Details

sample76.0ms

Algorithm

intervals

Results

31.0ms	90×	body	1280	valid
18.0ms	39×	body	640	valid
7.0ms	163×	body	80	valid
4.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	153
1	11	153
2	18	153
3	26	153
4	49	153
5	113	153
6	440	153
7	3255	153
done	5002	153

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.6b	(- (exp (* a x)) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

3.0ms	(exp (* a x))
10.0ms	(- (exp (* a x)) 1.0)

series69.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
55.0ms	(- (exp (* a x)) 1.0)

simplify1.4s

Counts

30 → 30

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	53	7474
1	116	5940
2	389	5900
3	2000	5702
done	5000	5662

prune162.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 a)
0.8b	(* (* 1/6 a) (* (* x a) (* x a)))
1.5b	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
11.6b	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1` `add-cbrt-cube` `add-exp-log`
33×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

4 → 93

Calls

4 calls:

10.0ms	(* 1/6 a)
86.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
345.0ms	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
110.0ms	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 1/6 a)
66.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
145.0ms	(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
169.0ms	(+ (* (* (* x a) (* x a)) 1/2) (* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a)))

simplify3.1s

Counts

105 → 105

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	152	32226
1	502	26305
2	3138	25019
done	5000	24659

prune364.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.2b	(* 3 (* a x))
3.8b	(- (exp (* 3 (* a x))) (* 1.0 (* 1.0 1.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `flip--`

Counts

4 → 50

Calls

4 calls:

3.0ms	(exp (* a x))
3.0ms	(exp (* a x))
18.0ms	(* 3 (* a x))
32.0ms	(- (exp (* 3 (* a x))) (* 1.0 (* 1.0 1.0)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(exp (* a x))
14.0ms	(exp (* a x))
25.0ms	(* 3 (* a x))
59.0ms	(- (exp (* 3 (* a x))) (* 1.0 (* 1.0 1.0)))

simplify1.1s

Counts

62 → 62

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	87	13780
1	223	11237
2	1050	10959
done	5001	10880

prune312.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (* a x))
0.8b	(* a (* (* a x) (* a x)))
3.4b	(* x (* a (* (* a x) (* a x))))
11.8b	(+ (* (* a x) (* a x)) (* x (* a (* (* a x) (* a x)))))

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

52×	`pow1` `add-cbrt-cube` `add-exp-log`
35×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
3×	`associate-r` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

22.0ms	(* 3 (* a x))
62.0ms	(* a (* (* a x) (* a x)))
245.0ms	(* x (* a (* (* a x) (* a x))))
41.0ms	(+ (* (* a x) (* a x)) (* x (* a (* (* a x) (* a x)))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* 3 (* a x))
76.0ms	(* a (* (* a x) (* a x)))
73.0ms	(* x (* a (* (* a x) (* a x))))
112.0ms	(+ (* (* a x) (* a x)) (* x (* a (* (* a x) (* a x)))))

simplify2.9s

Counts

99 → 99

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	123	26101
1	383	19117
2	3028	17082
done	5001	16522

prune458.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes545.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.5b

bsearch1.0ms

simplify44.0ms

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	40	1428
1	59	1388
2	62	1388
3	64	1388
done	64	1388

end0.0ms

sample1.8s

Algorithm

intervals

Results

842.0ms	2701×	body	1280	valid
242.0ms	5509×	body	80	valid
223.0ms	1304×	body	640	valid
148.0ms	804×	body	320	valid
30.0ms	387×	body	160	valid