Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	96×	body	1280	valid
5.0ms	49×	body	640	valid
3.0ms	169×	body	80	valid
2.0ms	26×	body	320	valid
0.0ms	6×	body	160	valid

simplify2.1s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
1.9b	(- (exp (* a x)) 1.0)

rewrite20.0ms

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:

5.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1.0)

series53.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(exp (* a x))
39.0ms	(- (exp (* a x)) 1.0)

simplify1.5s

Counts

30 → 30

Iterations

Useful iterations: done (1.5s)

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

prune68.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
0.3b	(* (* a x) 1/6)
0.7b	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
6.5b	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

rewrite193.0ms

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:

71.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
19.0ms	(* (* a x) 1/6)
17.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
83.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
20.0ms	(* (* a x) 1/6)
100.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
89.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: 2 (406.0ms)

Iter	Nodes	Cost
0	174	1752
1	501	1644
2	2029	1427
done	5000	1427

prune233.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (* 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))))

rewrite170.0ms

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:

108.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
22.0ms	(* (* a x) a)
19.0ms	(* (* a x) 1/6)
18.0ms	(* x (+ a (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))))

series213.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
21.0ms	(* (* a x) a)
20.0ms	(* (* a x) 1/6)
102.0ms	(* x (+ a (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))))

simplify1.1s

Counts

95 → 95

Iterations

Useful iterations: done (1.1s)

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

prune165.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
0.1b	(* (* a x) a)
0.3b	(* (* a x) 1/6)
3.6b	(* x (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2)))

rewrite375.0ms

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:

109.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
20.0ms	(* (* a x) a)
20.0ms	(* (* a x) 1/6)
222.0ms	(* x (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
20.0ms	(* (* a x) a)
21.0ms	(* (* a x) 1/6)
96.0ms	(* x (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2)))

simplify1.2s

Counts

103 → 103

Iterations

Useful iterations: done (1.2s)

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

prune172.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes149.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	33
1	26	33
done	26	33

end0.0ms

sample997.0ms

Algorithm

intervals

Results

415.0ms	2727×	body	1280	valid
131.0ms	1341×	body	640	valid
109.0ms	5418×	body	80	valid
47.0ms	742×	body	320	valid
17.0ms	390×	body	160	valid