Details

sample58.0ms

Algorithm

intervals

Results

23.0ms	84×	body	1280	valid
8.0ms	43×	body	640	valid
6.0ms	158×	body	80	valid
4.0ms	34×	body	320	valid
1.0ms	14×	body	160	valid

simplify3.6s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.9b	(- (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)

series70.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
46.0ms	(- (exp (* a x)) 1.0)

simplify1.6s

Counts

30 → 30

Iterations

Useful iterations: 3 (499.0ms)

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

prune88.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.4b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.2b	(* (* 1/2 (pow a 2)) x)
12.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
19.3b	(* (pow a 3) (pow x 3))

rewrite106.0ms

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:

19.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
23.0ms	(* (* 1/2 (pow a 2)) x)
28.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
32.0ms	(* (pow a 3) (pow x 3))

series329.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
24.0ms	(* (* 1/2 (pow a 2)) x)
148.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
79.0ms	(* (pow a 3) (pow x 3))

simplify3.0s

Counts

125 → 125

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	171	1786
1	517	1611
2	3514	1503
done	5001	1502

prune433.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 3)
1.0b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.2b	(* (* 1/2 (pow a 2)) x)
12.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite106.0ms

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:

12.0ms	(pow (* a x) 3)
31.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
33.0ms	(* (* 1/2 (pow a 2)) x)
26.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (* a x) 3)
89.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
39.0ms	(* (* 1/2 (pow a 2)) x)
169.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify2.0s

Counts

88 → 88

Iterations

Useful iterations: done (2.0s)

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

prune357.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

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)))
24.0ms	(* 1/6 (pow (* a x) 3))
7.0ms	(pow (* a x) 3)

series338.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(+ (* x a) (* 1/6 (pow (* a x) 3)))
101.0ms	(* 1/6 (pow (* a x) 3))
70.0ms	(pow (* a x) 3)

simplify1.1s

Counts

68 → 68

Iterations

Useful iterations: done (1.1s)

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

prune186.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.4b

regimes352.0ms

Accuracy

97.3% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 21.3b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	25
1	19	25
done	19	25

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2748×	body	1280	valid
235.0ms	5280×	body	80	valid
234.0ms	1346×	body	640	valid
115.0ms	754×	body	320	valid
75.0ms	415×	body	160	valid