Details

sample68.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
13.0ms	41×	body	640	valid
8.0ms	131×	body	80	valid
4.0ms	20×	body	320	valid
2.0ms	17×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	15	10
2	22	10
3	30	10
4	53	10
5	117	10
6	441	10
7	3433	10
done	5000	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`times-frac`
11×	`add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--`

Counts

2 → 48

Calls

2 calls:

27.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series204.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
148.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify2.2s

Counts

54 → 54

Iterations

Useful iterations: 3 (842.0ms)

Iter	Nodes	Cost
0	103	791
1	230	754
2	771	712
3	4062	705
done	5001	705

prune172.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.8b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite516.0ms

Algorithm

rewrite-expression-head

Rules

388×	`times-frac`
305×	`*-un-lft-identity`
233×	`sqrt-prod`
214×	`add-sqr-sqrt`
189×	`add-cube-cbrt`
57×	`distribute-lft-out`
30×	`associate-/l*`
22×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
10×	`div-inv`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 321

Calls

4 calls:

18.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
43.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
17.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
395.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series330.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
45.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
108.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
128.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify2.2s

Counts

333 → 333

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	354	10184
1	833	8589
2	3651	8111
done	5000	7697

prune806.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
0.9b	(* 5.551115123125783e-17 (pow x 4))
9.4b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `flip3-+` `unpow3` `sum-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

13.0ms	(* 0.33333333333333337 (pow x 3))
13.0ms	(* 5.551115123125783e-17 (pow x 4))
27.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* 0.33333333333333337 (pow x 3))
56.0ms	(* 5.551115123125783e-17 (pow x 4))
122.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify850.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (255.0ms)

Iter	Nodes	Cost
0	114	734
1	290	647
2	1118	602
done	5001	602

prune260.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes222.0ms

Accuracy

95.5% (1.4b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 30.1b

bsearch2.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	65
1	37	47
done	37	47

end0.0ms

sample1.8s

Algorithm

intervals

Results

683.0ms	1689×	body	1280	valid
385.0ms	1285×	body	640	valid
228.0ms	4054×	body	80	valid
170.0ms	635×	body	320	valid
34.0ms	337×	body	160	valid