Details

analyze13.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample66.0ms

Algorithm

intervals

Results

50.0ms	256×	body	80	valid
3.0ms	261×	pre	80	true
1.0ms	5×	body	80	invalid

simplify235.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (219.0ms)

Iter	Nodes	Cost
0	4938	55
1	4938	55

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 2.9b

Counts

2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7)))
0.6b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
2.6b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_1707`
23×	`add-sqr-sqrt_binary64_1692`
22×	`add-cube-cbrt_binary64_1678` `times-frac_binary64_1702`
15×	`sqrt-prod_binary64_1686`
14×	`add-log-exp_binary64_1672`
12×	`distribute-lft-out_binary64_1751`
9×	`frac-add_binary64_1697`
8×	`exp-prod_binary64_1657`
6×	`sum-log_binary64_1617` `add-cbrt-cube_binary64_1679` `associate-/r*_binary64_1770`
5×	`pow1_binary64_1649` `add-exp-log_binary64_1671`
3×	`flip3-+_binary64_1705` `flip-+_binary64_1732` `associate-/l*_binary64_1771` `unpow-prod-down_binary64_1638`
2×	`div-inv_binary64_1708`
1×	`frac-2neg_binary64_1700` `clear-num_binary64_1710` `sqr-pow_binary64_1739` `cbrt-undiv_binary64_1677` `div-exp_binary64_1656` `unpow2_binary64_1646` `pow1/2_binary64_1639` `rem-exp-log_binary64_1669` `rem-sqrt-square_binary64_1695` `sqrt-pow1_binary64_1688` `+-commutative_binary64_1774` `associate-+l+_binary64_1759`

Counts

4 → 92

Calls

4 calls:

64.0ms	(+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7)))
8.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
1.0ms	(sqrt.f64 PI.f64)
4.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

series811.0ms

Counts

4 → 10

Calls

4 calls:

299.0ms	(+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7)))
259.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
253.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	145	1959
1	145	1959
0	4868	1944
1	4868	1944
0	145	1959
1	145	1959
0	4868	1944
1	4868	1944
0	1	3
1	1	3
0	360	2013
1	360	2013
0	5204	1998
0	360	2013
1	360	2013
0	5204	1998
0	1	3
1	1	3
0	834	2310
1	834	2310
0	4901	2277
1	4901	2277
0	834	2310
1	834	2310
0	4901	2277
1	4901	2277
0	1	3
1	1	3

simplify156.0ms

Counts

102 → 102

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4947	2818
1	4947	2818

prune233.0ms

Filtered

71 candidates to 102 candidates (-43.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	83	19	102
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	19	104

Merged error: 0.8b

Counts

104 → 19

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7)))
0.6b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_1707`
46×	`times-frac_binary64_1702`
39×	`add-sqr-sqrt_binary64_1692`
38×	`add-cube-cbrt_binary64_1678`
27×	`sqrt-prod_binary64_1686`
24×	`unpow-prod-down_binary64_1638`
13×	`add-log-exp_binary64_1672`
12×	`distribute-lft-out_binary64_1751`
9×	`frac-add_binary64_1697`
8×	`sqr-pow_binary64_1739` `add-exp-log_binary64_1671`
7×	`associate-/l*_binary64_1771`
6×	`sum-log_binary64_1617` `pow1_binary64_1649` `add-cbrt-cube_binary64_1679` `associate-/r*_binary64_1770`
4×	`pow-pow_binary64_1631`
3×	`flip3-+_binary64_1705` `div-exp_binary64_1656` `flip-+_binary64_1732` `pow-unpow_binary64_1636` `exp-prod_binary64_1657`
2×	`pow-to-exp_binary64_1628` `pow-exp_binary64_1627` `div-inv_binary64_1708`
1×	`frac-2neg_binary64_1700` `clear-num_binary64_1710` `cbrt-undiv_binary64_1677` `pow1/2_binary64_1639` `rem-sqrt-square_binary64_1695` `sqrt-pow1_binary64_1688` `+-commutative_binary64_1774` `associate-+l+_binary64_1759`

Counts

4 → 126

Calls

4 calls:

66.0ms	(+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7)))
8.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
1.0ms	(sqrt.f64 PI.f64)
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series779.0ms

Counts

4 → 10

Calls

4 calls:

301.0ms	(+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7)))
202.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
276.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	142	2001
1	142	2001
0	5049	1980
0	142	2001
1	142	2001
0	5049	1980
0	1	3
1	1	3
0	357	2055
1	357	2055
0	5013	2034
0	357	2055
1	357	2055
0	5013	2034
0	1	3
1	1	3
0	834	2310
1	834	2310
0	4901	2277
1	4901	2277
0	834	2310
1	834	2310
0	4901	2277
1	4901	2277
0	1	3
1	1	3

simplify169.0ms

Counts

136 → 136

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4944	4004
1	4944	4004

prune284.0ms

Filtered

87 candidates to 136 candidates (-56.3%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	117	19	136
Fresh	13	5	18
Picked	0	1	1
Done	0	0	0
Total	130	25	155

Merged error: 0.2b

Counts

155 → 25

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.6b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow_binary64_1636` `add-sqr-sqrt_binary64_1692`
24×	`add-cube-cbrt_binary64_1678` `*-un-lft-identity_binary64_1707`
18×	`times-frac_binary64_1702`
8×	`pow1_binary64_1649` `pow-pow_binary64_1631`
6×	`sqrt-prod_binary64_1686` `exp-prod_binary64_1657` `unpow-prod-down_binary64_1638`
4×	`add-log-exp_binary64_1672` `add-exp-log_binary64_1671` `add-cbrt-cube_binary64_1679`
2×	`sqr-pow_binary64_1739` `pow1/2_binary64_1639` `rem-sqrt-square_binary64_1695` `pow-to-exp_binary64_1628` `pow-exp_binary64_1627` `sqrt-pow1_binary64_1688` `div-inv_binary64_1708`

Counts

4 → 86

Calls

4 calls:

6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series392.0ms

Counts

4 → 8

Calls

4 calls:

198.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
194.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	260	2028
1	260	2028
0	5385	2007
0	260	2028
1	260	2028
0	5385	2007
0	1	3
1	1	3
0	260	2028
1	260	2028
0	5385	2007
0	260	2028
1	260	2028
0	5385	2007
0	1	3
1	1	3

simplify213.0ms

Counts

94 → 94

Iterations

Useful iterations: 0 (186.0ms)

Iter	Nodes	Cost
0	4948	1266
1	4948	1266

prune272.0ms

Filtered

75 candidates to 94 candidates (-25.3%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	87	7	94
Fresh	1	22	23
Picked	0	1	1
Done	1	0	1
Total	89	30	119

Merged error: 0.2b

Counts

119 → 30

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (.f64 1/4 (fabs.f64 x))) (pow.f64 (exp.f64 (fabs.f64 x)) (.f64 1/4 (fabs.f64 x)))) (sqrt.f64 (sqrt.f64 PI.f64))))
0.6b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-sqr-sqrt_binary64_1692`
147×	`times-frac_binary64_1702`
144×	`sqrt-prod_binary64_1686`
131×	`add-exp-log_binary64_1671`
80×	`prod-exp_binary64_1654`
73×	`div-exp_binary64_1656`
67×	`associate-l_binary64_1767`
59×	`add-cube-cbrt_binary64_1678` `*-un-lft-identity_binary64_1707`
42×	`unpow-prod-down_binary64_1638`
40×	`unswap-sqr_binary64_1735`
36×	`pow-to-exp_binary64_1628` `pow-exp_binary64_1627`
25×	`add-cbrt-cube_binary64_1679`
22×	`sqr-pow_binary64_1739`
13×	`pow-unpow_binary64_1636` `associate-r_binary64_1766`
9×	`pow1_binary64_1649`
8×	`cbrt-unprod_binary64_1676`
7×	`cbrt-undiv_binary64_1677`
4×	`add-log-exp_binary64_1672` `pow-pow_binary64_1631`
3×	`exp-prod_binary64_1657` `div-inv_binary64_1708`
2×	`pow1/2_binary64_1639` `rem-sqrt-square_binary64_1695` `sqrt-pow1_binary64_1688`
1×	`associate-r/_binary64_1768` `-commutative_binary64_1775` `pow-prod-down_binary64_1630` `associate-*l/_binary64_1769` `frac-times_binary64_1699`

Counts

4 → 238

Calls

4 calls:

42.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (.f64 1/4 (fabs.f64 x))) (pow.f64 (exp.f64 (fabs.f64 x)) (.f64 1/4 (fabs.f64 x)))) (sqrt.f64 (sqrt.f64 PI.f64))))
6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series486.0ms

Counts

4 → 8

Calls

4 calls:

288.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (.f64 1/4 (fabs.f64 x))) (pow.f64 (exp.f64 (fabs.f64 x)) (.f64 1/4 (fabs.f64 x)))) (sqrt.f64 (sqrt.f64 PI.f64))))
198.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	260	2028
1	260	2028
0	5385	2007
0	260	2028
1	260	2028
0	5385	2007
0	1	3
1	1	3
0	703	2538
1	703	2538
0	4983	2088
1	4983	2088
0	703	2538
1	703	2538
0	4983	2088
1	4983	2088
0	1	3
1	1	3

simplify174.0ms

Counts

246 → 246

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5054	8285

prune398.0ms

Filtered

125 candidates to 246 candidates (-96.8%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	237	9	246
Fresh	9	19	28
Picked	1	0	1
Done	0	1	1
Total	247	29	276

Merged error: 0.2b

Counts

276 → 29

regimes254.0ms

Accuracy

0% (1.0b remaining)

Error of 1.3b against oracle of 0.3b and baseline of 1.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	85
1	36	85

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
91.0ms	8158×	pre	80	true
31.0ms	158×	body	80	invalid

Details

analyze13.0ms

sample66.0ms

simplify235.0ms

prune14.0ms

localize27.0ms

rewrite82.0ms

series811.0ms

simplify156.0ms

prune233.0ms

localize31.0ms

rewrite85.0ms

series779.0ms

simplify169.0ms

prune284.0ms

localize31.0ms

rewrite18.0ms

series392.0ms

simplify213.0ms

prune272.0ms

localize41.0ms

rewrite71.0ms

series486.0ms

simplify174.0ms

prune398.0ms

regimes254.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample1.8s

Profiling