Details

sample77.0ms

Algorithm

intervals

Results

36.0ms	101×	body	1280	valid
7.0ms	33×	body	640	valid
7.0ms	159×	body	80	valid
5.0ms	32×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.5s

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	111	6
6	273	6
7	810	6
8	2970	6
done	5001	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.5b	(- (exp (* a x)) 1.0)

rewrite18.0ms

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))
13.0ms	(- (exp (* a x)) 1.0)

series66.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(exp (* a x))
39.0ms	(- (exp (* a x)) 1.0)

simplify2.7s

Counts

30 → 30

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	53	263
1	116	248
2	282	232
3	751	228
4	2588	228
done	5000	224

prune109.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a x) 1/6)
0.5b	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
0.7b	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
7.6b	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

19.0ms	(* (* a x) 1/6)
89.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
33.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
134.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (* a x) 1/6)
100.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
154.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
129.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

simplify1.8s

Counts

108 → 108

Iterations

Useful iterations: 2 (640.0ms)

Iter	Nodes	Cost
0	174	1752
1	501	1640
2	2024	1427
done	5001	1427

prune389.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
0.1b	(* (* a x) a)
0.3b	(* (* a x) 1/6)
0.7b	(* x (+ a (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-r`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`associate-r/` `-commutative` `add-log-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`
1×	`unswap-sqr`

Counts

4 → 83

Calls

4 calls:

147.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
37.0ms	(* (* a x) a)
37.0ms	(* (* a x) 1/6)
18.0ms	(* x (+ a (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
27.0ms	(* (* a x) a)
26.0ms	(* (* a x) 1/6)
132.0ms	(* x (+ a (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))))

simplify1.6s

Counts

95 → 95

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	144	1407
1	429	1318
2	1899	1118
done	5000	1116

prune240.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
0.1b	(* (* a x) a)
0.3b	(* (* a x) 1/6)
2.1b	(* x (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2)))

rewrite518.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1` `add-exp-log` `add-cbrt-cube`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`associate-r`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r/` `associate-l*`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`*-commutative` `add-log-exp`
2×	`flip3-+` `flip-+`

Counts

4 → 91

Calls

4 calls:

149.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
36.0ms	(* (* a x) a)
19.0ms	(* (* a x) 1/6)
311.0ms	(* x (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
35.0ms	(* (* a x) a)
32.0ms	(* (* a x) 1/6)
142.0ms	(* x (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2)))

simplify1.7s

Counts

103 → 103

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	141	1565
1	404	1475
2	2022	1159
done	5000	1155

prune273.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes178.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.8b

bsearch1.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	42
1	30	42
done	30	42

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2733×	body	1280	valid
295.0ms	5586×	body	80	valid
269.0ms	1292×	body	640	valid
141.0ms	737×	body	320	valid
31.0ms	377×	body	160	valid