out`
11×	`add-cbrt-cube`
10×	`div-inv`
6×	`div-exp` `distribute-lft-out--`
5×	`cube-mult` `distribute-frac-neg` `difference-of-squares` `sqr-pow`
4×	`pow1` `cbrt-undiv` `associate--l-` `neg-sub0` `unpow3` `sum-log`
3×	`diff-log` `frac-sub`
2×	`distribute-lft-neg-in` `associate-+l-` `associate-+r-` `distribute-rgt-out` `frac-2neg` `flip3-+` `div-sub` `unsub-neg` `neg-log` `frac-add` `clear-num` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `pow-to-exp` `sub-neg` `distribute-neg-out` `flip3--` `pow-exp` `associate--l+` `flip--` `associate-/l/`

Counts

4 → 195

Calls

4 calls:

280.0ms	(+ (- (/ (/ 1.0 x) x)) (/ (- 3.0) x))
23.0ms	(/ (/ 1.0 x) x)
16.0ms	(/ 3.0 (pow x 3))
2.0s	(- (+ (- (/ (/ 1.0 x) x)) (/ (- 3.0) x)) (/ 3.0 (pow x 3)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (- (/ (/ 1.0 x) x)) (/ (- 3.0) x))
39.0ms	(/ (/ 1.0 x) x)
61.0ms	(/ 3.0 (pow x 3))
56.0ms	(- (+ (- (/ (/ 1.0 x) x)) (/ (- 3.0) x)) (/ 3.0 (pow x 3)))

simplify1.4s

Counts

207 → 207

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	322	2984
1	715	2695
2	2076	2484
done	5000	2477

prune434.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(pow (/ x (+ x 1.0)) 3)
3.9b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
13.9b	(/ (* x x) (* (+ x 1.0) (+ x 1.0)))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
153×	`times-frac`
142×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
61×	`distribute-lft-out--`
48×	`distribute-lft-out`
44×	`difference-of-squares`
42×	`add-cube-cbrt`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r/`
14×	`sqr-pow`
8×	`flip3-+` `flip-+`
6×	`pow1` `cbrt-undiv` `pow-unpow` `div-exp` `add-log-exp`
5×	`div-inv`
4×	`cube-div` `frac-times` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `associate-r/` `associate-l/`
1×	`difference-cubes` `sub-neg` `frac-2neg` `diff-log` `clear-num` `associate-/r` `frac-sub` `associate-/l`

Counts

4 → 244

Calls

4 calls:

29.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
24.0ms	(pow (/ x (+ x 1.0)) 3)
268.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
22.0ms	(/ (* x x) (* (+ x 1.0) (+ x 1.0)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
80.0ms	(pow (/ x (+ x 1.0)) 3)
370.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
74.0ms	(/ (* x x) (* (+ x 1.0) (+ x 1.0)))

simplify2.7s

Counts

256 → 256

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	334	5307
1	1050	4891
2	4114	4517
done	5001	4513

prune596.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes64.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.0b

bsearch1.0ms

simplify9.0ms

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	36	84
1	48	84
2	54	83
done	54	83

end0.0ms

sample1.4s

Algorithm

intervals

Results

568.0ms	4134×	body	80	valid
434.0ms	1685×	body	1280	valid
171.0ms	1271×	body	640	valid
64.0ms	611×	body	320	valid
25.0ms	299×	body	160	valid