Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	55×	body	1280	valid
4.0ms	39×	body	640	valid
3.0ms	124×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	13×	body	160	valid

simplify197.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite235.0ms

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))
31.0ms	(/ (+ x 1.0) (- x 1.0))
184.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series250.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ x (+ x 1.0))
57.0ms	(/ (+ x 1.0) (- x 1.0))
148.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: done (1.8s)

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

prune280.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 x) 3.0)
0.1b	(/ 3.0 (pow x 3))
0.3b	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
6.0b	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

15.0ms	(+ (/ 1.0 x) 3.0)
12.0ms	(/ 3.0 (pow x 3))
60.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
68.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (/ 1.0 x) 3.0)
42.0ms	(/ 3.0 (pow x 3))
78.0ms	(* (/ -1 x) (+ (/ 1.0 x) 3.0))
43.0ms	(- (* (/ -1 x) (+ (/ 1.0 x) 3.0)) (/ 3.0 (pow x 3)))

simplify1.6s

Counts

147 → 147

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	236	2019
1	634	1763
2	2205	1627
done	5001	1623

prune416.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 3.0) x) (/ 3.0 (pow x 3)))
0.1b	(/ 3.0 (pow x 3))
0.3b	(* (/ 1.0 x) (/ -1 x))
6.0b	(+ (* (/ 1.0 x) (/ -1 x)) (- (/ (- 3.0) x) (/ 3.0 (pow x 3))))

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 172

Calls

4 calls:

82.0ms	(- (/ (- 3.0) x) (/ 3.0 (pow x 3)))
8.0ms	(/ 3.0 (pow x 3))
30.0ms	(* (/ 1.0 x) (/ -1 x))
301.0ms	(+ (* (/ 1.0 x) (/ -1 x)) (- (/ (- 3.0) x) (/ 3.0 (pow x 3))))

series229.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (/ (- 3.0) x) (/ 3.0 (pow x 3)))
40.0ms	(/ 3.0 (pow x 3))
30.0ms	(* (/ 1.0 x) (/ -1 x))
38.0ms	(+ (* (/ 1.0 x) (/ -1 x)) (- (/ (- 3.0) x) (/ 3.0 (pow x 3))))

simplify2.1s

Counts

184 → 184

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	314	2925
1	833	2607
2	2946	2373
done	5000	2368

prune540.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.1b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
4.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite656.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
72×	`times-frac`
60×	`add-sqr-sqrt`
31×	`distribute-lft-out--`
26×	`add-cube-cbrt` `distribute-lft-out`
17×	`log-pow`
16×	`exp-prod`
13×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 135

Calls

4 calls:

21.0ms	(/ x (+ x 1.0))
32.0ms	(/ (+ x 1.0) (- x 1.0))
424.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
167.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ x (+ x 1.0))
47.0ms	(/ (+ x 1.0) (- x 1.0))
172.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
189.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.6s

Counts

147 → 147

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	211	2126
1	438	1956
2	1087	1832
3	2482	1817
done	5000	1813

prune437.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch111.0ms

Steps

Iters	Range		Point
9	110.15968793260775	1173724448.4928873	13783.80517657637
8	-66911392.43097515	-3231.0590912120524	-16146.607435637234

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	29	61
1	40	44
done	40	44

end0.0ms

sample775.0ms

Algorithm

intervals

Results

249.0ms	1733×	body	1280	valid
142.0ms	1254×	body	640	valid
131.0ms	4118×	body	80	valid
50.0ms	589×	body	320	valid
17.0ms	306×	body	160	valid