Details

sample31.0ms

Algorithm

intervals

Results

8.0ms	49×	body	1280	valid
7.0ms	49×	body	640	valid
4.0ms	119×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid

simplify182.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize14.0ms

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)))

rewrite181.0ms

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))
38.0ms	(/ (+ x 1.0) (- x 1.0))
126.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series286.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ x (+ x 1.0))
64.0ms	(/ (+ x 1.0) (- x 1.0))
179.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.9s

Counts

113 → 113

Iterations

Useful iterations: done (1.9s)

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

prune288.0ms

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)))

rewrite163.0ms

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:

95.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
10.0ms	(/ 3.0 (pow x 3))
50.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
74.0ms	(/ 3.0 (pow x 3))
41.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

simplify1.8s

Counts

132 → 132

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	229	1884
1	624	1631
2	2201	1511
done	5001	1507

prune299.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite363.0ms

Algorithm

rewrite-expression-head

Rules

58×	`times-frac`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
9×	`frac-add`
8×	`add-log-exp`
7×	`div-exp`
5×	`pow1` `cbrt-undiv`
4×	`cube-mult` `frac-times` `unpow3` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
3×	`flip3--` `frac-sub` `flip--` `div-inv` `associate-/l*`
2×	`associate-+r+` `sum-log`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `*-commutative` `flip-+`

Counts

3 → 139

Calls

3 calls:

24.0ms	(* (/ -1 x) (/ 1.0 x))
9.0ms	(/ 3.0 (pow x 3))
322.0ms	(+ (* (/ -1 x) (/ 1.0 x)) (- (/ (- 3.0) x) (/ 3.0 (pow x 3))))

series140.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (/ -1 x) (/ 1.0 x))
58.0ms	(/ 3.0 (pow x 3))
37.0ms	(+ (* (/ -1 x) (/ 1.0 x)) (- (/ (- 3.0) x) (/ 3.0 (pow x 3))))

simplify1.9s

Counts

148 → 148

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	270	2275
1	754	1955
2	2864	1783
done	5000	1778

prune393.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

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)))

rewrite442.0ms

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:

26.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
26.0ms	(pow (/ x (+ x 1.0)) 3)
341.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
32.0ms	(/ (* x x) (* (+ x 1.0) (+ x 1.0)))

series610.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
92.0ms	(pow (/ x (+ x 1.0)) 3)
381.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
60.0ms	(/ (* x x) (* (+ x 1.0) (+ x 1.0)))

simplify2.2s

Counts

256 → 256

Iterations

Useful iterations: done (2.2s)

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

prune631.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

99.4% (0.2b remaining)

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

bsearch1.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	85
1	48	85
done	48	85

end0.0ms

sample1.6s

Algorithm

intervals

Results

819.0ms	1685×	body	1280	valid
301.0ms	1271×	body	640	valid
221.0ms	4134×	body	80	valid
71.0ms	611×	body	320	valid
24.0ms	299×	body	160	valid