Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	51×	body	1280	valid
5.0ms	43×	body	640	valid
3.0ms	136×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify60.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	30	5
3	52	5
4	114	5
5	322	5
6	1627	5
7	5002	5
done	5002	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
3.2b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `times-frac` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 27

Calls

2 calls:

6.0ms	(+ 1.0 (exp (* -2.0 x)))
64.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series97.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
80.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify51.0ms

Counts

33 → 33

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	183	242
1	457	222
2	1597	217
3	5001	217
done	5001	217

prune80.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(* (sqrt (+ 1.0 (exp (* -2.0 x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.2b	(- (/ 2.0 (* (sqrt (+ 1.0 (exp (* -2.0 x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity` `sqrt-prod`
32×	`add-sqr-sqrt`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
8×	`flip3-+` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `difference-of-squares`
1×	`pow2` `sub-neg` `flip3--` `times-frac` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
9.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
50.0ms	(* (sqrt (+ 1.0 (exp (* -2.0 x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
67.0ms	(- (/ 2.0 (* (sqrt (+ 1.0 (exp (* -2.0 x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

series184.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
47.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
17.0ms	(* (sqrt (+ 1.0 (exp (* -2.0 x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
79.0ms	(- (/ 2.0 (* (sqrt (+ 1.0 (exp (* -2.0 x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

simplify44.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	295	1011
1	1036	921
2	5002	850
done	5002	850

prune256.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b	(pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) (/ 1 2))
0.5b	(pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4)
28.4b	(- (/ 2.0 (pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) (/ 1 2))) 1.0)

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`unpow-prod-down`
26×	`*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`pow-unpow`
15×	`times-frac`
13×	`sqrt-prod`
7×	`pow1` `add-exp-log` `difference-of-squares`
6×	`add-log-exp`
5×	`pow-exp` `sqr-pow`
4×	`pow-pow` `add-cbrt-cube`
3×	`pow-to-exp` `distribute-lft-out`
2×	`sqrt-pow1` `pow1/2` `sqrt-div`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `flip3-+` `diff-log` `sqrt-pow2` `flip--` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 97

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
25.0ms	(pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) (/ 1 2))
12.0ms	(pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4)
274.0ms	(- (/ 2.0 (pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) (/ 1 2))) 1.0)

series453.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
242.0ms	(pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) (/ 1 2))
89.0ms	(pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4)
81.0ms	(- (/ 2.0 (pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) (/ 1 2))) 1.0)

simplify57.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	492	990
1	1747	863
2	5002	838
done	5002	838

prune666.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b	(pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) 1/2)
0.5b	(pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4)
3.2b	(+ (- (* 1.0 1.0)) (/ (/ (* 2.0 2.0) (fabs (+ 1.0 (exp (* -2.0 x))))) (fabs (+ 1.0 (exp (* -2.0 x))))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

25×	`unpow-prod-down`
20×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-exp-log`
6×	`pow-unpow`
5×	`pow-exp`
4×	`pow-pow` `add-cbrt-cube` `distribute-lft-out`
3×	`pow-to-exp` `sqr-pow`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `sum-log` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `neg-log` `sqrt-pow2` `unpow1/2`

Counts

4 → 82

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
25.0ms	(pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) 1/2)
12.0ms	(pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4)
21.0ms	(+ (- (* 1.0 1.0)) (/ (/ (* 2.0 2.0) (fabs (+ 1.0 (exp (* -2.0 x))))) (fabs (+ 1.0 (exp (* -2.0 x))))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
282.0ms	(pow (pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4) 1/2)
87.0ms	(pow (sqrt (+ 1.0 (exp (* -2.0 x)))) 4)
59.0ms	(+ (- (* 1.0 1.0)) (/ (/ (* 2.0 2.0) (fabs (+ 1.0 (exp (* -2.0 x))))) (fabs (+ 1.0 (exp (* -2.0 x))))))

simplify51.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	423	892
1	1594	737
2	5001	702
done	5001	702

prune673.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes367.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.9b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	53
1	63	53
2	63	53
done	63	53

end0.0ms

sample857.0ms

Algorithm

intervals

Results

342.0ms	1700×	body	1280	valid
153.0ms	1222×	body	640	valid
104.0ms	4153×	body	80	valid
56.0ms	635×	body	320	valid
16.0ms	290×	body	160	valid