Details

sample465.0ms

Algorithm

intervals

Results

216.0ms	203×	body	10240	exit
25.0ms	384×	body	80	nan
15.0ms	245×	body	80	valid
2.0ms	16×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	175	12
6	479	12
7	1665	12
done	5000	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.1b	(- (exp x) 1.0)

rewrite118.0ms

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:

29.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
56.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series277.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
86.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
39.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp x) 1.0)

simplify1.9s

Counts

135 → 135

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	904	2169
3	2293	2156
done	5001	2154

prune517.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(sqrt (+ (exp x) 1.0))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`sub-neg` `flip3--` `flip3-+` `sqrt-div` `diff-log` `flip--` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-sum` `sum-log` `distribute-lft-out--`

Counts

4 → 56

Calls

4 calls:

19.0ms	(+ (exp x) 1.0)
24.0ms	(sqrt (+ (exp x) 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)
88.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series133.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (exp x) 1.0)
53.0ms	(sqrt (+ (exp x) 1.0))
41.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.4s

Counts

68 → 68

Iterations

Useful iterations: 3 (576.0ms)

Iter	Nodes	Cost
0	127	697
1	276	657
2	717	598
3	2084	585
done	5000	585

prune381.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (+ x x)) (* 1.0 1.0))
3.1b	(- 1.0 (exp x))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `pow-pow` `difference-of-squares`
3×	`sub-neg` `unpow-prod-down` `pow-unpow` `exp-prod` `flip3--` `diff-log` `cube-prod` `flip--`
2×	`distribute-lft-out--`
1×	`cube-mult` `pow-to-exp` `unpow3` `exp-sum` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

5.0ms	(pow (exp x) 3)
12.0ms	(- (exp (* 2.0 x)) 1.0)
98.0ms	(- (exp (+ x x)) (* 1.0 1.0))
7.0ms	(- 1.0 (exp x))

series110.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (exp x) 3)
33.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))
18.0ms	(- 1.0 (exp x))

simplify4.8s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	142	727
1	305	659
2	903	597
3	4842	586
done	5000	586

prune499.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

13.0ms	(- (exp (* 2.0 x)) 1.0)
12.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp (* 2.0 x)) 1.0)
59.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series171.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (exp (* 2.0 x)) 1.0)
44.0ms	(- (exp (* 2.0 x)) 1.0)
44.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.7s

Counts

68 → 68

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	78	760
1	171	736
2	433	656
3	1150	646
4	3602	638
done	5001	638

prune424.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

74.6% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.8b

bsearch79.0ms

Steps

Iters	Range		Point
8	-4.403108084983288e-07	-5.598498926449877e-10	-3.6396238490178844e-07

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	52
1	41	52
done	41	52

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.5s	6421×	body	10240	exit
1.0s	12501×	body	80	nan
649.0ms	7417×	body	80	valid
147.0ms	708×	body	160	valid