Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	86×	body	1280	valid
4.0ms	47×	body	640	valid
3.0ms	169×	body	80	valid
1.0ms	24×	body	320	valid
0.0ms	10×	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: 30.5b

localize10.0ms

Local error

Found 1 expressions with local error:

2.4b	(- (exp (* a x)) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

11.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify1.4s

Counts

17 → 17

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	45	188
1	105	183
2	266	167
3	722	165
4	2470	165
done	5001	161

prune44.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
0.5b	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
1.0b	(* a (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
5.3b	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
22×	`add-sqr-sqrt`
17×	`associate-l`
15×	`add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
10×	`pow1` `associate-r`
8×	`associate-*r/`
6×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+`
2×	`pow-to-exp` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

6.0ms	(* 1/6 a)
19.0ms	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
86.0ms	(* a (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
28.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* 1/6 a)
46.0ms	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
100.0ms	(* a (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
93.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

simplify931.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (346.0ms)

Iter	Nodes	Cost
0	169	1698
1	483	1592
2	1859	1405
done	5000	1405

prune224.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
0.5b	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
3.2b	(* (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) a)
5.3b	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

6.0ms	(* 1/6 a)
19.0ms	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
81.0ms	(* (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) a)
26.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* 1/6 a)
48.0ms	(* (pow x 2) (+ 1/2 (* x (* 1/6 a))))
91.0ms	(* (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) a)
91.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

simplify944.0ms

Counts

110 → 110

Iterations

Useful iterations: done (941.0ms)

Iter	Nodes	Cost
0	155	1718
1	437	1597
2	1787	1360
done	5000	1354

prune221.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.9b	(* (cbrt a) (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
5.3b	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
14×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-l`
8×	`pow1` `prod-exp`
6×	`associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `cbrt-unprod` `add-log-exp`
2×	`flip3-+` `pow1/3` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 73

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
87.0ms	(* (cbrt a) (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
25.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt a)
175.0ms	(cbrt a)
251.0ms	(* (cbrt a) (+ (* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a))))) x))
94.0ms	(* a (* (pow x 2) (+ 1/2 (* x (* 1/6 a)))))

simplify866.0ms

Counts

85 → 85

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	159	1349
1	454	1270
2	1899	1132
done	5002	1125

prune222.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.4b

regimes201.0ms

Accuracy

97.3% (0.6b remaining)

Error of 3.0b against oracle of 2.4b and baseline of 24.3b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	46
1	32	46
done	32	46

end0.0ms

sample908.0ms

Algorithm

intervals

Results

391.0ms	2660×	body	1280	valid
129.0ms	1342×	body	640	valid
94.0ms	5388×	body	80	valid
44.0ms	746×	body	320	valid
17.0ms	425×	body	160	valid