Details

sample506.0ms

Algorithm

intervals

Results

297.0ms	203×	body	10240	exit
32.0ms	384×	body	80	nan
22.0ms	245×	body	80	valid
3.0ms	16×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize27.0ms

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)

rewrite166.0ms

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:

58.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp x) 1.0)

series283.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(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)
38.0ms	(- (exp x) 1.0)

simplify1.8s

Counts

135 → 135

Iterations

Useful iterations: done (1.8s)

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

prune545.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`pow1` `add-sqr-sqrt`
5×	`sqrt-div`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`flip3-+` `flip-+` `difference-of-squares`
2×	`frac-times` `sub-neg` `flip3--` `sqrt-pow1` `diff-log` `associate-*r/` `flip--`
1×	`+-commutative` `pow1/2` `exp-sum` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 56

Calls

4 calls:

16.0ms	(+ (exp x) 1.0)
99.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
24.0ms	(- (exp (* 2.0 x)) 1.0)
85.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series241.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp x) 1.0)
160.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
40.0ms	(- (exp (* 2.0 x)) 1.0)
32.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.3s

Counts

68 → 68

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	144	989
1	337	935
2	976	860
3	3369	775
done	5001	757

prune364.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize48.0ms

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))

rewrite127.0ms

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)
15.0ms	(- (exp (* 2.0 x)) 1.0)
92.0ms	(- (exp (+ x x)) (* 1.0 1.0))
13.0ms	(- 1.0 (exp x))

series112.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (exp x) 3)
26.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (+ x x)) (* 1.0 1.0))
15.0ms	(- 1.0 (exp x))

simplify4.3s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.6s)

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

prune836.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (exp (* 2.0 x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

35.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
23.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
13.0ms	(- (exp (* 2.0 x)) 1.0)
97.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series210.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
52.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
45.0ms	(- (exp (* 2.0 x)) 1.0)
35.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify4.0s

Counts

96 → 96

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	140	1353
1	317	1136
2	901	1025
3	4885	1009
done	5000	1009

prune412.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

75.4% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 2.8b

bsearch58.0ms

Steps

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

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	51
1	44	51
done	44	51

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.0s	6421×	body	10240	exit
1.6s	12501×	body	80	nan
511.0ms	7417×	body	80	valid
138.0ms	708×	body	160	valid