Details

analyze2.0ms

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

sample21.0ms

Algorithm

intervals

Results

7.0ms	58×	body	1280	valid
4.0ms	38×	body	640	valid
4.0ms	137×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	4×	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: 28.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
1.2b	(-.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))

series717.0ms

Counts

2 → 6

Calls

2 calls:

337.0ms	(sqrt.f64 (+.f64 x 1))
380.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4493	9
1	4493	9
0	4493	9
1	4493	9
0	1	3
1	1	3
0	4445	9
1	4445	9
0	4445	9
1	4445	9
0	1	3
1	1	3

simplify101.0ms

Counts

42 → 42

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4856	504
1	4856	504

prune30.0ms

Filtered

28 candidates to 42 candidates (-50.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	3	43

Merged error: 0.2b

Counts

43 → 3

localize6.0ms

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)))

series1.2s

Counts

3 → 9

Calls

3 calls:

353.0ms	(sqrt.f64 (+.f64 x 1))
391.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
438.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4681	9
1	4681	9
0	4681	9
1	4681	9
0	1	3
1	1	3
0	4469	9
1	4469	9
0	4469	9
1	4469	9
0	1	3
1	1	3
0	4445	9
1	4445	9
0	4445	9
1	4445	9
0	1	3
1	1	3

simplify162.0ms

Counts

87 → 87

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	4801	1211
1	4801	1211

prune63.0ms

Filtered

53 candidates to 87 candidates (-64.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 0.0b

Counts

90 → 7

localize11.0ms

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)))
0.2b	(*.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)))))

rewrite116.0ms

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:

18.0ms	(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)))
14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
48.0ms	(*.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)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

440.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
433.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
448.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
505.0ms	(*.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 (6.0ms)

Iter	Nodes	Cost
0	5061	9
1	5061	9
0	5061	9
1	5061	9
0	1	3
1	1	3
0	4681	9
1	4681	9
0	4681	9
1	4681	9
0	1	3
1	1	3
0	4681	9
1	4681	9
0	4681	9
1	4681	9
0	1	3
1	1	3
0	4649	9
1	4649	9
0	4649	9
1	4649	9
0	1	3
1	1	3

simplify173.0ms

Counts

294 → 294

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5030	6027

prune201.0ms

Filtered

124 candidates to 294 candidates (-137.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	288	6	294
Fresh	3	2	5
Picked	0	1	1
Done	1	0	1
Total	292	9	301

Merged error: 0.0b

Counts

301 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

702×	`sqrt-prod_binary64`
655×	`*-un-lft-identity_binary64`
461×	`times-frac_binary64`
264×	`distribute-lft-out_binary64`
197×	`add-sqr-sqrt_binary64`
192×	`add-cube-cbrt_binary64`
30×	`associate-/l*_binary64`
26×	`associate-/r/_binary64`
15×	`associate-/r*_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
13×	`div-inv_binary64`
12×	`pow1_binary64`
10×	`add-exp-log_binary64` `sqrt-pow1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `pow-div_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `insert-posit16` `pow-flip_binary64`
3×	`div-exp_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `1-exp_binary64` `sqrt-undiv_binary64` `rec-exp_binary64`

Counts

4 → 405

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
17.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
34.0ms	(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series1.8s

Counts

4 → 12

Calls

4 calls:

390.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
436.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
528.0ms	(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
441.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4681	9
1	4681	9
0	4681	9
1	4681	9
0	1	3
1	1	3
0	5163	9
1	5163	9
0	5163	9
1	5163	9
0	1	3
1	1	3
0	4649	9
1	4649	9
0	4649	9
1	4649	9
0	1	3
1	1	3
0	4417	9
1	4417	9
0	4417	9
1	4417	9
0	1	3
1	1	3

simplify271.0ms

Counts

417 → 417

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4838	16615
1	4838	16615

prune262.0ms

Filtered

140 candidates to 417 candidates (-197.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	415	2	417
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	418	8	426

Merged error: 0.0b

Counts

426 → 8

regimes23.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	15	31
1	15	31

end0.0ms

sample617.0ms

Algorithm

intervals

Results

224.0ms	1772×	body	1280	valid
123.0ms	1201×	body	640	valid
111.0ms	4094×	body	80	valid
48.0ms	623×	body	320	valid
15.0ms	310×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze2.0ms

sample21.0ms

simplify24.0ms

prune1.0ms

localize8.0ms

rewrite16.0ms

series717.0ms

simplify101.0ms

prune30.0ms

localize6.0ms

rewrite30.0ms

series1.2s

simplify162.0ms

prune63.0ms

localize11.0ms

rewrite116.0ms

series1.8s

simplify173.0ms

prune201.0ms

localize10.0ms

rewrite116.0ms

series1.8s

simplify271.0ms

prune262.0ms

regimes23.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample617.0ms

Profiling