Details

sample52.0ms

Algorithm

intervals

Results

20.0ms	76×	body	1280	valid
7.0ms	41×	body	640	valid
6.0ms	172×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	13×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.2b	(- (exp (* a x)) 1.0)

rewrite35.0ms

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:

8.0ms	(exp (* a x))
26.0ms	(- (exp (* a x)) 1.0)

series94.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(exp (* a x))
76.0ms	(- (exp (* a x)) 1.0)

simplify2.5s

Counts

30 → 30

Iterations

Useful iterations: done (2.5s)

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

prune115.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a x) 1/6)
1.0b	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
1.3b	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
5.8b	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

rewrite281.0ms

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)
16.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
100.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
143.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* a x) 1/6)
144.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
67.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
129.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

simplify1.9s

Counts

108 → 108

Iterations

Useful iterations: 2 (666.0ms)

Iter	Nodes	Cost
0	174	1752
1	501	1640
2	2020	1427
done	5002	1427

prune316.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
0.2b	(* (* x a) a)
0.3b	(* (* a x) 1/6)
1.0b	(* x (+ a (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))))

rewrite220.0ms

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:

141.0ms	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
31.0ms	(* (* x a) a)
25.0ms	(* (* a x) 1/6)
18.0ms	(* x (+ a (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
29.0ms	(* (* x a) a)
40.0ms	(* (* a x) 1/6)
175.0ms	(* x (+ a (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))))

simplify1.8s

Counts

95 → 95

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	150	1407
1	450	1318
2	2115	1118
done	5000	1116

prune281.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
0.2b	(* (* x a) a)
0.3b	(* (* a x) 1/6)
3.1b	(* x (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2)))

rewrite588.0ms

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:

169.0ms	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
18.0ms	(* (* x a) a)
23.0ms	(* (* a x) 1/6)
371.0ms	(* x (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
47.0ms	(* (* x a) a)
30.0ms	(* (* a x) 1/6)
144.0ms	(* x (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2)))

simplify2.0s

Counts

103 → 103

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	147	1565
1	432	1475
2	2225	1159
done	5001	1145

prune213.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes244.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	34
1	27	34
done	27	34

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2658×	body	1280	valid
273.0ms	5416×	body	80	valid
226.0ms	1340×	body	640	valid
124.0ms	759×	body	320	valid
30.0ms	401×	body	160	valid