Details

sample48.0ms

Algorithm

intervals

Results

14.0ms	51×	body	1280	valid
8.0ms	39×	body	640	valid
7.0ms	130×	body	80	valid
3.0ms	21×	body	320	valid
2.0ms	15×	body	160	valid

simplify239.0ms

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: 29.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite234.0ms

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:

23.0ms	(/ x (+ x 1.0))
55.0ms	(/ (+ x 1.0) (- x 1.0))
146.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series316.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ x (+ x 1.0))
62.0ms	(/ (+ x 1.0) (- x 1.0))
204.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.1s

Counts

113 → 113

Iterations

Useful iterations: done (2.1s)

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

prune345.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.0b	(/ x (+ x 1.0))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
7.4b	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
44×	`times-frac`
33×	`add-cube-cbrt`
21×	`associate-l`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `frac-sub` `flip-+` `distribute-lft-out`
4×	`frac-times` `associate-r/` `associate-r*` `prod-exp`
3×	`cbrt-undiv` `flip3--` `flip--` `div-inv` `unswap-sqr`
2×	`distribute-rgt-in` `rec-exp` `frac-2neg` `distribute-lft-in` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod` `associate--r+`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 143

Calls

4 calls:

26.0ms	(/ 1 (- x 1.0))
24.0ms	(/ x (+ x 1.0))
98.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
120.0ms	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (- x 1.0))
42.0ms	(/ x (+ x 1.0))
45.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
230.0ms	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

simplify1.9s

Counts

155 → 155

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	241	2054
1	683	1761
2	2033	1617
done	5001	1600

prune351.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ x (- x 1.0))
0.0b	(- (- (/ x (+ x 1.0)) (/ x (- x 1.0))) (* (/ 1 (- x 1.0)) 1.0))
4.5b	(- (/ x (+ x 1.0)) (/ x (- x 1.0)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
55×	`times-frac`
51×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
25×	`distribute-lft-out--`
11×	`add-log-exp`
10×	`distribute-lft-out`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/r/` `associate-/l*`
5×	`frac-sub` `flip--`
4×	`pow1` `flip3--` `diff-log` `div-inv`
3×	`sub-neg` `associate-*l/`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `associate--l+` `clear-num` `flip-+`
1×	`associate--l-` `flip3-+`

Counts

4 → 121

Calls

4 calls:

22.0ms	(/ x (+ x 1.0))
14.0ms	(/ x (- x 1.0))
871.0ms	(- (- (/ x (+ x 1.0)) (/ x (- x 1.0))) (* (/ 1 (- x 1.0)) 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ x (- x 1.0)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ x (+ x 1.0))
54.0ms	(/ x (- x 1.0))
196.0ms	(- (- (/ x (+ x 1.0)) (/ x (- x 1.0))) (* (/ 1 (- x 1.0)) 1.0))
293.0ms	(- (/ x (+ x 1.0)) (/ x (- x 1.0)))

simplify2.6s

Counts

133 → 133

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	219	2073
1	517	1877
2	1414	1813
3	4219	1781
done	5000	1781

prune335.0ms

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 (- x 1.0))
0.0b	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- (- x 1.0) (+ x 1.0))) (* (/ 1 (- x 1.0)) 1.0))
3.9b	(- (- x 1.0) (+ x 1.0))
12.9b	(/ x (- (* x x) (* 1.0 1.0)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
27×	`times-frac`
25×	`frac-sub`
23×	`add-cube-cbrt`
18×	`add-log-exp`
14×	`associate-*l/` `associate--l+`
12×	`flip3--` `flip--`
10×	`add-exp-log` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
8×	`add-cbrt-cube`
7×	`sub-neg` `diff-log`
6×	`frac-times` `flip3-+` `associate-r/` `flip-+` `associate-/l`
5×	`pow1`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
3×	`div-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `sum-log` `div-inv` `distribute-lft-out`
1×	`associate--l-` `rec-exp` `pow-flip` `1-exp` `associate--r+` `inv-pow`

Counts

4 → 135

Calls

4 calls:

18.0ms	(/ 1 (- x 1.0))
131.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- (- x 1.0) (+ x 1.0))) (* (/ 1 (- x 1.0)) 1.0))
69.0ms	(- (- x 1.0) (+ x 1.0))
33.0ms	(/ x (- (* x x) (* 1.0 1.0)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (- x 1.0))
95.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- (- x 1.0) (+ x 1.0))) (* (/ 1 (- x 1.0)) 1.0))
11.0ms	(- (- x 1.0) (+ x 1.0))
71.0ms	(/ x (- (* x x) (* 1.0 1.0)))

simplify2.6s

Counts

147 → 147

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	322	3185
1	845	2886
2	3331	2734
done	5000	2562

prune403.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes27.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.1b

bsearch117.0ms

Steps

Iters	Range		Point
8	1810750790637.4219	7.620297985740285e+16	7051386931030.598
9	-5.452804783141298e+22	-4418200179179808.0	-7534224028620261.0

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	29	65
1	40	50
done	40	50

end0.0ms

sample1.2s

Algorithm

intervals

Results

385.0ms	1741×	body	1280	valid
281.0ms	1222×	body	640	valid
210.0ms	4107×	body	80	valid
97.0ms	614×	body	320	valid
23.0ms	316×	body	160	valid