Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	76×	body	1280	valid
6.0ms	59×	body	640	valid
3.0ms	188×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	16×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.9b	(- (exp x) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

11.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series57.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify2.3s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	99	596
1	221	572
2	501	542
3	1229	537
4	4072	536
done	5001	536

prune114.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

3.0ms	(+ (* x 1/6) 1/2)
10.0ms	(* x (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)

series102.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x 1/6) 1/2)
58.0ms	(* x (+ (* x 1/6) 1/2))
14.0ms	(* x 1/6)

simplify1.9s

Counts

60 → 60

Iterations

Useful iterations: 3 (301.0ms)

Iter	Nodes	Cost
0	78	480
1	204	439
2	502	399
3	1461	397
done	5000	397

prune99.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (sqrt (exp x)) (sqrt 1.0)) (/ x (- (sqrt (exp x)) (sqrt 1.0))))
0.2b	(sqrt (exp x))
0.2b	(sqrt (exp x))
3.9b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

332×	`*-un-lft-identity`
327×	`times-frac`
274×	`add-sqr-sqrt`
188×	`sqrt-prod`
120×	`add-cube-cbrt`
76×	`difference-of-squares`
68×	`distribute-lft-out`
38×	`distribute-lft-out--`
33×	`associate-/r*`
13×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1`
7×	`flip3--` `flip--` `div-inv`
6×	`pow1` `exp-prod` `add-log-exp`
5×	`associate-/l*`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `pow1/2` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+`

Counts

4 → 270

Calls

4 calls:

39.0ms	(/ (+ (sqrt (exp x)) (sqrt 1.0)) (/ x (- (sqrt (exp x)) (sqrt 1.0))))
1.0ms	(sqrt (exp x))
1.0ms	(sqrt (exp x))
8.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series211.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ (sqrt (exp x)) (sqrt 1.0)) (/ x (- (sqrt (exp x)) (sqrt 1.0))))
12.0ms	(sqrt (exp x))
12.0ms	(sqrt (exp x))
38.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify935.0ms

Counts

282 → 282

Iterations

Useful iterations: 2 (251.0ms)

Iter	Nodes	Cost
0	287	6997
1	632	6409
2	2258	5855
done	5000	5855

prune377.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes15.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch32.0ms

Steps

Iters	Range		Point
9	-5.7596417613087905	-8.638519114283913e-09	-0.0002022345445868293

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	28
1	26	28
done	26	28

end0.0ms

sample880.0ms

Algorithm

intervals

Results

390.0ms	2245×	body	1280	valid
180.0ms	1677×	body	640	valid
100.0ms	5529×	body	80	valid
57.0ms	839×	body	320	valid
19.0ms	432×	body	160	valid