Details

analyze266.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample76.0ms

Algorithm

intervals

Results

37.0ms	77×	body	1280	valid
13.0ms	48×	body	640	valid
10.0ms	30×	body	2560	valid
6.0ms	33×	body	320	valid
2.0ms	57×	body	80	valid
1.0ms	11×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

prune2.0ms

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: 53.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

1.8b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
1.9b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_1707`
6×	`add-sqr-sqrt_binary64_1692`
5×	`add-cube-cbrt_binary64_1678` `pow1_binary64_1649` `add-log-exp_binary64_1672`
4×	`log-prod_binary64_1621` `add-exp-log_binary64_1671`
3×	`sqrt-prod_binary64_1686` `flip3-+_binary64_1705` `flip-+_binary64_1732` `add-cbrt-cube_binary64_1679`
2×	`sqrt-div_binary64_1687` `distribute-lft-out_binary64_1751` `log-div_binary64_1622`
1×	`sum-log_binary64_1617` `pow1/2_binary64_1639` `rem-log-exp_binary64_1670` `rem-sqrt-square_binary64_1695` `sqrt-pow1_binary64_1688` `+-commutative_binary64_1774` `log-pow_binary64_1624`

Counts

3 → 42

Calls

3 calls:

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

series787.0ms

Counts

3 → 9

Calls

3 calls:

256.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
269.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
262.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3
0	221	1819
1	221	1819
0	6032	1372
0	221	1819
1	221	1819
0	6032	1372
0	1	3
1	1	3
0	274	1905
1	274	1905
0	5821	1614
0	274	1905
1	274	1905
0	5821	1614
0	1	3
1	1	3

simplify120.0ms

Counts

51 → 51

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4920	692
1	4920	692

prune59.0ms

Filtered

36 candidates to 51 candidates (-41.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Merged error: 42.2b

Counts

52 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.9b	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
1.8b	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64_1692`
42×	`*-un-lft-identity_binary64_1707`
36×	`times-frac_binary64_1702`
26×	`add-cube-cbrt_binary64_1678`
24×	`log-prod_binary64_1621`
16×	`difference-of-squares_binary64_1736`
11×	`sqrt-prod_binary64_1686`
9×	`add-exp-log_binary64_1671`
8×	`distribute-lft-out--_binary64_1752`
6×	`pow1_binary64_1649` `add-log-exp_binary64_1672` `add-cbrt-cube_binary64_1679` `associate-/r*_binary64_1770`
4×	`associate-/r/_binary64_1772`
3×	`flip3--_binary64_1706` `flip--_binary64_1733` `associate-/l*_binary64_1771`
2×	`div-exp_binary64_1656` `sqrt-div_binary64_1687` `rem-log-exp_binary64_1670` `div-inv_binary64_1708`
1×	`frac-2neg_binary64_1700` `clear-num_binary64_1710` `flip3-+_binary64_1705` `cbrt-undiv_binary64_1677` `flip-+_binary64_1732` `pow1/2_binary64_1639` `rem-sqrt-square_binary64_1695` `diff-log_binary64_1618` `sub-neg_binary64_1711` `sqrt-pow1_binary64_1688` `log-div_binary64_1622` `log-pow_binary64_1624`

Counts

4 → 105

Calls

4 calls:

11.0ms	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
8.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
10.0ms	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

260.0ms	(/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
271.0ms	(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
278.0ms	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))))
266.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3
0	430	2074
1	430	2074
0	4939	1859
1	4939	1859
0	430	2074
1	430	2074
0	4939	1859
1	4939	1859
0	1	3
1	1	3
0	221	1819
1	221	1819
0	4779	1374
1	4779	1374
0	221	1819
1	221	1819
0	4779	1374
1	4779	1374
0	1	3
1	1	3
0	440	2026
1	440	2026
0	4948	1877
1	4948	1877
0	440	2026
1	440	2026
0	4948	1877
1	4948	1877
0	1	3
1	1	3

simplify147.0ms

Counts

117 → 117

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5282	2513

prune101.0ms

Filtered

78 candidates to 117 candidates (-50.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	117	8	125

Merged error: 39.3b

Counts

125 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.8b	(log.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1)) x))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_1692`
10×	`sqrt-prod_binary64_1686` `*-un-lft-identity_binary64_1707`
8×	`add-cube-cbrt_binary64_1678` `pow1_binary64_1649`
6×	`log-prod_binary64_1621` `sqrt-div_binary64_1687`
5×	`add-exp-log_binary64_1671`
4×	`add-log-exp_binary64_1672` `add-cbrt-cube_binary64_1679`
3×	`flip3-+_binary64_1705` `flip-+_binary64_1732` `pow1/2_binary64_1639` `rem-sqrt-square_binary64_1695` `sqrt-pow1_binary64_1688`
2×	`difference-of-squares_binary64_1736` `log-div_binary64_1622`
1×	`distribute-lft-out--_binary64_1752` `flip3--_binary64_1706` `rem-log-exp_binary64_1670` `flip--_binary64_1733` `log-pow_binary64_1624`

Counts

4 → 62

Calls

4 calls:

10.0ms	(log.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1)) x))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

267.0ms	(log.f64 (-.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1)) x))
267.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
263.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
279.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3
0	274	1905
1	274	1905
0	6053	1596
0	274	1905
1	274	1905
0	6053	1596
0	1	3
1	1	3

simplify123.0ms

Counts

74 → 74

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4953	950
1	4953	950

prune113.0ms

Filtered

52 candidates to 74 candidates (-42.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	74	8	82

Merged error: 39.3b

Counts

82 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_1686` `add-sqr-sqrt_binary64_1692`
8×	`add-cube-cbrt_binary64_1678` `pow1_binary64_1649` `sqrt-div_binary64_1687` `*-un-lft-identity_binary64_1707`
4×	`flip3-+_binary64_1705` `flip-+_binary64_1732` `add-log-exp_binary64_1672` `add-exp-log_binary64_1671` `pow1/2_binary64_1639` `rem-sqrt-square_binary64_1695` `add-cbrt-cube_binary64_1679` `sqrt-pow1_binary64_1688`

Counts

4 → 60

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
8.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series1.0s

Counts

4 → 12

Calls

4 calls:

259.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
263.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
262.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
258.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	232	1696
1	232	1696
0	4783	1318
1	4783	1318
0	1	3
1	1	3

simplify165.0ms

Counts

72 → 72

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	4834	764
1	4834	764

prune132.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 39.3b

Counts

80 → 8

regimes69.0ms

Accuracy

99.6% (0.0b remaining)

Error of 40.4b against oracle of 40.3b and baseline of 52.9b

bsearch64.0ms

Steps

Iters	Range		Point
10	7.710175986358551e+151	1.5270275014681933e+162	1.352819344293148e+154
8	-0.01603808476389547	-1.6900487893620504e-05	-0.005692362598187211
6	-5.063466496796278e+154	-4.197350103045724e+153	-1.330733025502329e+154

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	39	64
1	39	64

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2359×	body	1280	valid
443.0ms	1565×	body	640	valid
271.0ms	807×	body	2560	valid
142.0ms	820×	body	320	valid
86.0ms	2053×	body	80	valid
42.0ms	396×	body	160	valid

Details

analyze266.0ms

sample76.0ms

simplify20.0ms

prune2.0ms

localize10.0ms

rewrite23.0ms

series787.0ms

simplify120.0ms

prune59.0ms

localize8.0ms

rewrite41.0ms

series1.1s

simplify147.0ms

prune101.0ms

localize12.0ms

rewrite30.0ms

series1.1s

simplify123.0ms

prune113.0ms

localize20.0ms

rewrite27.0ms

series1.0s

simplify165.0ms

prune132.0ms

regimes69.0ms

bsearch64.0ms

simplify7.0ms

end0.0ms

sample2.2s

Profiling