Details

analyze322.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

sample30.0ms

Algorithm

intervals

Results

13.0ms	72×	body	1280	valid
6.0ms	52×	body	640	valid
2.0ms	91×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	13×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	11	11
1	11	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: 41.5b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.5b	(-.f64 (exp.f64 x) 1)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64`
5×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`add-exp-log_binary64` `associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `insert-posit16` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 62

Calls

2 calls:

9.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series468.0ms

Counts

2 → 6

Calls

2 calls:

209.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
259.0ms	(-.f64 (exp.f64 x) 1)

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	238	216
1	238	216
0	238	216
1	238	216
0	5116	12
0	499	1200
1	499	1200
0	499	1200
1	499	1200
0	108	57
1	108	57

simplify33.0ms

Counts

68 → 68

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	161	1177
1	161	1177

prune44.0ms

Filtered

50 candidates to 68 candidates (-36.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Merged error: 0.7b

Counts

69 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (*.f64 x x) 2)
0.0b	(+.f64 x (/.f64 (*.f64 x x) 2))
0.0b	(/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
7×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `insert-posit16`
2×	`flip3-+_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`cbrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 69

Calls

3 calls:

6.0ms	(/.f64 (*.f64 x x) 2)
6.0ms	(+.f64 x (/.f64 (*.f64 x x) 2))
9.0ms	(/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2)))

series1.2s

Counts

3 → 9

Calls

3 calls:

300.0ms	(/.f64 (*.f64 x x) 2)
256.0ms	(+.f64 x (/.f64 (*.f64 x x) 2))
684.0ms	(/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2)))

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	3031	1160
1	3031	1160
0	3031	1160
1	3031	1160
0	5276	3
0	28	99
1	28	99
0	28	99
1	28	99
0	1	3
1	1	3
0	533	494
1	533	494
0	533	494
1	533	494
0	5359	15

simplify130.0ms

Counts

78 → 78

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5250	1179

prune53.0ms

Filtered

56 candidates to 78 candidates (-39.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0.7b

Counts

81 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 x x) 2)
0.0b	(+.f64 x (/.f64 (*.f64 x x) 2))
0.0b	(.f64 (exp.f64 x) (/.f64 1 (+.f64 x (/.f64 (.f64 x x) 2))))
0.7b	(/.f64 1 (+.f64 x (/.f64 (*.f64 x x) 2)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

6.0ms	(/.f64 (*.f64 x x) 2)
6.0ms	(+.f64 x (/.f64 (*.f64 x x) 2))
16.0ms	(.f64 (exp.f64 x) (/.f64 1 (+.f64 x (/.f64 (.f64 x x) 2))))
9.0ms	(/.f64 1 (+.f64 x (/.f64 (*.f64 x x) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

300.0ms	(/.f64 (*.f64 x x) 2)
261.0ms	(+.f64 x (/.f64 (*.f64 x x) 2))
587.0ms	(.f64 (exp.f64 x) (/.f64 1 (+.f64 x (/.f64 (.f64 x x) 2))))
572.0ms	(/.f64 1 (+.f64 x (/.f64 (*.f64 x x) 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	28	90
1	28	90
0	28	90
1	28	90
0	1	3
1	1	3
0	27	135
1	27	135
0	27	135
1	27	135
0	1	3
1	1	3
0	28	99
1	28	99
0	28	99
1	28	99
0	1	3
1	1	3
0	533	494
1	533	494
0	533	494
1	533	494
0	5359	15

simplify134.0ms

Counts

127 → 127

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5603	1830

prune73.0ms

Filtered

79 candidates to 127 candidates (-60.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	127	4	131

Merged error: 0.7b

Counts

131 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 x x) 2))
0.0b	(/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2)))
0.2b	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2))) 3)
25.3b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2))) 3))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
47×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
42×	`cbrt-prod_binary64`
36×	`unpow-prod-down_binary64` `cube-prod_binary64`
17×	`distribute-lft-out_binary64`
10×	`associate-/r/_binary64`
9×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
5×	`pow1_binary64` `div-inv_binary64`
4×	`associate-/r*_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `associate-/l*_binary64`
2×	`cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 157

Calls

4 calls:

6.0ms	(+.f64 x (/.f64 (*.f64 x x) 2))
9.0ms	(/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2)))
12.0ms	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2))) 3)
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2))) 3))

series1.9s

Counts

4 → 12

Calls

4 calls:

253.0ms	(+.f64 x (/.f64 (*.f64 x x) 2))
679.0ms	(/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2)))
749.0ms	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2))) 3)
173.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (/.f64 (*.f64 x x) 2))) 3))

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	178	1788
1	178	1788
0	178	1788
1	178	1788
0	4921	31
1	4921	31
0	3230	1428
1	3230	1428
0	3230	1428
1	3230	1428
0	5276	3
0	3031	1160
1	3031	1160
0	3031	1160
1	3031	1160
0	5276	3
0	28	99
1	28	99
0	28	99
1	28	99
0	1	3
1	1	3

simplify121.0ms

Counts

169 → 169

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4964	3932
1	4964	3932

prune86.0ms

Filtered

88 candidates to 169 candidates (-92.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	169	4	173

Merged error: 0.7b

Counts

173 → 4

regimes15.0ms

Accuracy

52% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 1.1b

bsearch12.0ms

Steps

Iters	Range		Point
7	-5.8693967229284094e-05	-7.740052622955988e-07	-4.229675408144548e-06

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	46
1	28	46

end0.0ms

sample868.0ms

Algorithm

intervals

Results

409.0ms	2308×	body	1280	valid
187.0ms	1656×	body	640	valid
64.0ms	2769×	body	80	valid
63.0ms	845×	body	320	valid
21.0ms	422×	body	160	valid
1.0ms	2×	body	1280	invalid

Details

analyze322.0ms

sample30.0ms

simplify20.0ms

prune1.0ms

localize4.0ms

rewrite17.0ms

series468.0ms

simplify33.0ms

prune44.0ms

localize7.0ms

rewrite25.0ms

series1.2s

simplify130.0ms

prune53.0ms

localize8.0ms

rewrite41.0ms

series1.7s

simplify134.0ms

prune73.0ms

localize12.0ms

rewrite47.0ms

series1.9s

simplify121.0ms

prune86.0ms

regimes15.0ms

bsearch12.0ms

simplify6.0ms

end0.0ms

sample868.0ms

Profiling