Details

sample38.0ms

Algorithm

intervals

Results

12.0ms	76×	body	1280	valid
5.0ms	187×	body	80	valid
5.0ms	43×	body	640	valid
2.0ms	24×	body	320	valid
1.0ms	15×	body	160	valid

simplify1.1s

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	2684	6
done	5000	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)

rewrite5.0ms

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)

simplify837.0ms

Counts

17 → 17

Iterations

Useful iterations: 4 (302.0ms)

Iter	Nodes	Cost
0	45	188
1	105	183
2	313	167
3	889	165
4	2471	163
done	5000	163

prune45.0ms

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

rewrite31.0ms

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:

6.0ms	(* x (+ a (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))))
10.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
7.0ms	(* (* 1/6 (pow a 3)) x)
7.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* x (+ a (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))))
28.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
5.0ms	(* (* 1/6 (pow a 3)) x)
10.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

simplify806.0ms

Counts

86 → 86

Iterations

Useful iterations: done (803.0ms)

Iter	Nodes	Cost
0	137	1638
1	412	1545
2	1824	1386
done	5000	1368

prune166.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

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

Merged error: 1.4b

Counts

89 → 5

localize12.0ms

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))

simplify507.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	112	981
1	287	881
2	1250	680
done	5000	680

prune115.0ms

Filtered

51 candidates to 89 candidates (-74.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	89	5	94

Merged error: 0.1b

Counts

94 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

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

series17.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(pow (* x a) 2)
12.0ms	(+ (* a x) (* 1/2 (pow (* x a) 2)))

simplify1.3s

Counts

35 → 35

Iterations

Useful iterations: 3 (286.0ms)

Iter	Nodes	Cost
0	58	392
1	163	358
2	600	306
3	2880	302
done	5000	302

prune46.0ms

Filtered

22 candidates to 35 candidates (-59.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	34	6	40

Merged error: 0.1b

Counts

40 → 6

regimes200.0ms

Accuracy

98.5% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	43
1	30	43
done	30	43

end0.0ms

sample1.1s

Algorithm

intervals

Results

420.0ms	2611×	body	1280	valid
154.0ms	1304×	body	640	valid
136.0ms	5517×	body	80	valid
64.0ms	799×	body	320	valid
22.0ms	411×	body	160	valid

Details

sample38.0ms

simplify1.1s

prune3.0ms

localize5.0ms

rewrite5.0ms

series8.0ms

simplify837.0ms

prune45.0ms

localize13.0ms

rewrite31.0ms

series68.0ms

simplify806.0ms

prune166.0ms

localize12.0ms

rewrite17.0ms

series22.0ms

simplify507.0ms

prune115.0ms

localize8.0ms

rewrite9.0ms

series17.0ms

simplify1.3s

prune46.0ms

regimes200.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

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