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

7.0ms	60×	body	1280	valid
3.0ms	127×	body	80	valid
3.0ms	34×	body	640	valid
2.0ms	25×	body	320	valid
0.0ms	10×	body	160	valid

simplify25.0ms

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` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 36

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
11.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series586.0ms

Counts

2 → 6

Calls

2 calls:

274.0ms	(sqrt.f64 (+.f64 x 1))
312.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	390	547
1	390	547
0	13	9
1	13	9
0	390	547
1	390	547
0	13	9
1	13	9
0	4912	39
1	4912	39
0	248	271
1	248	271
0	11	9
1	11	9
0	248	271
1	248	271
0	11	9
1	11	9
0	77	39
1	77	39

simplify111.0ms

Counts

42 → 42

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4995	576
1	4995	576

prune36.0ms

Filtered

31 candidates to 42 candidates (-35.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	4	43

Merged error: 0.1b

Counts

43 → 4

localize8.0ms

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`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `insert-posit16` `flip-+_binary64`
2×	`associate-/r/_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

3 → 78

Calls

3 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
10.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series1.1s

Counts

3 → 9

Calls

3 calls:

275.0ms	(sqrt.f64 (+.f64 x 1))
381.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
490.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	584	1187
1	584	1187
0	5555	837
0	584	1187
1	584	1187
0	5555	837
0	5199	168
0	390	547
1	390	547
0	12	9
1	12	9
0	390	547
1	390	547
0	12	9
1	12	9
0	4988	42
1	4988	42
0	248	271
1	248	271
0	11	9
1	11	9
0	248	271
1	248	271
0	11	9
1	11	9
0	77	39
1	77	39

simplify69.0ms

Counts

87 → 87

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4979	1440
1	4979	1440

prune77.0ms

Filtered

58 candidates to 87 candidates (-50.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	81	10	91

Merged error: 0.0b

Counts

91 → 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)))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity_binary64`
290×	`sqrt-prod_binary64`
168×	`times-frac_binary64`
136×	`add-sqr-sqrt_binary64`
116×	`distribute-lft-out_binary64`
88×	`add-cube-cbrt_binary64`
43×	`swap-sqr_binary64`
31×	`pow1_binary64`
27×	`associate-r_binary64` `associate-l_binary64` `sqrt-pow1_binary64`
16×	`unswap-sqr_binary64`
14×	`add-exp-log_binary64` `associate-/r/_binary64`
12×	`associate-/r*_binary64`
11×	`inv-pow_binary64` `pow-flip_binary64`
10×	`add-cbrt-cube_binary64`
9×	`pow1/2_binary64` `pow-prod-up_binary64` `div-inv_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-/l*_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64` `insert-posit16`
3×	`rem-sqrt-square_binary64`
2×	`1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 282

Calls

4 calls:

14.0ms	(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)))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
50.0ms	(*.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)))))

series2.2s

Counts

4 → 12

Calls

4 calls:

573.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
489.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
490.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
683.0ms	(*.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 (157.0ms)

Iter	Nodes	Cost
0	765	1843
1	765	1843
0	5016	1505
0	765	1843
1	765	1843
0	5016	1505
0	4966	100
1	4966	100
0	584	1187
1	584	1187
0	5555	837
0	584	1187
1	584	1187
0	5555	837
0	5199	168
0	584	1187
1	584	1187
0	5555	837
0	584	1187
1	584	1187
0	5555	837
0	5199	168
0	694	1343
1	694	1343
0	4934	1176
1	4934	1176
0	694	1343
1	694	1343
0	4934	1176
1	4934	1176
0	5868	143

simplify174.0ms

Counts

294 → 294

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4873	6574
1	4873	6574

prune241.0ms

Filtered

132 candidates to 294 candidates (-122.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	289	5	294
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	294	10	304

Merged error: 0b

Counts

304 → 10

localize13.0ms

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)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

158×	`sqrt-prod_binary64`
142×	`*-un-lft-identity_binary64`
76×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
58×	`unpow-prod-down_binary64`
52×	`distribute-lft-out_binary64`
49×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`add-exp-log_binary64` `rem-sqrt-square_binary64`
8×	`associate-/r/_binary64`
7×	`sqrt-pow1_binary64`
6×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
5×	`pow-pow_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `div-inv_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow-unpow_binary64` `pow1/2_binary64` `sqr-pow_binary64` `inv-pow_binary64` `associate-/l*_binary64` `pow-flip_binary64`
2×	`div-exp_binary64`
1×	`pow-to-exp_binary64` `sqrt-pow2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`

Counts

4 → 180

Calls

4 calls:

14.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
20.0ms	(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)))
18.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)

series2.4s

Counts

4 → 12

Calls

4 calls:

579.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
707.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
488.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
654.0ms	(pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4)

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	945	1606
1	945	1606
0	865	1249
1	865	1249
0	945	1606
1	945	1606
0	865	1249
1	865	1249
0	4968	144
1	4968	144
0	584	1187
1	584	1187
0	5555	837
0	584	1187
1	584	1187
0	5555	837
0	5199	168
0	999	1685
1	999	1685
0	4996	1567
1	4996	1567
0	999	1685
1	999	1685
0	4996	1567
1	4996	1567
0	4992	152
1	4992	152
0	694	1343
1	694	1343
0	4934	1176
1	4934	1176
0	694	1343
1	694	1343
0	4934	1176
1	4934	1176
0	5868	143

simplify160.0ms

Counts

192 → 192

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4893	4403
1	4893	4403

prune143.0ms

Filtered

104 candidates to 192 candidates (-84.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	192	10	202

Merged error: 0b

Counts

202 → 10

regimes41.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms

sample601.0ms

Algorithm

intervals

Results

210.0ms	1658×	body	1280	valid
121.0ms	1255×	body	640	valid
114.0ms	4143×	body	80	valid
47.0ms	610×	body	320	valid
16.0ms	334×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze3.0ms

sample26.0ms

simplify25.0ms

prune1.0ms

localize5.0ms

rewrite16.0ms

series586.0ms

simplify111.0ms

prune36.0ms

localize8.0ms

rewrite30.0ms

series1.1s

simplify69.0ms

prune77.0ms

localize9.0ms

rewrite112.0ms

series2.2s

simplify174.0ms

prune241.0ms

localize13.0ms

rewrite76.0ms

series2.4s

simplify160.0ms

prune143.0ms

regimes41.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample601.0ms

Profiling