Details

sample50.0ms

Algorithm

intervals

Results

22.0ms	90×	body	1280	valid
6.0ms	39×	body	640	valid
5.0ms	163×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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)

series78.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(exp (* a x))
59.0ms	(- (exp (* a x)) 1.0)

simplify1.2s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
3	2000
2	389
1	116
0	53

prune176.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.4b

localize47.0ms

Local error

Found 4 expressions with local error:

1.2b	(* x (+ (* (* a a) (* 1/2 x)) a))
8.0b	(* (* a a) (* 1/2 x))
11.6b	(+ (* (* 1/6 (pow a 3)) (pow x 3)) (* x (+ (* (* a a) (* 1/2 x)) a)))
18.7b	(* (* 1/6 (pow a 3)) (pow x 3))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
30×	`prod-exp`
23×	`add-cbrt-cube`
18×	`pow1`
16×	`associate-r`
12×	`cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
7×	`pow-to-exp` `pow-exp`
6×	`add-log-exp`
5×	`associate-l`
3×	`unpow-prod-down` `cube-prod` `*-commutative`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+`
1×	`cube-mult` `+-commutative` `sum-log` `unpow3` `unswap-sqr` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

98.0ms	(* x (+ (* (* a a) (* 1/2 x)) a))
27.0ms	(* (* a a) (* 1/2 x))
36.0ms	(+ (* (* 1/6 (pow a 3)) (pow x 3)) (* x (+ (* (* a a) (* 1/2 x)) a)))
23.0ms	(* (* 1/6 (pow a 3)) (pow x 3))

series341.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* x (+ (* (* a a) (* 1/2 x)) a))
27.0ms	(* (* a a) (* 1/2 x))
171.0ms	(+ (* (* 1/6 (pow a 3)) (pow x 3)) (* x (+ (* (* a a) (* 1/2 x)) a)))
73.0ms	(* (* 1/6 (pow a 3)) (pow x 3))

simplify2.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	3555
1	536
0	163

prune510.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

localize27.0ms

Local error

Found 2 expressions with local error:

3.2b	(+ (* (* a a) (* (* x x) 1/2)) (* x a))
15.1b	(* (* a a) (* (* x x) 1/2))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
2×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
1×	`+-commutative` `sum-log` `flip3-+` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

2 → 39

Calls

2 calls:

58.0ms	(+ (* (* a a) (* (* x x) 1/2)) (* x a))
59.0ms	(* (* a a) (* (* x x) 1/2))

series138.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(+ (* (* a a) (* (* x x) 1/2)) (* x a))
51.0ms	(* (* a a) (* (* x x) 1/2))

simplify1.5s

Counts

45 → 45

Iterations

Iter	Nodes
done	5000
2	2131
1	287
0	80

prune141.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* (* x 1/2) a))
3.2b	(+ (* a (* x (* (* x 1/2) a))) (* x a))
3.8b	(* a (* x (* (* x 1/2) a)))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1` `add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

3 → 56

Calls

3 calls:

47.0ms	(* x (* (* x 1/2) a))
125.0ms	(+ (* a (* x (* (* x 1/2) a))) (* x a))
166.0ms	(* a (* x (* (* x 1/2) a)))

series185.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* x (* (* x 1/2) a))
93.0ms	(+ (* a (* x (* (* x 1/2) a))) (* x a))
59.0ms	(* a (* x (* (* x 1/2) a)))

simplify1.2s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
2	1737
1	286
0	95

prune213.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes279.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.8b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	25
3	25
2	23
1	21
0	16

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	2701×	body	1280	valid
256.0ms	1304×	body	640	valid
224.0ms	5509×	body	80	valid
89.0ms	804×	body	320	valid
28.0ms	387×	body	160	valid