Details

sample412.0ms

Algorithm

intervals

Results

61.0ms	226×	body	10240	exit
11.0ms	375×	body	80	nan
9.0ms	237×	body	80	valid
2.0ms	21×	body	160	valid

simplify75.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7
done	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp x) 1.0)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

28.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
42.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms	(- (exp (* 2.0 x)) 1.0)
12.0ms	(- (exp x) 1.0)

series204.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

simplify120.0ms

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293
done	5003	1293

prune326.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (exp (* 2.0 x)))
0.3b	(sqrt (exp (* 2.0 x)))
4.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.6b	(- (exp x) 1.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `sqrt-prod`
10×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-pow1`
5×	`difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `pow1/2` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

5.0ms	(sqrt (exp (* 2.0 x)))
3.0ms	(sqrt (exp (* 2.0 x)))
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series111.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (exp (* 2.0 x)))
23.0ms	(sqrt (exp (* 2.0 x)))
47.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify103.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	168	382
1	414	365
2	1068	363
3	3163	361
4	5001	361
done	5001	361

prune208.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp 2.0) (* 1/2 x))
0.3b	(sqrt (exp (* 2.0 x)))
4.6b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.6b	(- (exp x) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-log-exp`
7×	`add-cube-cbrt` `difference-of-squares`
6×	`pow1` `sqrt-prod`
5×	`unpow-prod-down`
4×	`add-exp-log` `exp-prod` `pow-pow` `add-cbrt-cube`
3×	`sqrt-pow1` `sqr-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `exp-to-pow` `pow1/2` `pow-exp`

Counts

4 → 66

Calls

4 calls:

7.0ms	(pow (exp 2.0) (* 1/2 x))
3.0ms	(sqrt (exp (* 2.0 x)))
27.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series124.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (exp 2.0) (* 1/2 x))
26.0ms	(sqrt (exp (* 2.0 x)))
54.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify65.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	243	428
1	686	409
2	2418	406
3	5002	404
done	5002	404

prune266.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- (exp x) 1.0) 3))
0.3b	(sqrt (exp (* 2.0 x)))
4.6b	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
4.6b	(- (exp x) 1.0)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
16×	`cbrt-prod` `*-un-lft-identity`
9×	`add-log-exp` `difference-of-squares`
8×	`add-cube-cbrt`
7×	`unpow-prod-down`
6×	`sqrt-prod`
5×	`pow1` `cube-prod`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
3×	`flip3--` `sqrt-pow1` `flip--` `sqr-pow`
2×	`cube-div` `sub-neg` `cbrt-div` `diff-log`
1×	`cube-mult` `rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `pow1/3` `unpow3` `rem-cbrt-cube`

Counts

4 → 75

Calls

4 calls:

12.0ms	(cbrt (pow (- (exp x) 1.0) 3))
3.0ms	(sqrt (exp (* 2.0 x)))
29.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)

series107.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt (pow (- (exp x) 1.0) 3))
22.0ms	(sqrt (exp (* 2.0 x)))
55.0ms	(- (pow (exp 2.0) (* 1/2 x)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify104.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	293	489
1	928	475
2	3891	471
3	5001	471
done	5001	471

prune289.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

75.2% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.9b

bsearch31.0ms

Steps

Iters	Range		Point
5	-1.7281007446970404e-10	-4.560344852981834e-11	-1.6932215378213687e-10

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20
done	35	20

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6893×	body	10240	exit
394.0ms	12839×	body	80	nan
241.0ms	7396×	body	80	valid
55.0ms	727×	body	160	valid