Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample27.0ms

Algorithm

intervals

Results

8.0ms	57×	body	640	valid
7.0ms	38×	body	1280	valid
5.0ms	127×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	76	17
1	76	17

prune2.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 19.7b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
2.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64` `times-frac_binary64`
64×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`
25×	`difference-of-squares_binary64`
13×	`associate-/r*_binary64` `distribute-lft-out--_binary64`
12×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-flip_binary64`
4×	`div-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 166

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
39.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series1.5s

Counts

4 → 12

Calls

4 calls:

259.0ms	(sqrt.f64 (+.f64 x 1))
490.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
422.0ms	(/.f64 1 (sqrt.f64 x))
352.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	712	1160
1	712	1160
0	62	783
1	62	783
0	712	1160
1	712	1160
0	62	783
1	62	783
0	399	141
1	399	141
0	435	849
1	435	849
0	19	9
1	19	9
0	435	849
1	435	849
0	19	9
1	19	9
0	5063	42
0	398	721
1	398	721
0	4949	481
1	4949	481
0	398	721
1	398	721
0	4949	481
1	4949	481
0	4886	69
1	4886	69
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

simplify56.0ms

Counts

178 → 178

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	376	3268
1	376	3268

prune137.0ms

Filtered

105 candidates to 178 candidates (-69.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	167	11	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	11	179

Merged error: 19.2b

Counts

179 → 11

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
39×	`sqrt-prod_binary64`
36×	`*-un-lft-identity_binary64`
12×	`difference-of-squares_binary64`
11×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/l*_binary64` `times-frac_binary64`
9×	`pow1_binary64` `distribute-lft-out--_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `sqrt-div_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-*r/_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-unprod_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series1.3s

Counts

4 → 12

Calls

4 calls:

261.0ms	(sqrt.f64 (+.f64 1 x))
533.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
235.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
300.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (8.0ms)

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	468	827
1	468	827
0	54	102
1	54	102
0	468	827
1	468	827
0	54	102
1	54	102
0	153	57
1	153	57
0	704	1528
1	704	1528
0	1722	1038
1	1722	1038
0	704	1528
1	704	1528
0	1722	1038
1	1722	1038
0	4820	75
1	4820	75
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

simplify98.0ms

Counts

123 → 123

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5269	2157

prune98.0ms

Filtered

85 candidates to 123 candidates (-44.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	131	3	134

Merged error: 0.2b

Counts

134 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
55×	`sqrt-prod_binary64`
49×	`add-sqr-sqrt_binary64`
42×	`distribute-lft-out_binary64`
40×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`
27×	`associate-/l*_binary64`
20×	`add-cbrt-cube_binary64`
14×	`div-exp_binary64`
10×	`pow1_binary64`
8×	`associate-/r/_binary64`
7×	`associate-/r_binary64` `associate-r*_binary64` `cbrt-undiv_binary64`
6×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64` `sqrt-div_binary64`
5×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `rec-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 172

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
24.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series1.6s

Counts

4 → 12

Calls

4 calls:

263.0ms	(sqrt.f64 (+.f64 1 x))
468.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
607.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
234.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	468	827
1	468	827
0	54	102
1	54	102
0	468	827
1	468	827
0	54	102
1	54	102
0	153	57
1	153	57
0	898	1724
1	898	1724
0	290	54
1	290	54
0	898	1724
1	898	1724
0	290	54
1	290	54
0	5026	54
0	584	1187
1	584	1187
0	5555	837
0	584	1187
1	584	1187
0	5555	837
0	5199	168
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

simplify149.0ms

Counts

184 → 184

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4922	3872
1	4922	3872

prune175.0ms

Filtered

111 candidates to 184 candidates (-65.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	177	7	184
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	179	8	187

Merged error: 0.0b

Counts

187 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.1b	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
0.2b	(/.f64 1 (sqrt.f64 x))
0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64`
82×	`times-frac_binary64`
66×	`*-un-lft-identity_binary64`
54×	`add-exp-log_binary64`
53×	`add-cube-cbrt_binary64`
38×	`sqrt-prod_binary64`
29×	`associate-r_binary64`
28×	`associate-l_binary64`
22×	`add-cbrt-cube_binary64`
20×	`div-exp_binary64`
19×	`unswap-sqr_binary64`
17×	`prod-exp_binary64`
15×	`pow1_binary64`
12×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
10×	`associate-/r*_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
8×	`frac-add_binary64`
7×	`distribute-rgt-out_binary64`
6×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `pow-flip_binary64`
5×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `inv-pow_binary64` `div-inv_binary64` `insert-posit16`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64` `sqrt-unprod_binary64` `un-div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 217

Calls

4 calls:

10.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
31.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
5.0ms	(/.f64 1 (sqrt.f64 x))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

series1.8s

Counts

4 → 12

Calls

4 calls:

601.0ms	(/.f64 1 (+.f64 (+.f64 x 1) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
553.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 x 1) (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))))
412.0ms	(/.f64 1 (sqrt.f64 x))
233.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	468	827
1	468	827
0	54	102
1	54	102
0	468	827
1	468	827
0	54	102
1	54	102
0	153	57
1	153	57
0	435	849
1	435	849
0	19	9
1	19	9
0	435	849
1	435	849
0	19	9
1	19	9
0	5063	42
0	974	1761
1	974	1761
0	171	1368
1	171	1368
0	974	1761
1	974	1761
0	171	1368
1	171	1368
0	5334	59
0	694	1447
1	694	1447
0	5003	1221
0	694	1447
1	694	1447
0	5003	1221
0	4992	205
1	4992	205

simplify171.0ms

Counts

229 → 229

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4961	5366
1	4961	5366

prune199.0ms

Filtered

137 candidates to 229 candidates (-67.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	229	8	237

Merged error: 0.0b

Counts

237 → 8

regimes22.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	26
1	18	26

end0.0ms

sample780.0ms

Algorithm

intervals

Results

250.0ms	1805×	body	640	valid
196.0ms	1113×	body	1280	valid
151.0ms	4140×	body	80	valid
62.0ms	609×	body	320	valid
25.0ms	333×	body	160	valid

Details

analyze1.0ms

sample27.0ms

simplify25.0ms

prune2.0ms

localize11.0ms

rewrite65.0ms

series1.5s

simplify56.0ms

prune137.0ms

localize7.0ms

rewrite48.0ms

series1.3s

simplify98.0ms

prune98.0ms

localize8.0ms

rewrite61.0ms

series1.6s

simplify149.0ms

prune175.0ms

localize9.0ms

rewrite68.0ms

series1.8s

simplify171.0ms

prune199.0ms

regimes22.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample780.0ms

Profiling