Details

sample37.0ms

Algorithm

intervals

Results

12.0ms	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

simplify2.9s

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	107	6
6	246	6
7	704	6
8	2436	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)

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)

simplify1.8s

Counts

17 → 17

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	45	188
1	105	183
2	297	167
3	707	165
4	2049	165
done	5000	165

prune50.0ms

Filtered

12 candidates to 17 candidates (-41.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	12	5	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	5	18

Merged error: 9.5b

Counts

18 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`log-pow`
5×	`log-prod` `exp-prod`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1`
2×	`add-exp-log` `sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 34

Calls

2 calls:

5.0ms	(log (exp (- (exp (* a x)) 1.0)))
5.0ms	(- (exp (* a x)) 1.0)

series16.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(log (exp (- (exp (* a x)) 1.0)))
8.0ms	(- (exp (* a x)) 1.0)

simplify3.1s

Counts

40 → 40

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	73	447
1	143	395
2	343	360
3	1016	356
4	4535	352
done	5000	352

prune61.0ms

Filtered

28 candidates to 40 candidates (-42.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	41	4	45

Merged error: 4.8b

Counts

45 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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:

12.0ms	(* x (+ (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))) a))
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)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* x (+ (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))) a))
27.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
6.0ms	(* (* 1/6 (pow a 3)) x)
9.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

simplify872.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	137	1638
1	404	1522
2	1679	1362
done	5000	1362

prune158.0ms

Filtered

55 candidates to 86 candidates (-56.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	84	6	90

Merged error: 1.4b

Counts

90 → 6

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))

simplify857.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (220.0ms)

Iter	Nodes	Cost
0	112	981
1	280	846
2	1076	672
done	5000	672

prune93.0ms

Filtered

50 candidates to 89 candidates (-78.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	90	5	95

Merged error: 0.1b

Counts

95 → 5

regimes265.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 22.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	19	25
done	19	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

427.0ms	2611×	body	1280	valid
145.0ms	1304×	body	640	valid
143.0ms	5517×	body	80	valid
67.0ms	799×	body	320	valid
22.0ms	411×	body	160	valid

Details

sample37.0ms

simplify2.9s

prune3.0ms

localize5.0ms

rewrite5.0ms

series8.0ms

simplify1.8s

prune50.0ms

localize8.0ms

rewrite11.0ms

series16.0ms

simplify3.1s

prune61.0ms

localize13.0ms

rewrite37.0ms

series65.0ms

simplify872.0ms

prune158.0ms

localize9.0ms

rewrite17.0ms

series22.0ms

simplify857.0ms

prune93.0ms

regimes265.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

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