Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

sample30.0ms

Algorithm

intervals

Results

13.0ms	68×	body	1280	valid
7.0ms	56×	body	640	valid
3.0ms	35×	body	320	valid
2.0ms	88×	body	80	valid
0.0ms	9×	body	160	valid

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 40.5b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
3.5b	(-.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-/l*_binary64`
5×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `consolidate-/-/-b_binary64_1` `insert-posit16`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 65

Calls

2 calls:

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

series251.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
132.0ms	(-.f64 (exp.f64 x) 1)

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	51	1926
1	51	1926
0	212	9
1	212	9
0	51	1926
1	51	1926
0	212	9
1	212	9
0	1	3
1	1	3
0	9	1008
1	9	1008
0	11	9
1	11	9
0	9	1008
1	9	1008
0	11	9
1	11	9
0	1	3
1	1	3

simplify142.0ms

Counts

71 → 71

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	5376	1003

prune43.0ms

Filtered

45 candidates to 71 candidates (-57.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 40.2b

Counts

72 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (exp.f64 x) x)
3.4b	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `div-inv_binary64`
5×	`distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `distribute-rgt-out--_binary64` `add-exp-log_binary64` `associate-/l_binary64`
2×	`pow1_binary64` `insert-posit16`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

2 → 56

Calls

2 calls:

5.0ms	(/.f64 (exp.f64 x) x)
19.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))

series281.0ms

Counts

2 → 6

Calls

2 calls:

169.0ms	(/.f64 (exp.f64 x) x)
113.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	9	1035
1	9	1035
0	14	9
1	14	9
0	9	1035
1	9	1035
0	14	9
1	14	9
0	1	3
1	1	3
0	22	1908
1	22	1908
0	160	9
1	160	9
0	22	1908
1	22	1908
0	160	9
1	160	9
0	1	3
1	1	3

simplify48.0ms

Counts

62 → 62

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	851	827
1	851	827

prune54.0ms

Filtered

47 candidates to 62 candidates (-31.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	54	12	66

Merged error: 39.2b

Counts

66 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (exp.f64 x))
0.0b	(cbrt.f64 (exp.f64 x))
0.0b	(/.f64 (*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x))) (/.f64 x (cbrt.f64 (exp.f64 x))))
3.4b	(-.f64 (/.f64 (*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x))) (/.f64 x (cbrt.f64 (exp.f64 x)))) (/.f64 1 x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
27×	`cbrt-prod_binary64`
22×	`associate-/r*_binary64`
16×	`add-exp-log_binary64`
12×	`difference-of-squares_binary64`
10×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow1_binary64` `div-inv_binary64` `insert-posit16`
2×	`cbrt-unprod_binary64` `pow1/3_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `consolidate-/-/-b_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 117

Calls

4 calls:

2.0ms	(cbrt.f64 (exp.f64 x))
2.0ms	(cbrt.f64 (exp.f64 x))
14.0ms	(/.f64 (*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x))) (/.f64 x (cbrt.f64 (exp.f64 x))))
32.0ms	(-.f64 (/.f64 (*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x))) (/.f64 x (cbrt.f64 (exp.f64 x)))) (/.f64 1 x))

series689.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt.f64 (exp.f64 x))
98.0ms	(cbrt.f64 (exp.f64 x))
155.0ms	(/.f64 (*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x))) (/.f64 x (cbrt.f64 (exp.f64 x))))
336.0ms	(-.f64 (/.f64 (*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x))) (/.f64 x (cbrt.f64 (exp.f64 x)))) (/.f64 1 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4857	1950
1	4857	1950
0	377	9
1	377	9
0	4857	1950
1	4857	1950
0	377	9
1	377	9
0	1	3
1	1	3
0	31	1863
1	31	1863
0	6	9
1	6	9
0	31	1863
1	31	1863
0	6	9
1	6	9
0	1	3
1	1	3
0	45	1917
1	45	1917
0	21	9
1	21	9
0	45	1917
1	45	1917
0	21	9
1	21	9
0	1	3
1	1	3
0	45	1917
1	45	1917
0	21	9
1	21	9
0	45	1917
1	45	1917
0	21	9
1	21	9
0	1	3
1	1	3

simplify118.0ms

Counts

129 → 129

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5028	2380

prune108.0ms

Filtered

101 candidates to 129 candidates (-27.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	123	6	129
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	126	15	141

Merged error: 39.1b

Counts

141 → 15

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (/.f64 (exp.f64 x) x))
0.6b	(cbrt.f64 (/.f64 (exp.f64 x) x))
0.6b	(cbrt.f64 (/.f64 (exp.f64 x) x))
27.2b	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 x) x)) (cbrt.f64 (/.f64 (exp.f64 x) x))) (cbrt.f64 (/.f64 (exp.f64 x) x))) (/.f64 1 x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod_binary64`
36×	`cbrt-div_binary64`
27×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
17×	`frac-sub_binary64`
8×	`consolidate-mult-two_binary64` `frac-times_binary64` `associate-*l/_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `associate-*r/_binary64` `consolidate-mult-outside_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow1/3_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 98

Calls

4 calls:

4.0ms	(cbrt.f64 (/.f64 (exp.f64 x) x))
4.0ms	(cbrt.f64 (/.f64 (exp.f64 x) x))
4.0ms	(cbrt.f64 (/.f64 (exp.f64 x) x))
25.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 x) x)) (cbrt.f64 (/.f64 (exp.f64 x) x))) (cbrt.f64 (/.f64 (exp.f64 x) x))) (/.f64 1 x))

series627.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt.f64 (/.f64 (exp.f64 x) x))
151.0ms	(cbrt.f64 (/.f64 (exp.f64 x) x))
150.0ms	(cbrt.f64 (/.f64 (exp.f64 x) x))
174.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (exp.f64 x) x)) (cbrt.f64 (/.f64 (exp.f64 x) x))) (cbrt.f64 (/.f64 (exp.f64 x) x))) (/.f64 1 x))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	73	1962
1	73	1962
0	218	9
1	218	9
0	73	1962
1	73	1962
0	218	9
1	218	9
0	1	3
1	1	3
0	23	1926
1	23	1926
0	10	9
1	10	9
0	23	1926
1	23	1926
0	10	9
1	10	9
0	1	3
1	1	3
0	23	1926
1	23	1926
0	10	9
1	10	9
0	23	1926
1	23	1926
0	10	9
1	10	9
0	1	3
1	1	3
0	23	1926
1	23	1926
0	10	9
1	10	9
0	23	1926
1	23	1926
0	10	9
1	10	9
0	1	3
1	1	3

simplify84.0ms

Counts

110 → 110

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	3929	1955
1	3929	1955

prune89.0ms

Filtered

85 candidates to 110 candidates (-29.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	7	7	14
Picked	0	1	1
Done	0	0	0
Total	108	17	125

Merged error: 26.0b

Counts

125 → 17

regimes69.0ms

Accuracy

93.7% (0.8b remaining)

Error of 28.0b against oracle of 27.1b and baseline of 40.4b

bsearch71.0ms

Steps

Iters	Range	Point
8	1.1243428984893551e-106	1.8201749220237786e-103	1.7508536288384564e-103
8	-3.143110137509433e-100	-4.8742704842197894e-104	-1.782095466920453e-103
10	-6.047893989702066e-05	-2.616162183356906e-15	-5.90810225076708e-09

Iters

Range

Point

1.1243428984893551e-106

1.8201749220237786e-103

1.7508536288384564e-103

-3.143110137509433e-100

-4.8742704842197894e-104

-1.782095466920453e-103

-6.047893989702066e-05

-2.616162183356906e-15

-5.90810225076708e-09

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	61	84
1	61	84

end0.0ms

sample895.0ms

Algorithm

intervals

Results

429.0ms	2291×	body	1280	valid
206.0ms	1678×	body	640	valid
68.0ms	860×	body	320	valid
63.0ms	2749×	body	80	valid
22.0ms	422×	body	160	valid

Details

analyze4.0ms

sample30.0ms

simplify100.0ms

prune3.0ms

localize4.0ms

rewrite17.0ms

series251.0ms

simplify142.0ms

prune43.0ms

localize5.0ms

rewrite27.0ms

series281.0ms

simplify48.0ms

prune54.0ms

localize9.0ms

rewrite57.0ms

series689.0ms

simplify118.0ms

prune108.0ms

localize9.0ms

rewrite41.0ms

series627.0ms

simplify84.0ms

prune89.0ms

regimes69.0ms

bsearch71.0ms

simplify7.0ms

end0.0ms

sample895.0ms

Profiling