Details

analyze2.0ms

Algorithm

Search

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

sample27.0ms

Algorithm

intervals

Results

9.0ms	67×	body	640	valid
5.0ms	28×	body	1280	valid
5.0ms	128×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	76	17
1	76	17

prune3.0ms

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: 23.4b

Counts

2 → 1

localize8.0ms

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))
2.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite70.0ms

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))
40.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series8.5s

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt.f64 (+.f64 x 1))
2.1s	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
549.0ms	(/.f64 1 (sqrt.f64 x))
3.9s	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	14889	1650
1	14889	1650
0	14889	1650
1	14889	1650
0	5215	20
0	1100	1157
1	1100	1157
0	1100	1157
1	1100	1157
0	4961	14
1	4961	14
0	9681	1235
1	9681	1235
0	9681	1235
1	9681	1235
0	5326	9
0	10670	588
1	10670	588
0	10670	588
1	10670	588
0	4960	9
1	4960	9

simplify164.0ms

Counts

178 → 178

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4869	3006
1	4869	3006

prune136.0ms

Filtered

95 candidates to 178 candidates (-87.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	165	13	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	13	179

Merged error: 22.8b

Counts

179 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (sqrt.f64 x))
0.2b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
2.3b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

1318×	`*-un-lft-identity_binary64`
1237×	`times-frac_binary64`
717×	`add-sqr-sqrt_binary64`
426×	`distribute-lft-out_binary64`
304×	`sqrt-prod_binary64`
285×	`add-cube-cbrt_binary64`
180×	`distribute-lft-out--_binary64`
167×	`div-inv_binary64`
162×	`difference-of-squares_binary64`
29×	`associate-/r*_binary64`
28×	`associate-/l*_binary64`
14×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `pow-flip_binary64`
5×	`associate-/r/_binary64` `div-exp_binary64`
4×	`insert-posit16`
3×	`associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-add_binary64` `div-sub_binary64`

Counts

4 → 540

Calls

4 calls:

8.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
6.0ms	(/.f64 1 (sqrt.f64 x))
78.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
26.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series23.8s

Counts

4 → 12

Calls

4 calls:

2.0s	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
532.0ms	(/.f64 1 (sqrt.f64 x))
10.7s	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
10.6s	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

Iterations

Useful iterations: 0 (199.0ms)

Iter	Nodes	Cost
0	40491	287
1	40491	287
0	39288	287
1	39288	287
0	5178	15
0	47020	1930
1	47020	1930
0	38564	1930
1	38564	1930
0	4878	6
1	4878	6
0	1100	1157
1	1100	1157
0	1100	1157
1	1100	1157
0	4961	14
1	4961	14
0	9681	1235
1	9681	1235
0	9681	1235
1	9681	1235
0	5326	9

simplify244.0ms

Counts

552 → 552

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5463	21631

prune284.0ms

Filtered

142 candidates to 552 candidates (-288.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	548	4	552
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	560	5	565

Merged error: 4.5b

Counts

565 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (sqrt.f64 x))
0.7b	(/.f64 1 (*.f64 x (+.f64 1 x)))
4.7b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

417×	`times-frac_binary64`
399×	`*-un-lft-identity_binary64`
164×	`distribute-lft-out_binary64`
148×	`sqrt-prod_binary64`
141×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
61×	`div-inv_binary64`
42×	`add-exp-log_binary64`
41×	`associate-/r/_binary64`
36×	`associate-*r/_binary64`
30×	`associate-/r*_binary64`
22×	`add-cbrt-cube_binary64`
20×	`flip3-+_binary64` `flip-+_binary64`
19×	`div-exp_binary64`
18×	`associate-/l*_binary64`
11×	`pow1_binary64`
9×	`cbrt-undiv_binary64`
8×	`pow-flip_binary64`
6×	`1-exp_binary64` `prod-exp_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `insert-posit16`
3×	`inv-pow_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `frac-add_binary64`

Counts

4 → 323

Calls

4 calls:

8.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))
8.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
54.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

series8.6s

Counts

4 → 12

Calls

4 calls:

1.9s	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
536.0ms	(/.f64 1 (sqrt.f64 x))
1.8s	(/.f64 1 (*.f64 x (+.f64 1 x)))
4.3s	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	18140	1969
1	18140	1969
0	18140	1969
1	18140	1969
0	4878	6
1	4878	6
0	9869	1154
1	9869	1154
0	9869	1154
1	9869	1154
0	1	3
1	1	3
0	1100	1157
1	1100	1157
0	1100	1157
1	1100	1157
0	4961	14
1	4961	14
0	9681	1235
1	9681	1235
0	9681	1235
1	9681	1235
0	5326	9

simplify187.0ms

Counts

335 → 335

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5077	9150

prune234.0ms

Filtered

124 candidates to 335 candidates (-170.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	326	9	335
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	330	10	340

Merged error: 0.0b

Counts

340 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.1b	(*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.2b	(/.f64 1 (sqrt.f64 x))
0.4b	(/.f64 (/.f64 1 x) (*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity_binary64`
88×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
57×	`add-cube-cbrt_binary64`
40×	`sqrt-prod_binary64`
36×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
21×	`distribute-lft-out_binary64`
19×	`associate-/l*_binary64`
16×	`associate-r_binary64` `div-exp_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
14×	`associate-/r*_binary64`
13×	`associate-/r/_binary64`
12×	`frac-times_binary64`
10×	`pow1_binary64`
9×	`div-inv_binary64`
8×	`cbrt-undiv_binary64`
6×	`associate-*r/_binary64` `frac-add_binary64` `pow-flip_binary64`
5×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `associate-l_binary64` `rec-exp_binary64` `insert-posit16` `associate-*l/_binary64`
3×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 206

Calls

4 calls:

8.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
51.0ms	(*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
5.0ms	(/.f64 1 (sqrt.f64 x))
51.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))

series14.1s

Counts

4 → 12

Calls

4 calls:

2.0s	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
6.5s	(*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
541.0ms	(/.f64 1 (sqrt.f64 x))
5.1s	(/.f64 (/.f64 1 x) (*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))

Iterations

Useful iterations: 0 (201.0ms)

Iter	Nodes	Cost
0	24144	1913
1	24144	1913
0	24144	1913
1	24144	1913
0	4878	6
1	4878	6
0	1100	1157
1	1100	1157
0	1100	1157
1	1100	1157
0	4961	14
1	4961	14
0	37727	1767
1	37727	1767
0	37727	1767
1	37727	1767
0	5574	20
0	9681	1235
1	9681	1235
0	9681	1235
1	9681	1235
0	5326	9

simplify122.0ms

Counts

218 → 218

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4980	3947
1	4980	3947

prune189.0ms

Filtered

127 candidates to 218 candidates (-71.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	220	8	228

Merged error: 0b

Counts

228 → 8

regimes22.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	28
1	16	28

end0.0ms

sample795.0ms

Algorithm

intervals

Results

259.0ms	1853×	body	640	valid
212.0ms	1198×	body	1280	valid
147.0ms	4047×	body	80	valid
64.0ms	610×	body	320	valid
22.0ms	292×	body	160	valid

Details

analyze2.0ms

sample27.0ms

simplify29.0ms

prune3.0ms

localize8.0ms

rewrite70.0ms

series8.5s

simplify164.0ms

prune136.0ms

localize12.0ms

rewrite205.0ms

series23.8s

simplify244.0ms

prune284.0ms

localize11.0ms

rewrite110.0ms

series8.6s

simplify187.0ms

prune234.0ms

localize11.0ms

rewrite127.0ms

series14.1s

simplify122.0ms

prune189.0ms

regimes22.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample795.0ms

Profiling