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

sample21.0ms

Algorithm

intervals

Results

5.0ms	54×	body	640	valid
5.0ms	41×	body	1280	valid
3.0ms	128×	body	80	valid
2.0ms	25×	body	320	valid
0.0ms	8×	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: 30.3b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.3b	(-.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))

series4.2s

Counts

2 → 6

Calls

2 calls:

2.0s	(sqrt.f64 (+.f64 x 1))
2.2s	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Iterations

Useful iterations: 0 (188.0ms)

Iter	Nodes	Cost
0	10668	991
1	10668	991
0	10668	991
1	10668	991
0	4932	17
1	4932	17
0	10670	588
1	10670	588
0	10670	588
1	10670	588
0	4960	9
1	4960	9

simplify177.0ms

Counts

42 → 42

Iterations

Useful iterations: 0 (157.0ms)

Iter	Nodes	Cost
0	4863	524
1	4863	524

prune30.0ms

Filtered

30 candidates to 42 candidates (-40.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	5	43

Merged error: 0.1b

Counts

43 → 5

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)))

series6.3s

Counts

3 → 9

Calls

3 calls:

1.9s	(sqrt.f64 (+.f64 x 1))
2.1s	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.3s	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

Iterations

Useful iterations: 0 (184.0ms)

Iter	Nodes	Cost
0	10376	1596
1	10376	1596
0	10376	1596
1	10376	1596
0	4963	17
1	4963	17
0	10619	991
1	10619	991
0	10619	991
1	10619	991
0	5030	17
0	10670	588
1	10670	588
0	10670	588
1	10670	588
0	4960	9
1	4960	9

simplify164.0ms

Counts

87 → 87

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	4727	1245
1	4727	1245

prune67.0ms

Filtered

56 candidates to 87 candidates (-55.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	85	7	92

Merged error: 0.0b

Counts

92 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
13×	`cbrt-prod_binary64`
10×	`associate-r_binary64` `add-exp-log_binary64`
9×	`times-frac_binary64` `sqrt-prod_binary64`
8×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`cbrt-div_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `insert-posit16` `flip-+_binary64`
3×	`associate-/r_binary64` `distribute-lft-out_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
2×	`associate-*r/_binary64` `pow1/3_binary64` `associate-/r/_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

14.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
11.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
4.0ms	(cbrt.f64 (+.f64 1 x))
4.0ms	(cbrt.f64 (+.f64 1 x))

series1.3s

Counts

4 → 12

Calls

4 calls:

755.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
223.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
156.0ms	(cbrt.f64 (+.f64 1 x))
155.0ms	(cbrt.f64 (+.f64 1 x))

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	60	1626
1	60	1626
0	60	1626
1	60	1626
0	5099	14
0	60	1626
1	60	1626
0	60	1626
1	60	1626
0	5099	14
0	542	1761
1	542	1761
0	542	1761
1	542	1761
0	5209	23
0	1670	1881
1	1670	1881
0	1670	1881
1	1670	1881
0	4968	28
1	4968	28

simplify189.0ms

Counts

106 → 106

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	4946	2245
1	4946	2245

prune117.0ms

Filtered

79 candidates to 106 candidates (-34.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	105	8	113

Merged error: 0.0b

Counts

113 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64`
700×	`sqrt-prod_binary64`
594×	`times-frac_binary64`
280×	`distribute-lft-out_binary64`
254×	`add-sqr-sqrt_binary64`
252×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
28×	`sqrt-div_binary64`
24×	`associate-/r/_binary64`
18×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `insert-posit16`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `pow-flip_binary64`
2×	`1-exp_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`associate-/l/_binary64` `inv-pow_binary64`

Counts

4 → 457

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
10.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
15.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
39.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

series9.3s

Counts

4 → 12

Calls

4 calls:

2.2s	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.2s	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
2.3s	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
2.6s	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	12786	1789
1	12786	1789
0	12786	1789
1	12786	1789
0	5403	17
0	11449	1728
1	11449	1728
0	11449	1728
1	11449	1728
0	4964	19
1	4964	19
0	10911	1403
1	10911	1403
0	10911	1403
1	10911	1403
0	5102	19
0	10911	1403
1	10911	1403
0	10911	1403
1	10911	1403
0	5102	19

simplify323.0ms

Counts

469 → 469

Iterations

Useful iterations: 0 (169.0ms)

Iter	Nodes	Cost
0	5353	16411

prune234.0ms

Filtered

132 candidates to 469 candidates (-255.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	465	4	469
Fresh	3	1	4
Picked	1	0	1
Done	2	1	3
Total	471	6	477

Merged error: 0b

Counts

477 → 6

regimes22.0ms

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 (2.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms

sample820.0ms

Algorithm

intervals

Results

316.0ms	4051×	body	80	valid
229.0ms	1820×	body	1280	valid
122.0ms	1224×	body	640	valid
44.0ms	610×	body	320	valid
15.0ms	295×	body	160	valid
0.0ms	3×	body	80	nan

Details

analyze3.0ms

sample21.0ms

simplify24.0ms

prune1.0ms

localize5.0ms

rewrite16.0ms

series4.2s

simplify177.0ms

prune30.0ms

localize6.0ms

rewrite30.0ms

series6.3s

simplify164.0ms

prune67.0ms

localize10.0ms

rewrite36.0ms

series1.3s

simplify189.0ms

prune117.0ms

localize13.0ms

rewrite130.0ms

series9.3s

simplify323.0ms

prune234.0ms

regimes22.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample820.0ms

Profiling