Details

analyze9.0ms

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

sample67.0ms

Algorithm

intervals

Results

53.0ms	256×	body	80	valid
3.0ms	257×	pre	80	true
0.0ms	1×	body	80	invalid

simplify241.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (224.0ms)

Iter	Nodes	Cost
0	5682	55

prune9.0ms

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: 2.4b

Counts

2 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.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))))
0.4b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
2.3b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
22×	`associate-l_binary64`
18×	`frac-add_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`associate-r_binary64` `exp-prod_binary64`
7×	`pow1_binary64` `associate-*r/_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
5×	`add-log-exp_binary64`
4×	`insert-posit16`
3×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `unpow2_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

78.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.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))

series3.2s

Counts

4 → 10

Calls

4 calls:

3.0s	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.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))))
93.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
68.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	583	9
1	583	9
0	583	9
1	583	9
0	1	3
1	1	3
0	859	9
1	859	9
0	859	9
1	859	9
0	1	3
1	1	3
0	21925	9
1	21925	9
0	21925	9
1	21925	9
0	1	3
1	1	3

simplify113.0ms

Counts

145 → 145

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5307	5981

prune373.0ms

Filtered

102 candidates to 145 candidates (-42.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	126	19	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	19	147

Merged error: 0.7b

Counts

147 → 19

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.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))))
0.4b	(/.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))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

94×	`times-frac_binary64`
86×	`*-un-lft-identity_binary64`
85×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
51×	`sqrt-prod_binary64`
46×	`associate-l_binary64`
44×	`unpow-prod-down_binary64`
18×	`frac-add_binary64`
17×	`add-exp-log_binary64`
16×	`sqr-pow_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`associate-r/_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `prod-exp_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `div-inv_binary64` `pow-exp_binary64` `exp-prod_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 199

Calls

4 calls:

81.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.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))))
7.0ms	(/.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))

series3.5s

Counts

4 → 10

Calls

4 calls:

3.4s	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.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))))
77.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
55.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	364	9
1	364	9
0	364	9
1	364	9
0	1	3
1	1	3
0	640	9
1	640	9
0	640	9
1	640	9
0	1	3
1	1	3
0	22240	9
1	22240	9
0	22240	9
1	22240	9
0	1	3
1	1	3

simplify149.0ms

Counts

209 → 209

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5434	9400

prune472.0ms

Filtered

142 candidates to 209 candidates (-47.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	187	22	209
Fresh	14	4	18
Picked	1	0	1
Done	0	0	0
Total	202	26	228

Merged error: 0.2b

Counts

228 → 26

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.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	(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)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
70×	`add-sqr-sqrt_binary64` `times-frac_binary64`
51×	`add-cube-cbrt_binary64`
46×	`associate-l_binary64`
27×	`sqrt-prod_binary64`
26×	`pow-unpow_binary64` `unpow-prod-down_binary64`
18×	`frac-add_binary64`
13×	`add-exp-log_binary64`
12×	`distribute-lft-out_binary64`
10×	`sqr-pow_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
8×	`associate-r_binary64` `pow-pow_binary64`
7×	`associate-*r/_binary64` `unswap-sqr_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `flip-+_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `div-inv_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `div-exp_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 170

Calls

4 calls:

82.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.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))))
5.0ms	(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)

series4.9s

Counts

4 → 10

Calls

4 calls:

4.7s	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.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))))
71.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
76.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	601	9
1	601	9
0	601	9
1	601	9
0	1	3
1	1	3
0	601	9
1	601	9
0	601	9
1	601	9
0	1	3
1	1	3
0	23942	9
1	23942	9
0	23942	9
1	23942	9
0	1	3
1	1	3

simplify140.0ms

Counts

180 → 180

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5609	8407

prune576.0ms

Filtered

139 candidates to 180 candidates (-29.5%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	168	12	180
Fresh	10	15	25
Picked	1	0	1
Done	0	0	0
Total	179	27	206

Merged error: 0.1b

Counts

206 → 27

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 (fabs.f64 x) 5))
0.5b	(*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
21×	`unpow-prod-down_binary64`
20×	`distribute-lft-out_binary64` `add-cube-cbrt_binary64`
19×	`swap-sqr_binary64`
18×	`add-exp-log_binary64`
13×	`pow1_binary64` `associate-r_binary64` `associate-l_binary64`
11×	`sqr-pow_binary64`
10×	`unswap-sqr_binary64` `prod-exp_binary64`
9×	`frac-times_binary64`
8×	`flip3-+_binary64` `frac-add_binary64` `add-cbrt-cube_binary64` `times-frac_binary64` `div-inv_binary64` `flip-+_binary64`
7×	`pow-to-exp_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `associate-r/_binary64` `sqrt-prod_binary64` `associate-l/_binary64` `exp-prod_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 146

Calls

4 calls:

9.0ms	(*.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 (fabs.f64 x) 5))
68.0ms	(*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
1.0ms	(sqrt.f64 PI.f64)
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

series840.0ms

Counts

4 → 10

Calls

4 calls:

90.0ms	(*.f64 (pow.f64 (fabs.f64 x) 5) (pow.f64 (fabs.f64 x) 5))
693.0ms	(*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))))
0.0ms	(sqrt.f64 PI.f64)
57.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	364	9
1	364	9
0	364	9
1	364	9
0	1	3
1	1	3
0	5437	9
1	5437	9
0	5437	9
1	5437	9
0	1	3
1	1	3
0	1054	9
1	1054	9
0	1054	9
1	1054	9
0	1	3
1	1	3

simplify90.0ms

Counts

156 → 156

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5025	3530

prune491.0ms

Filtered

85 candidates to 156 candidates (-83.5%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	150	6	156
Fresh	1	25	26
Picked	1	0	1
Done	0	0	0
Total	152	31	183

Merged error: 0.1b

Counts

183 → 31

regimes312.0ms

Accuracy

0% (1.1b remaining)

Error of 1.3b against oracle of 0.2b and baseline of 1.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	67
1	34	67

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
84.0ms	8118×	pre	80	true
23.0ms	118×	body	80	invalid

Details

analyze9.0ms

sample67.0ms

simplify241.0ms

prune9.0ms

localize28.0ms

rewrite98.0ms

series3.2s

simplify113.0ms

prune373.0ms

localize28.0ms

rewrite110.0ms

series3.5s

simplify149.0ms

prune472.0ms

localize34.0ms

rewrite105.0ms

series4.9s

simplify140.0ms

prune576.0ms

localize40.0ms

rewrite95.0ms

series840.0ms

simplify90.0ms

prune491.0ms

regimes312.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample1.8s

Profiling