Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	49×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	124×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	14×	body	160	valid

simplify251.0ms

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: 30.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

22.0ms	(/ x (+ x 1.0))
26.0ms	(/ (+ x 1.0) (- x 1.0))
156.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series336.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ x (+ x 1.0))
50.0ms	(/ (+ x 1.0) (- x 1.0))
240.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify4.1s

Counts

605 → 605

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	523	34216
1	1199	30851
2	2823	22735
done	5000	16848

prune619.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.4b	(/ 3.0 (pow x 3))
0.7b	(/ 1.0 (* x x))
6.3b	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`fma-def` `add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp` `frac-add` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `sum-log` `log1p-expm1-u` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
2×	`+-commutative` `frac-2neg` `clear-num`
1×	`pow-to-exp` `associate-+l+` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

52.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
9.0ms	(/ 3.0 (pow x 3))
8.0ms	(/ 1.0 (* x x))
306.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
79.0ms	(/ 3.0 (pow x 3))
50.0ms	(/ 1.0 (* x x))
35.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify1.3s

Counts

148 → 148

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	202	1801
1	455	1547
2	1624	1460
done	5000	1457

prune361.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
0.2b	(/ (- x 1.0) (sqrt (+ x 1.0)))
8.6b	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

13737×	`times-frac`
12948×	`*-un-lft-identity`
8314×	`add-sqr-sqrt`
6367×	`add-cube-cbrt`
5834×	`sqrt-prod`
5256×	`prod-diff`
2340×	`distribute-lft-out`
960×	`difference-of-squares`
949×	`distribute-lft-out--`
877×	`associate-/r/`
448×	`div-inv`
430×	`flip3-+` `flip-+`
272×	`sqrt-div`
52×	`associate-/r*`
18×	`fma-neg`
15×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log` `div-sub` `frac-sub`

Counts

4 → 5761

Calls

4 calls:

16.0ms	(/ x (+ x 1.0))
47.0ms	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
36.0ms	(/ (- x 1.0) (sqrt (+ x 1.0)))
697.0ms	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ x (+ x 1.0))
57.0ms	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
129.0ms	(/ (- x 1.0) (sqrt (+ x 1.0)))
206.0ms	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

simplify2.8s

Counts

5773 → 5773

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	3009	598978
done	5000	598274

prune16.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(fma 2.0 (fma x x x) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

31.0ms	(/ x (+ x 1.0))
1.0ms	(fma 2.0 (fma x x x) 1.0)

series93.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ x (+ x 1.0))
49.0ms	(fma 2.0 (fma x x x) 1.0)

simplify2.7s

Counts

51 → 51

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	90	513
1	188	484
2	454	438
3	1036	437
4	3564	435
done	5000	435

prune182.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.6b

bsearch108.0ms

Steps

Iters	Range		Point
9	0.21963308938311268	137362616.0762091	9050.184745868966
11	-2445851338.3862987	-4.2674702477225e-16	-1.0064602849522295

simplify12.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	59
1	34	44
2	41	44
3	44	44
done	44	44

end0.0ms

sample1.4s

Algorithm

intervals

Results

564.0ms	1705×	body	1280	valid
250.0ms	4080×	body	80	valid
243.0ms	1262×	body	640	valid
135.0ms	633×	body	320	valid
33.0ms	320×	body	160	valid