Details

analyze7.0ms

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

sample22.0ms

Algorithm

intervals

Results

7.0ms	60×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	124×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	8×	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: 31.8b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64`
3×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64`

Counts

1 → 19

Calls

1 calls:

10.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series434.0ms

Counts

1 → 3

Calls

1 calls:

434.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (195.0ms)

Iter	Nodes	Cost
0	756	888
1	756	888
0	756	888
1	756	888
0	4932	17
1	4932	17

simplify140.0ms

Counts

22 → 22

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4894	357
1	4894	357

prune17.0ms

Filtered

15 candidates to 22 candidates (-46.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	2	23

Merged error: 0.1b

Counts

23 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
20×	`distribute-lft-out_binary64` `sqrt-prod_binary64`
18×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `div-exp_binary64` `insert-posit16` `flip-+_binary64`
1×	`1-exp_binary64` `cbrt-undiv_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

2 → 61

Calls

2 calls:

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

series785.0ms

Counts

2 → 6

Calls

2 calls:

308.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
477.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	985	1443
1	985	1443
0	985	1443
1	985	1443
0	4963	17
1	4963	17
0	756	888
1	756	888
0	756	888
1	756	888
0	5030	17

simplify184.0ms

Counts

67 → 67

Iterations

Useful iterations: 0 (158.0ms)

Iter	Nodes	Cost
0	4843	1078
1	4843	1078

prune46.0ms

Filtered

40 candidates to 67 candidates (-67.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	63	6	69

Merged error: 0.0b

Counts

69 → 6

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)))))

rewrite115.0ms

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)))
47.0ms	(*.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)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

520.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
465.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
469.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
808.0ms	(*.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 (168.0ms)

Iter	Nodes	Cost
0	1677	1732
1	1677	1732
0	1677	1732
1	1677	1732
0	5403	17
0	986	1443
1	986	1443
0	986	1443
1	986	1443
0	4963	17
1	4963	17
0	986	1443
1	986	1443
0	986	1443
1	986	1443
0	4963	17
1	4963	17
0	1220	1664
1	1220	1664
0	1220	1664
1	1220	1664
0	5103	22

simplify206.0ms

Counts

294 → 294

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4972	6088
1	4972	6088

prune214.0ms

Filtered

129 candidates to 294 candidates (-127.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	292	2	294
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	293	7	300

Merged error: 0.0b

Counts

300 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.1b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.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 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

266×	`sqrt-prod_binary64`
213×	`*-un-lft-identity_binary64`
147×	`times-frac_binary64`
142×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
68×	`distribute-lft-out_binary64`
63×	`associate-l_binary64`
58×	`sqrt-pow1_binary64`
41×	`pow1_binary64`
37×	`associate-r_binary64`
35×	`pow-flip_binary64`
24×	`unswap-sqr_binary64`
22×	`sqrt-div_binary64`
21×	`pow-prod-up_binary64`
19×	`add-exp-log_binary64`
16×	`pow-prod-down_binary64` `pow1/2_binary64`
15×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
13×	`inv-pow_binary64`
10×	`associate-/r/_binary64`
6×	`associate-r/_binary64` `associate-/l_binary64` `frac-times_binary64`
5×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-exp_binary64` `insert-posit16` `associate-*l/_binary64`
3×	`sqrt-unprod_binary64`
2×	`1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `pow3_binary64` `frac-2neg_binary64` `rec-exp_binary64` `*-commutative_binary64`

Counts

4 → 291

Calls

4 calls:

16.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
65.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
56.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))

series3.0s

Counts

4 → 12

Calls

4 calls:

582.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
1.1s	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
462.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
876.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))

Iterations

Useful iterations: 0 (144.0ms)

Iter	Nodes	Cost
0	2027	2015
1	2027	2015
0	2027	2015
1	2027	2015
0	5214	37
0	986	1443
1	986	1443
0	986	1443
1	986	1443
0	4963	17
1	4963	17
0	2137	2268
1	2137	2268
0	2137	2268
1	2137	2268
0	5132	32
0	1220	1685
1	1220	1685
0	1220	1685
1	1220	1685
0	4964	19
1	4964	19

simplify175.0ms

Counts

303 → 303

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5402	9308

prune385.0ms

Filtered

158 candidates to 303 candidates (-91.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	303	7	310

Merged error: 0.0b

Counts

310 → 7

regimes36.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms

sample606.0ms

Algorithm

intervals

Results

223.0ms	1765×	body	1280	valid
119.0ms	1239×	body	640	valid
107.0ms	4039×	body	80	valid
46.0ms	640×	body	320	valid
16.0ms	317×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze7.0ms

sample22.0ms

simplify25.0ms

prune1.0ms

localize5.0ms

rewrite11.0ms

series434.0ms

simplify140.0ms

prune17.0ms

localize6.0ms

rewrite26.0ms

series785.0ms

simplify184.0ms

prune46.0ms

localize9.0ms

rewrite115.0ms

series2.3s

simplify206.0ms

prune214.0ms

localize13.0ms

rewrite173.0ms

series3.0s

simplify175.0ms

prune385.0ms

regimes36.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample606.0ms

Profiling