Details

sample309.0ms

Algorithm

intervals

Results

93.0ms	240×	body	80	valid
74.0ms	194×	body	10240	exit
25.0ms	433×	body	80	nan
3.0ms	23×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	343
1	19	343
2	28	343
3	40	343
4	74	343
5	179	343
6	752	343
done	5000	343

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.3b	(- (exp x) 1.0)

rewrite137.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 123

Calls

4 calls:

27.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
65.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
19.0ms	(- (exp (* 2.0 x)) 1.0)
17.0ms	(- (exp x) 1.0)

series262.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
76.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
54.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

135 → 135

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	189	64260
1	396	60394
2	1219	60114
done	5001	59954

prune601.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (exp (* 2.0 x)))
0.3b	(sqrt (exp (* 2.0 x)))
4.3b	(- (exp x) 1.0)
4.3b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
2.0ms	(sqrt (exp (* 2.0 x)))
8.0ms	(- (exp x) 1.0)
14.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series149.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (exp (* 2.0 x)))
34.0ms	(sqrt (exp (* 2.0 x)))
23.0ms	(- (exp x) 1.0)
68.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: 3 (370.0ms)

Iter	Nodes	Cost
0	87	19082
1	174	16883
2	449	16883
3	1377	16684
done	5000	16684

prune426.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp 2.0) (/ x 2))
0.3b	(sqrt (exp (* 2.0 x)))
4.3b	(- (exp x) 1.0)
4.3b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

5.0ms	(pow (exp 2.0) (/ x 2))
4.0ms	(sqrt (exp (* 2.0 x)))
16.0ms	(- (exp x) 1.0)
46.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

series146.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (exp 2.0) (/ x 2))
32.0ms	(sqrt (exp (* 2.0 x)))
19.0ms	(- (exp x) 1.0)
66.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

simplify924.0ms

Counts

90 → 90

Iterations

Useful iterations: done (910.0ms)

Iter	Nodes	Cost
0	150	33072
1	358	29457
2	1142	29206
done	5000	29006

prune834.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp 2.0) (/ x 2))
0.1b	(pow (exp 2.0) (/ x 2))
4.3b	(- (exp x) 1.0)
4.3b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
26×	`pow-unpow` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
8×	`unpow-prod-down` `pow-pow` `add-log-exp`
7×	`difference-of-squares`
6×	`pow1` `exp-prod`
4×	`add-cbrt-cube` `add-exp-log` `sqr-pow`
3×	`sqrt-prod`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

4 → 93

Calls

4 calls:

6.0ms	(pow (exp 2.0) (/ x 2))
5.0ms	(pow (exp 2.0) (/ x 2))
11.0ms	(- (exp x) 1.0)
38.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

series205.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow (exp 2.0) (/ x 2))
49.0ms	(pow (exp 2.0) (/ x 2))
26.0ms	(- (exp x) 1.0)
74.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

simplify916.0ms

Counts

105 → 105

Iterations

Useful iterations: done (894.0ms)

Iter	Nodes	Cost
0	134	41850
1	337	37159
2	1106	37078
done	5000	36918

prune726.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

75% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.0b

bsearch54.0ms

Steps

Iters	Range		Point
5	-6.8406817238881764e-12	-3.323511487531625e-12	-6.780812387076979e-12

simplify18.0ms

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	35	1408
1	42	1408
done	42	1408

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.4s	6720×	body	10240	exit
2.1s	12340×	body	80	nan
695.0ms	7398×	body	80	valid
185.0ms	753×	body	160	valid