Details

sample891.0ms

Algorithm

intervals

Results

641.0ms	235×	body	80	valid
88.0ms	213×	body	10240	exit
30.0ms	424×	body	80	nan
4.0ms	26×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5043
8	4148
7	1069
6	332
5	133
4	65
3	37
2	27
1	19
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize21.0ms

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))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp x) 1.0)

rewrite87.0ms

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:

23.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
37.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
9.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp x) 1.0)

series259.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
73.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
42.0ms	(- (exp (* 2.0 x)) 1.0)
27.0ms	(- (exp x) 1.0)

simplify2.2s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
3	3133
2	999
1	396
0	189

prune750.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(sqrt (exp (* 2.0 x)))
5.4b	(- (exp x) 1.0)
5.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite44.0ms

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:

5.0ms	(sqrt (exp (* 2.0 x)))
5.0ms	(sqrt (exp (* 2.0 x)))
15.0ms	(- (exp x) 1.0)
16.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series188.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (exp (* 2.0 x)))
40.0ms	(sqrt (exp (* 2.0 x)))
26.0ms	(- (exp x) 1.0)
93.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify1.9s

Counts

74 → 74

Iterations

Iter	Nodes
done	5005
4	2307
3	938
2	409
1	173
0	87

prune351.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp 2.0) (/ x 2))
0.0b	(sqrt (exp (* 2.0 x)))
5.4b	(- (exp x) 1.0)
5.4b	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

rewrite65.0ms

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:

8.0ms	(pow (exp 2.0) (/ x 2))
4.0ms	(sqrt (exp (* 2.0 x)))
14.0ms	(- (exp x) 1.0)
36.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

series174.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (exp 2.0) (/ x 2))
28.0ms	(sqrt (exp (* 2.0 x)))
25.0ms	(- (exp x) 1.0)
78.0ms	(- (pow (exp 2.0) (/ x 2)) (sqrt 1.0))

simplify1.8s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	2403
2	837
1	351
0	150

prune584.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (exp x) 1.0)
5.4b	(- (exp x) 1.0)
5.4b	(- (exp x) 1.0)
5.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

rewrite79.0ms

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` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `flip--`

Counts

4 → 60

Calls

4 calls:

19.0ms	(- (exp x) 1.0)
16.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)
27.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

series166.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (exp x) 1.0)
27.0ms	(- (exp x) 1.0)
26.0ms	(- (exp x) 1.0)
83.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))

simplify1.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
4	2265
3	926
2	391
1	162
0	76

prune469.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

99.5% (0.0b remaining)

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

bsearch150.0ms

Steps

Iters	Range		Point
8	1.1912796939881877e-06	0.0022991053059264813	1.5780242412218974e-06
10	-945.2327765630807	-4.034181863829644e-08	-9.813313662631737e-06

simplify8.0ms

Iterations

Iter	Nodes
done	39
1	39
0	30

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.7s	6574×	body	10240	exit
1.1s	12433×	body	80	nan
663.0ms	7385×	body	80	valid
106.0ms	733×	body	160	valid