Details

sample67.0ms

Algorithm

intervals

Results

26.0ms	78×	body	1280	valid
10.0ms	47×	body	640	valid
7.0ms	146×	body	80	valid
4.0ms	25×	body	320	valid
2.0ms	19×	body	160	valid

simplify4.0s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize16.0ms

Local error

Found 1 expressions with local error:

4.7b	(- (exp (* a x)) 1.0)

rewrite27.0ms

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:

27.0ms

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

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

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

simplify1.7s

Counts

17 → 17

Iterations

Useful iterations: 3 (896.0ms)

Iter	Nodes	Cost
0	45	188
1	105	183
2	366	167
3	1792	165
done	5001	165

prune73.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/2 (pow a 2))
5.2b	(* (* 1/6 (pow a 3)) x)
12.1b	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
14.4b	(* (pow x 2) (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
23×	`add-sqr-sqrt`
14×	`associate-r`
13×	`prod-exp` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `unswap-sqr`
6×	`pow1` `add-log-exp`
5×	`cbrt-unprod`
4×	`unpow2` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `sum-log`

Counts

4 → 88

Calls

4 calls:

19.0ms	(* 1/2 (pow a 2))
38.0ms	(* (* 1/6 (pow a 3)) x)
18.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
45.0ms	(* (pow x 2) (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 1/2 (pow a 2))
39.0ms	(* (* 1/6 (pow a 3)) x)
87.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
187.0ms	(* (pow x 2) (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

simplify3.2s

Counts

100 → 100

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	157	1531
1	457	1410
2	2942	1240
done	5000	1239

prune480.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize44.0ms

Local error

Found 4 expressions with local error:

4.1b	(* (pow x (/ 2 2)) (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))
5.2b	(* (* 1/6 (pow a 3)) x)
7.0b	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
12.1b	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

82.0ms	(* (pow x (/ 2 2)) (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))
28.0ms	(* (* 1/6 (pow a 3)) x)
64.0ms	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
22.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

series490.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (pow x (/ 2 2)) (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))
34.0ms	(* (* 1/6 (pow a 3)) x)
162.0ms	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
108.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

simplify2.9s

Counts

94 → 94

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	145	1897
1	473	1731
2	3210	1427
done	5001	1418

prune396.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (- (exp (* a x)) 1.0) 3)
0.0b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
4.7b	(- (exp (* a x)) 1.0)

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt`
5×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
4×	`pow1` `add-exp-log` `cube-div` `add-cbrt-cube`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

3 → 70

Calls

3 calls:

31.0ms	(pow (- (exp (* a x)) 1.0) 3)
31.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
35.0ms	(- (exp (* a x)) 1.0)

series181.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(pow (- (exp (* a x)) 1.0) 3)
45.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
62.0ms	(- (exp (* a x)) 1.0)

simplify1.6s

Counts

79 → 79

Iterations

Useful iterations: 2 (330.0ms)

Iter	Nodes	Cost
0	109	1159
1	325	963
2	1777	872
done	5002	872

prune195.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.9b

regimes324.0ms

Accuracy

96% (0.9b remaining)

Error of 5.1b against oracle of 4.2b and baseline of 25.9b

bsearch4.0ms

simplify26.0ms

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	29	48
1	40	46
2	48	44
3	56	44
4	58	44
done	58	44

end0.0ms

sample1.9s

Algorithm

intervals

Results

830.0ms	2735×	body	1280	valid
303.0ms	1310×	body	640	valid
253.0ms	5364×	body	80	valid
86.0ms	753×	body	320	valid
37.0ms	437×	body	160	valid