Details

sample70.0ms

Algorithm

intervals

Results

32.0ms	89×	body	1280	valid
9.0ms	36×	body	640	valid
8.0ms	167×	body	80	valid
4.0ms	26×	body	320	valid
1.0ms	6×	body	160	valid

simplify3.3s

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: 29.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.1b	(- (exp (* a x)) 1.0)

rewrite36.0ms

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

series65.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(exp (* a x))
44.0ms	(- (exp (* a x)) 1.0)

simplify2.2s

Counts

30 → 30

Iterations

Useful iterations: done (2.2s)

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

prune121.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a x) 1/6)
0.5b	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
0.9b	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
6.2b	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

rewrite260.0ms

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)))))
101.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
117.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* a x) 1/6)
151.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
65.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
113.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

simplify1.8s

Counts

108 → 108

Iterations

Useful iterations: 2 (682.0ms)

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

prune434.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
0.1b	(* (* x a) a)
0.3b	(* (* a x) 1/6)
0.5b	(* x (+ a (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))))

rewrite225.0ms

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:

145.0ms	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
18.0ms	(* (* x a) a)
24.0ms	(* (* a x) 1/6)
33.0ms	(* x (+ a (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))
50.0ms	(* (* x a) a)
34.0ms	(* (* a x) 1/6)
177.0ms	(* x (+ a (* (* (* x a) a) (+ (* (* a x) 1/6) 1/2))))

simplify1.7s

Counts

95 → 95

Iterations

Useful iterations: done (1.7s)

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

prune295.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.0b	(exp (* 2 (* a x)))
2.1b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`difference-of-squares`
14×	`*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod` `add-log-exp`
8×	`sqr-pow`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 64

Calls

4 calls:

4.0ms	(exp (* a x))
9.0ms	(exp (* a x))
9.0ms	(exp (* 2 (* a x)))
52.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series131.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (* a x))
26.0ms	(exp (* a x))
26.0ms	(exp (* 2 (* a x)))
65.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify2.0s

Counts

76 → 76

Iterations

Useful iterations: 3 (645.0ms)

Iter	Nodes	Cost
0	101	975
1	236	894
2	658	855
3	2455	843
done	5000	843

prune318.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes280.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.3b

bsearch2.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	49
1	38	49
done	38	49

end0.0ms

sample2.2s

Algorithm

intervals

Results

808.0ms	2705×	body	1280	valid
659.0ms	5432×	body	80	valid
250.0ms	1331×	body	640	valid
159.0ms	787×	body	320	valid
29.0ms	372×	body	160	valid