Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	76×	body	1280	valid
5.0ms	43×	body	640	valid
5.0ms	187×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	15×	body	160	valid

simplify987.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	26	6
4	49	6
5	108	6
6	261	6
7	768	6
8	2603	6
done	5001	6

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.4b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

3.9b	(- (exp (* a x)) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

4.0ms

(- (exp (* a x)) 1.0)

series8.0ms

Counts

1 → 3

Calls

1 calls:

8.0ms

(- (exp (* a x)) 1.0)

simplify789.0ms

Counts

17 → 17

Iterations

Useful iterations: 4 (288.0ms)

Iter	Nodes	Cost
0	45	188
1	105	183
2	309	167
3	817	165
4	2458	163
done	5000	163

prune42.0ms

Filtered

12 candidates to 17 candidates (-41.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	14	3	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	15	3	18

Merged error: 4.8b

Counts

18 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
6.4b	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
6.7b	(* (* 1/6 (pow a 3)) x)
10.5b	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
13×	`add-sqr-sqrt` `add-cbrt-cube`
10×	`pow1`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `prod-exp`
7×	`associate-l`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`associate-*r/`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `pow-exp` `sum-log`

Counts

4 → 74

Calls

4 calls:

5.0ms	(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
10.0ms	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
7.0ms	(* (* 1/6 (pow a 3)) x)
5.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

series63.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
24.0ms	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
5.0ms	(* (* 1/6 (pow a 3)) x)
9.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

simplify571.0ms

Counts

86 → 86

Iterations

Useful iterations: done (568.0ms)

Iter	Nodes	Cost
0	137	1638
1	413	1526
2	1831	1362
done	5000	1360

prune178.0ms

Filtered

57 candidates to 86 candidates (-50.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 1.4b

Counts

89 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow a 2)
6.2b	(+ (* a x) (* 1/2 (* (pow a 2) (pow x 2))))
15.8b	(* (pow a 2) (pow x 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`unpow-prod-down`
16×	`add-exp-log` `unswap-sqr`
11×	`unpow2` `sqr-pow`
9×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
8×	`associate-r` `associate-l`
7×	`pow-to-exp` `pow-exp`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`pow-unpow`
1×	`+-commutative` `pow-pow` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

3 → 80

Calls

3 calls:

2.0ms	(pow a 2)
4.0ms	(+ (* a x) (* 1/2 (* (pow a 2) (pow x 2))))
8.0ms	(* (pow a 2) (pow x 2))

series22.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(pow a 2)
12.0ms	(+ (* a x) (* 1/2 (* (pow a 2) (pow x 2))))
7.0ms	(* (pow a 2) (pow x 2))

simplify416.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	112	981
1	287	846
2	1173	672
done	5001	672

prune116.0ms

Filtered

48 candidates to 89 candidates (-85.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 0.1b

Counts

94 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(pow (* a x) 2)
6.2b	(+ (* a x) (* 1/2 (pow (* a x) 2)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `add-exp-log`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
2×	`pow-pow` `pow-exp` `add-cbrt-cube`
1×	`+-commutative` `pow-to-exp` `unpow-prod-down` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `flip-+` `unpow2` `sqr-pow`

Counts

2 → 29

Calls

2 calls:

4.0ms	(pow (* a x) 2)
6.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))

series18.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(pow (* a x) 2)
12.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))

simplify1.7s

Counts

35 → 35

Iterations

Useful iterations: 3 (352.0ms)

Iter	Nodes	Cost
0	57	392
1	162	340
2	662	306
3	4593	302
done	5000	302

prune43.0ms

Filtered

22 candidates to 35 candidates (-59.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Merged error: 0.1b

Counts

39 → 5

regimes203.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 22.2b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	43
1	30	43
done	30	43

end0.0ms

sample1.2s

Algorithm

intervals

Results

455.0ms	2611×	body	1280	valid
161.0ms	1304×	body	640	valid
152.0ms	5517×	body	80	valid
75.0ms	799×	body	320	valid
27.0ms	411×	body	160	valid

Details

sample40.0ms

simplify987.0ms

prune3.0ms

localize5.0ms

rewrite4.0ms

series8.0ms

simplify789.0ms

prune42.0ms

localize13.0ms

rewrite29.0ms

series63.0ms

simplify571.0ms

prune178.0ms

localize9.0ms

rewrite17.0ms

series22.0ms

simplify416.0ms

prune116.0ms

localize7.0ms

rewrite11.0ms

series18.0ms

simplify1.7s

prune43.0ms

regimes203.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample1.2s

Profiling