Details

sample78.0ms

Algorithm

intervals

Results

33.0ms	84×	body	1280	valid
11.0ms	49×	body	640	valid
9.0ms	186×	body	80	valid
4.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	26	6
4	49	6
5	111	6
6	273	6
7	810	6
8	2970	6
done	5001	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize11.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (exp (* a x)) 1.0)

rewrite13.0ms

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:

13.0ms

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

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

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

simplify2.4s

Counts

17 → 17

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	45	188
1	105	183
2	266	167
3	722	165
4	2470	165
done	5001	161

prune90.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
0.3b	(* 1/6 a)
1.7b	(* a (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
4.4b	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
22×	`add-sqr-sqrt`
17×	`associate-l`
15×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
10×	`pow1` `associate-r`
8×	`associate-*r/`
6×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`pow-to-exp` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

35.0ms	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
7.0ms	(* 1/6 a)
119.0ms	(* a (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
41.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
28.0ms	(* 1/6 a)
139.0ms	(* a (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
140.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: 2 (555.0ms)

Iter	Nodes	Cost
0	169	1698
1	483	1592
2	1858	1405
done	5000	1405

prune318.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
0.3b	(* 1/6 a)
4.2b	(* (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) a)
4.4b	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
23×	`prod-exp`
22×	`add-cbrt-cube`
19×	`add-sqr-sqrt`
15×	`associate-l`
13×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity` `cbrt-unprod`
10×	`associate-r/` `associate-r*`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
3×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+`
2×	`associate-*l/` `unpow2` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

42.0ms	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
15.0ms	(* 1/6 a)
117.0ms	(* (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) a)
31.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
16.0ms	(* 1/6 a)
121.0ms	(* (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) a)
125.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

simplify1.5s

Counts

110 → 110

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	155	1718
1	438	1595
2	1791	1360
done	5000	1354

prune361.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.2b

localize17.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (exp (* a x)) 1.0)
2.6b	(log (exp (- (exp (* a x)) 1.0)))

rewrite60.0ms

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:

20.0ms	(- (exp (* a x)) 1.0)
38.0ms	(log (exp (- (exp (* a x)) 1.0)))

series103.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (exp (* a x)) 1.0)
57.0ms	(log (exp (- (exp (* a x)) 1.0)))

simplify2.5s

Counts

40 → 40

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	73	447
1	142	395
2	312	360
3	799	356
4	2669	356
done	5001	348

prune127.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes314.0ms

Accuracy

87.4% (3.0b remaining)

Error of 3.2b against oracle of 0.2b and baseline of 23.9b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	31
1	30	31
done	30	31

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2746×	body	1280	valid
270.0ms	1330×	body	640	valid
265.0ms	5371×	body	80	valid
131.0ms	749×	body	320	valid
69.0ms	367×	body	160	valid