Details

sample389.0ms

Algorithm

intervals

Results

56.0ms	195×	body	10240	exit
13.0ms	399×	body	80	nan
7.0ms	233×	body	80	valid
2.0ms	30×	body	160	valid

simplify71.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 5.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.5b	(- (exp (* 2.0 x)) 1.0)
6.6b	(- (exp x) 1.0)

rewrite101.0ms

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:

27.0ms	(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)

series201.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify118.0ms

Counts

135 → 135

Iterations

Useful iterations: 3 (106.0ms)

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

prune336.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

6.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.6b	(- (exp x) 1.0)
6.6b	(- (exp x) 1.0)
6.6b	(- (exp x) 1.0)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-log-exp`
7×	`difference-of-squares`
6×	`sqrt-prod`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--`

Counts

4 → 60

Calls

4 calls:

19.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms	(- (exp x) 1.0)
10.0ms	(- (exp x) 1.0)
10.0ms	(- (exp x) 1.0)

series94.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)

simplify92.0ms

Counts

72 → 72

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	156	394
1	399	367
2	1035	363
3	2831	363
4	5002	363
done	5002	363

prune244.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
0.3b	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
6.6b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.8b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

212×	`add-sqr-sqrt`
172×	`*-un-lft-identity`
156×	`sqrt-prod`
106×	`times-frac`
88×	`difference-of-squares`
44×	`distribute-lft-out--`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
14×	`associate-/r` `associate-/l`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`div-sub`

Counts

4 → 203

Calls

4 calls:

60.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
59.0ms	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
17.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series353.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
123.0ms	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
51.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
38.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify60.0ms

Counts

215 → 215

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	511	3486
1	1665	3371
2	5001	3320
done	5001	3320

prune437.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))) (- (sqrt (exp x)) (sqrt 1.0)))
0.3b	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
6.8b	(- (sqrt (exp x)) (sqrt 1.0))
6.8b	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
66×	`sqrt-prod`
60×	`add-sqr-sqrt`
34×	`times-frac`
24×	`distribute-lft-out`
21×	`difference-of-squares`
18×	`add-cube-cbrt`
14×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l/`
9×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`flip3--` `flip--` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`pow1` `frac-times` `associate-/r/`
3×	`cbrt-undiv` `div-exp`
2×	`sub-neg` `frac-2neg` `diff-log` `associate-r/` `associate-l/` `clear-num` `div-inv`
1×	`prod-exp` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

79.0ms	(/ (* (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))) (- (sqrt (exp x)) (sqrt 1.0)))
58.0ms	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
15.0ms	(- (sqrt (exp x)) (sqrt 1.0))
26.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

series817.0ms

Counts

4 → 12

Calls

4 calls:

499.0ms	(/ (* (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))) (- (sqrt (exp x)) (sqrt 1.0)))
132.0ms	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
37.0ms	(- (sqrt (exp x)) (sqrt 1.0))
149.0ms	(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

simplify77.0ms

Counts

148 → 148

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	661	2445
1	2996	2105
2	5001	2045
done	5001	2045

prune484.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes39.0ms

Accuracy

98.7% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 3.3b

bsearch95.0ms

Steps

Iters	Range		Point
7	1.14976441626985e-06	0.00021078761332869983	1.2338198931570103e-06
8	-1.2730755148939865e-07	-2.0640863993498756e-10	-1.0486325841563261e-07

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	44
1	54	44
done	54	44

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	6515×	body	10240	exit
384.0ms	12164×	body	80	nan
238.0ms	7421×	body	80	valid
53.0ms	699×	body	160	valid