Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample26.0ms

Algorithm

intervals

Results

8.0ms	34×	body	640	valid
8.0ms	60×	body	1280	valid
3.0ms	127×	body	80	valid
2.0ms	25×	body	320	valid
0.0ms	10×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune1.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.2b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_10312` `add-sqr-sqrt_binary64_10297` `sqrt-prod_binary64_10291`
4×	`add-log-exp_binary64_10277` `difference-of-squares_binary64_10341`
3×	`add-cube-cbrt_binary64_10283` `pow1_binary64_10254` `distribute-lft-out--_binary64_10357`
2×	`add-exp-log_binary64_10276` `distribute-lft-out_binary64_10356` `add-cbrt-cube_binary64_10284` `sqrt-div_binary64_10292`
1×	`sub-neg_binary64_10316` `diff-log_binary64_10223` `flip3--_binary64_10311` `flip-+_binary64_10337` `rem-sqrt-square_binary64_10300` `pow1/2_binary64_10244` `flip3-+_binary64_10310` `flip--_binary64_10338` `sqrt-pow1_binary64_10293`

Counts

2 → 34

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series496.0ms

Counts

2 → 6

Calls

2 calls:

236.0ms	(sqrt.f64 (+.f64 x 1))
260.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	177	1594
1	177	1594
0	4803	1361
1	4803	1361
0	177	1594
1	177	1594
0	4803	1361
1	4803	1361
0	1	3
1	1	3
0	137	1388
1	137	1388
0	5205	1150
0	137	1388
1	137	1388
0	5205	1150
0	1	3
1	1	3

simplify143.0ms

Counts

40 → 40

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5092	483

prune34.0ms

Filtered

26 candidates to 40 candidates (-53.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Merged error: 0.1b

Counts

41 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_10312`
24×	`sqrt-prod_binary64_10291`
21×	`distribute-lft-out_binary64_10356`
18×	`times-frac_binary64_10307`
16×	`add-sqr-sqrt_binary64_10297`
15×	`add-cube-cbrt_binary64_10283`
7×	`add-exp-log_binary64_10276`
6×	`associate-/r*_binary64_10375`
5×	`add-log-exp_binary64_10277` `pow1_binary64_10254` `add-cbrt-cube_binary64_10284`
3×	`flip-+_binary64_10337` `flip3-+_binary64_10310` `associate-/l*_binary64_10376`
2×	`associate-/r/_binary64_10377` `div-exp_binary64_10261` `sqrt-div_binary64_10292`
1×	`1-exp_binary64_10272` `cbrt-undiv_binary64_10282` `rec-exp_binary64_10260` `div-inv_binary64_10313` `frac-2neg_binary64_10305` `sum-log_binary64_10222` `+-commutative_binary64_10379` `rem-sqrt-square_binary64_10300` `pow-flip_binary64_10238` `pow1/2_binary64_10244` `clear-num_binary64_10315` `inv-pow_binary64_10230` `sqrt-pow1_binary64_10293`

Counts

3 → 75

Calls

3 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
10.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series756.0ms

Counts

3 → 9

Calls

3 calls:

229.0ms	(sqrt.f64 (+.f64 x 1))
261.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
266.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	276	1935
1	276	1935
0	5240	1684
0	276	1935
1	276	1935
0	5240	1684
0	1	3
1	1	3
0	177	1594
1	177	1594
0	4870	1361
1	4870	1361
0	177	1594
1	177	1594
0	4870	1361
1	4870	1361
0	1	3
1	1	3
0	137	1388
1	137	1388
0	5205	1150
0	137	1388
1	137	1388
0	5205	1150
0	1	3
1	1	3

simplify155.0ms

Counts

84 → 84

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	5219	1174

prune67.0ms

Filtered

50 candidates to 84 candidates (-68.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	78	10	88

Merged error: 0.0b

Counts

88 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity_binary64_10312`
290×	`sqrt-prod_binary64_10291`
168×	`times-frac_binary64_10307`
136×	`add-sqr-sqrt_binary64_10297`
116×	`distribute-lft-out_binary64_10356`
88×	`add-cube-cbrt_binary64_10283`
43×	`swap-sqr_binary64_10339`
31×	`pow1_binary64_10254`
27×	`associate-l_binary64_10372` `associate-r_binary64_10371` `sqrt-pow1_binary64_10293`
16×	`unswap-sqr_binary64_10340`
14×	`associate-/r/_binary64_10377` `add-exp-log_binary64_10276`
12×	`associate-/r*_binary64_10375`
11×	`pow-flip_binary64_10238` `inv-pow_binary64_10230`
10×	`add-cbrt-cube_binary64_10284`
9×	`pow-prod-up_binary64_10234` `div-inv_binary64_10313` `pow1/2_binary64_10244`
7×	`flip-+_binary64_10337` `flip3-+_binary64_10310`
6×	`associate-/l*_binary64_10376`
5×	`pow-sqr_binary64_10345` `sqrt-div_binary64_10292` `pow-prod-down_binary64_10235`
4×	`add-log-exp_binary64_10277` `div-exp_binary64_10261`
3×	`rem-sqrt-square_binary64_10300`
2×	`1-exp_binary64_10272` `cbrt-undiv_binary64_10282` `rec-exp_binary64_10260` `frac-2neg_binary64_10305` `clear-num_binary64_10315`
1×	`prod-exp_binary64_10259` `-commutative_binary64_10380` `rem-square-sqrt_binary64_10299` `pow2_binary64_10245` `associate-l/_binary64_10374` `sqrt-unprod_binary64_10295` `associate-*r/_binary64_10373` `pow-plus_binary64_10249` `frac-times_binary64_10304` `cbrt-unprod_binary64_10281`

Counts

4 → 278

Calls

4 calls:

17.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
44.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

series978.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
267.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
258.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
206.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	324	2265
1	324	2265
0	5157	1778
0	324	2265
1	324	2265
0	5157	1778
0	1	3
1	1	3
0	276	1935
1	276	1935
0	5240	1684
0	276	1935
1	276	1935
0	5240	1684
0	1	3
1	1	3
0	276	1935
1	276	1935
0	5240	1684
0	276	1935
1	276	1935
0	5240	1684
0	1	3
1	1	3
0	321	1997
1	321	1997
0	5019	1926
0	321	1997
1	321	1997
0	5019	1926
0	1	3
1	1	3

simplify173.0ms

Counts

290 → 290

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5152	5917

prune189.0ms

Filtered

119 candidates to 290 candidates (-143.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	285	5	290
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	290	10	300

Merged error: 0b

Counts

300 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.5b	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

158×	`sqrt-prod_binary64_10291`
142×	`*-un-lft-identity_binary64_10312`
76×	`times-frac_binary64_10307`
59×	`add-sqr-sqrt_binary64_10297`
58×	`unpow-prod-down_binary64_10243`
52×	`distribute-lft-out_binary64_10356`
49×	`add-cube-cbrt_binary64_10283`
10×	`pow1_binary64_10254`
9×	`add-exp-log_binary64_10276` `rem-sqrt-square_binary64_10300`
8×	`associate-/r/_binary64_10377`
7×	`sqrt-pow1_binary64_10293`
6×	`associate-/r*_binary64_10375` `add-cbrt-cube_binary64_10284`
5×	`pow-pow_binary64_10236`
4×	`div-inv_binary64_10313` `add-log-exp_binary64_10277` `flip-+_binary64_10337` `flip3-+_binary64_10310`
3×	`sqr-pow_binary64_10344` `pow-unpow_binary64_10241` `pow-flip_binary64_10238` `pow1/2_binary64_10244` `associate-/l*_binary64_10376` `inv-pow_binary64_10230`
2×	`div-exp_binary64_10261`
1×	`1-exp_binary64_10272` `cbrt-undiv_binary64_10282` `rec-exp_binary64_10260` `frac-2neg_binary64_10305` `sqrt-div_binary64_10292` `pow-exp_binary64_10232` `clear-num_binary64_10315` `sqrt-pow2_binary64_10294` `pow-to-exp_binary64_10233`

Counts

4 → 176

Calls

4 calls:

13.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
18.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
17.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)

series982.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
276.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
257.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
198.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	382	2082
1	382	2082
0	5996	2061
0	382	2082
1	382	2082
0	5996	2061
0	1	3
1	1	3
0	276	1935
1	276	1935
0	5240	1684
0	276	1935
1	276	1935
0	5240	1684
0	1	3
1	1	3
0	442	2100
1	442	2100
0	4971	2034
1	4971	2034
0	442	2100
1	442	2100
0	4971	2034
1	4971	2034
0	1	3
1	1	3
0	321	1997
1	321	1997
0	5019	1926
0	321	1997
1	321	1997
0	5019	1926
0	1	3
1	1	3

simplify182.0ms

Counts

188 → 188

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4831	3613
1	4831	3613

prune111.0ms

Filtered

93 candidates to 188 candidates (-102.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	188	10	198

Merged error: 0b

Counts

198 → 10

regimes40.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms

sample621.0ms

Algorithm

intervals

Results

222.0ms	1658×	body	1280	valid
126.0ms	1255×	body	640	valid
112.0ms	4143×	body	80	valid
49.0ms	610×	body	320	valid
19.0ms	334×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze3.0ms

sample26.0ms

simplify24.0ms

prune1.0ms

localize5.0ms

rewrite16.0ms

series496.0ms

simplify143.0ms

prune34.0ms

localize7.0ms

rewrite30.0ms

series756.0ms

simplify155.0ms

prune67.0ms

localize9.0ms

rewrite109.0ms

series978.0ms

simplify173.0ms

prune189.0ms

localize10.0ms

rewrite72.0ms

series982.0ms

simplify182.0ms

prune111.0ms

regimes40.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample621.0ms

Profiling