Details

sample94.0ms

Algorithm

intervals

Results

42.0ms	93×	body	1280	valid
19.0ms	181×	body	80	valid
11.0ms	37×	body	640	valid
5.0ms	25×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	1575
6	382
5	135
4	56
3	29
2	19
1	14
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.6b	(- (exp (* a x)) 1)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

12×	`exp-prod`
11×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `difference-of-squares`
1×	`sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr` `rem-exp-log`

Counts

2 → 39

Calls

2 calls:

22.0ms	(exp (* a x))
79.0ms	(- (exp (* a x)) 1)

series57.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(exp (* a x))
39.0ms	(- (exp (* a x)) 1)

simplify2.7s

Counts

45 → 45

Iterations

Iter	Nodes
done	5000
4	3728
3	1219
2	373
1	161
0	78

prune151.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x a) (* x a))
0.3b	(* (* 1/2 (* a x)) (* a x))
2.4b	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
8.8b	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* (* 1/2 (* a x)) (* a x)) (* a x)))

rewrite5.1s

Algorithm

rewrite-expression-head

Rules

167×	`associate-l`
140×	`*-un-lft-identity`
92×	`associate-r`
87×	`add-sqr-sqrt`
64×	`pow1` `distribute-lft-out`
37×	`add-cbrt-cube` `add-exp-log`
34×	`unswap-sqr`
32×	`pow-prod-down`
30×	`add-cube-cbrt`
24×	`distribute-rgt-out`
23×	`prod-exp` `cbrt-unprod`
14×	`swap-sqr` `*-commutative`
11×	`add-log-exp`
4×	`sum-log` `pow-sqr` `pow-prod-up` `insert-posit16`
3×	`+-commutative` `distribute-lft1-in`
2×	`associate-+r+` `flip3-+` `pow-plus` `flip-+`
1×	`pow2`

Counts

4 → 229

Calls

4 calls:

78.0ms	(* (* x a) (* x a))
218.0ms	(* (* 1/2 (* a x)) (* a x))
508.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
4.3s	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* (* 1/2 (* a x)) (* a x)) (* a x)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* x a) (* x a))
73.0ms	(* (* 1/2 (* a x)) (* a x))
106.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
127.0ms	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (+ (* (* 1/2 (* a x)) (* a x)) (* a x)))

simplify2.8s

Counts

241 → 241

Iterations

Iter	Nodes
done	5001
2	3261
1	916
0	254

prune739.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a x) (+ (* 1/2 (* a x)) 1))
0.1b	(* (* (* x a) (* (* x a) (* x a))) 1/6)
0.3b	(* (* x a) (* x a))
8.8b	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (* (* a x) (+ (* 1/2 (* a x)) 1)))

rewrite4.7s

Algorithm

rewrite-expression-head

Rules

237×	`add-sqr-sqrt`
201×	`associate-l`
142×	`unswap-sqr`
109×	`associate-r`
101×	`pow1`
74×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
62×	`pow-prod-down`
53×	`prod-exp` `cbrt-unprod`
38×	`add-cube-cbrt`
36×	`swap-sqr`
21×	`*-commutative`
16×	`distribute-lft-out`
6×	`add-log-exp`
5×	`+-commutative`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow-sqr` `pow-prod-up` `insert-posit16`
2×	`flip3-+` `pow-plus` `associate-*r/` `flip-+`
1×	`pow2` `sum-log`

Counts

4 → 290

Calls

4 calls:

342.0ms	(* (* a x) (+ (* 1/2 (* a x)) 1))
1.0s	(* (* (* x a) (* (* x a) (* x a))) 1/6)
46.0ms	(* (* x a) (* x a))
3.3s	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (* (* a x) (+ (* 1/2 (* a x)) 1)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* a x) (+ (* 1/2 (* a x)) 1))
90.0ms	(* (* (* x a) (* (* x a) (* x a))) 1/6)
40.0ms	(* (* x a) (* x a))
149.0ms	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (* (* a x) (+ (* 1/2 (* a x)) 1)))

simplify3.0s

Counts

302 → 302

Iterations

Iter	Nodes
done	5001
2	4609
1	1145
0	329

prune965.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* a (* x a))
0.3b	(* (* x a) (* x a))
2.1b	(* x (+ a (* (* a (* x a)) 1/2)))
8.8b	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (* x (+ a (* (* a (* x a)) 1/2))))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

87×	`associate-l`
59×	`-un-lft-identity` `associate-r*`
58×	`add-sqr-sqrt`
50×	`pow1`
29×	`add-cube-cbrt`
27×	`distribute-lft-out`
23×	`add-cbrt-cube` `add-exp-log`
21×	`pow-prod-down`
17×	`unswap-sqr`
14×	`swap-sqr`
12×	`prod-exp` `cbrt-unprod`
8×	`*-commutative`
6×	`add-log-exp`
5×	`+-commutative`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow-sqr` `pow-prod-up` `insert-posit16`
2×	`flip3-+` `pow-plus` `associate-*r/` `flip-+`
1×	`pow2` `sum-log`

Counts

4 → 169

Calls

4 calls:

52.0ms	(* a (* x a))
81.0ms	(* (* x a) (* x a))
566.0ms	(* x (+ a (* (* a (* x a)) 1/2)))
4.3s	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (* x (+ a (* (* a (* x a)) 1/2))))

series331.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* a (* x a))
51.0ms	(* (* x a) (* x a))
91.0ms	(* x (+ a (* (* a (* x a)) 1/2)))
158.0ms	(+ (* (* (* x a) (* (* x a) (* x a))) 1/6) (* x (+ a (* (* a (* x a)) 1/2))))

simplify2.5s

Counts

181 → 181

Iterations

Iter	Nodes
done	5008
2	2922
1	692
0	199

prune684.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes224.0ms

Accuracy

95% (1.1b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 21.2b

bsearch1.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	35
1	35
0	23

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	2805×	body	1280	valid
709.0ms	5339×	body	80	valid
320.0ms	1263×	body	640	valid
124.0ms	715×	body	320	valid
45.0ms	381×	body	160	valid