Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	82×	body	1280	valid
5.0ms	48×	body	640	valid
3.0ms	175×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify2.8s

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	247	6
7	872	6
8	3564	6
done	5000	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.1b	(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

1.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series46.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify610.0ms

Counts

30 → 30

Iterations

Useful iterations: done (609.0ms)

Iter	Nodes	Cost
0	53	263
1	116	248
2	312	232
3	1052	228
done	5000	226

prune68.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(* x (+ a (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))))
5.7b	(* (* 1/6 (pow a 3)) x)
6.7b	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
8.6b	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

rewrite59.0ms

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:

7.0ms	(* x (+ a (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))))
9.0ms	(* (* 1/6 (pow a 3)) x)
32.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
9.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* x (+ a (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))))
28.0ms	(* (* 1/6 (pow a 3)) x)
113.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
61.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

simplify756.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (189.0ms)

Iter	Nodes	Cost
0	137	1638
1	403	1522
2	1847	1362
done	5001	1362

prune213.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

localize9.0ms

Local error

Found 2 expressions with local error:

4.4b	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
15.5b	(* (pow a 2) (pow x 2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`add-exp-log` `unpow-prod-down`
10×	`unpow2` `sqr-pow`
9×	`prod-exp`
8×	`associate-r` `associate-l`
6×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow1`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 62

Calls

2 calls:

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

series93.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
35.0ms	(* (pow a 2) (pow x 2))

simplify949.0ms

Counts

68 → 68

Iterations

Useful iterations: 2 (190.0ms)

Iter	Nodes	Cost
0	101	872
1	258	768
2	1195	596
done	5000	596

prune116.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* a (fabs x)) (* a (fabs x)))
4.4b	(+ (* 1/2 (* (* a (fabs x)) (* a (fabs x)))) (* a x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

41×	`pow1`
17×	`pow-prod-down`
14×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-plus`
1×	`+-commutative` `pow2` `flip3-+` `swap-sqr` `associate-r` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

2 → 45

Calls

2 calls:

10.0ms	(* (* a (fabs x)) (* a (fabs x)))
25.0ms	(+ (* 1/2 (* (* a (fabs x)) (* a (fabs x)))) (* a x))

series77.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(* (* a (fabs x)) (* a (fabs x)))
56.0ms	(+ (* 1/2 (* (* a (fabs x)) (* a (fabs x)))) (* a x))

simplify486.0ms

Counts

51 → 51

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	66	706
1	203	605
2	841	481
done	5000	481

prune75.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.9b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	38
1	27	38
done	27	38

end0.0ms

sample915.0ms

Algorithm

intervals

Results

425.0ms	2638×	body	1280	valid
131.0ms	1335×	body	640	valid
106.0ms	5515×	body	80	valid
48.0ms	743×	body	320	valid
19.0ms	440×	body	160	valid