Details

sample47.0ms

Algorithm

intervals

Results

18.0ms	93×	body	1280	valid
6.0ms	41×	body	640	valid
5.0ms	176×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.7s

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	113	6
6	440	6
7	3314	6
done	5002	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.1b	(- (exp (* a x)) 1.0)

rewrite22.0ms

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:

4.0ms	(exp (* a x))
18.0ms	(- (exp (* a x)) 1.0)

series54.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
40.0ms	(- (exp (* a x)) 1.0)

simplify1.4s

Counts

30 → 30

Iterations

Useful iterations: 3 (506.0ms)

Iter	Nodes	Cost
0	53	263
1	116	248
2	388	232
3	2010	228
done	5001	228

prune104.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
4.8b	(* (* 1/2 (pow a 2)) x)
12.3b	(* (pow a 3) (pow x 3))
13.3b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
28×	`add-exp-log`
18×	`associate-r`
17×	`prod-exp` `unswap-sqr`
16×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
13×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`sqr-pow`
8×	`pow1`
7×	`pow-to-exp` `pow-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
3×	`pow-prod-down` `*-commutative`
2×	`distribute-rgt-in` `cube-mult` `associate-+l+` `distribute-lft-in` `flip3-+` `unpow3` `associate-*r/` `flip-+`
1×	`+-commutative` `sum-log`

Counts

4 → 113

Calls

4 calls:

35.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
45.0ms	(* (* 1/2 (pow a 2)) x)
55.0ms	(* (pow a 3) (pow x 3))
33.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
35.0ms	(* (* 1/2 (pow a 2)) x)
78.0ms	(* (pow a 3) (pow x 3))
174.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))

simplify3.1s

Counts

125 → 125

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	171	1786
1	518	1611
2	3534	1505
done	5000	1502

prune566.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 3)
1.2b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
4.8b	(* (* 1/2 (pow a 2)) x)
13.3b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-cbrt-cube`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`prod-exp`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
5×	`cbrt-unprod`
4×	`associate-l`
3×	`pow-unpow` `pow-prod-down` `pow-exp`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `pow-pow` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `flip-+` `rem-cube-cbrt`
1×	`+-commutative` `cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sum-log` `unswap-sqr` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

13.0ms	(pow (* a x) 3)
19.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
39.0ms	(* (* 1/2 (pow a 2)) x)
28.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(pow (* a x) 3)
84.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
43.0ms	(* (* 1/2 (pow a 2)) x)
167.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify1.9s

Counts

88 → 88

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	134	1211
1	433	1092
2	2747	1006
done	5000	1005

prune306.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x a) (* 1/6 (pow (* a x) 3)))
0.1b	(* 1/6 (pow (* a x) 3))
0.2b	(pow (* a x) 3)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log`
9×	`add-sqr-sqrt`
8×	`associate-r` `add-cbrt-cube`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `prod-exp`
5×	`add-log-exp`
4×	`pow-exp`
3×	`pow-unpow` `associate-l` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

3 → 59

Calls

3 calls:

9.0ms	(+ (* x a) (* 1/6 (pow (* a x) 3)))
19.0ms	(* 1/6 (pow (* a x) 3))
6.0ms	(pow (* a x) 3)

series300.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(+ (* x a) (* 1/6 (pow (* a x) 3)))
92.0ms	(* 1/6 (pow (* a x) 3))
59.0ms	(pow (* a x) 3)

simplify927.0ms

Counts

68 → 68

Iterations

Useful iterations: done (925.0ms)

Iter	Nodes	Cost
0	84	699
1	249	600
2	1349	553
done	5001	551

prune178.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes305.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 22.1b

bsearch2.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	34
1	25	34
2	27	34
3	29	34
done	29	34

end0.0ms

sample2.1s

Algorithm

intervals

Results

792.0ms	2712×	body	1280	valid
620.0ms	5455×	body	80	valid
198.0ms	1272×	body	640	valid
79.0ms	779×	body	320	valid
28.0ms	407×	body	160	valid