Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample30.0ms

Algorithm

intervals

Results

13.0ms	63×	body	640	valid
5.0ms	131×	body	80	valid
4.0ms	37×	body	320	valid
2.0ms	11×	body	1280	valid
1.0ms	14×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	193	22
1	193	22

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: 8.2b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
17×	`distribute-lft-out_binary64`
14×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64`
11×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`add-cbrt-cube_binary64` `div-inv_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `div-exp_binary64` `insert-posit16`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 139

Calls

4 calls:

7.0ms	(/.f64 1 (-.f64 x 1))
7.0ms	(/.f64 1 (+.f64 x 1))
22.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series1.5s

Counts

4 → 12

Calls

4 calls:

291.0ms	(/.f64 1 (-.f64 x 1))
360.0ms	(/.f64 1 (+.f64 x 1))
580.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
251.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	5672	951
0	5672	951
0	1	3
1	1	3
0	3991	137
1	3991	137
0	3991	137
1	3991	137
0	5273	39
0	971	166
1	971	166
0	971	166
1	971	166
0	5268	24
0	669	164
1	669	164
0	669	164
1	669	164
0	4885	24
1	4885	24

simplify122.0ms

Counts

151 → 151

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4953	2497
1	4953	2497

prune133.0ms

Filtered

92 candidates to 151 candidates (-64.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	141	10	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	10	152

Merged error: 7.7b

Counts

152 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))
0.2b	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
4.7b	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
16.2b	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

774×	`*-un-lft-identity_binary64`
753×	`times-frac_binary64`
635×	`add-sqr-sqrt_binary64`
260×	`distribute-lft-out--_binary64`
245×	`difference-of-squares_binary64`
150×	`add-cube-cbrt_binary64`
81×	`div-inv_binary64`
58×	`frac-sub_binary64`
52×	`difference-of-sqr-1_binary64`
37×	`flip3--_binary64` `flip--_binary64`
35×	`associate-/l*_binary64`
27×	`frac-times_binary64`
24×	`distribute-lft-out_binary64`
23×	`associate-/r*_binary64` `associate-/r/_binary64`
21×	`swap-sqr_binary64`
18×	`associate-/l/_binary64`
17×	`add-exp-log_binary64`
14×	`pow1_binary64`
13×	`associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`associate-r/_binary64` `associate-l/_binary64`
7×	`div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`sub-neg_binary64`
4×	`cbrt-undiv_binary64` `insert-posit16`
2×	`pow-div_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `1-exp_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-sub_binary64` `inv-pow_binary64` `prod-exp_binary64` `rec-exp_binary64` `pow-sqr_binary64` `pow-flip_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 548

Calls

4 calls:

19.0ms	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))
54.0ms	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
100.0ms	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
158.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))

series1.2s

Counts

4 → 12

Calls

4 calls:

514.0ms	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))
182.0ms	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
369.0ms	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
179.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	4754	2137
1	4754	2137
0	4754	2137
1	4754	2137
0	1	3
1	1	3
0	4661	1256
1	4661	1256
0	4661	1256
1	4661	1256
0	5276	3
0	3016	310
1	3016	310
0	3016	310
1	3016	310
0	1	3
1	1	3
0	1768	716
1	1768	716
0	1768	716
1	1768	716
0	5479	21

simplify294.0ms

Counts

560 → 560

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5165	27368

prune1.4s

Filtered

218 candidates to 560 candidates (-156.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	547	13	560
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	556	14	570

Merged error: 7.7b

Counts

570 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(cbrt.f64 (-.f64 x 1))
8.2b	(-.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (*.f64 (-.f64 x 1) (cbrt.f64 (-.f64 x 1)))))
25.5b	(/.f64 (-.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (*.f64 (-.f64 x 1) (cbrt.f64 (-.f64 x 1))))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

234×	`*-un-lft-identity_binary64`
134×	`times-frac_binary64`
102×	`distribute-lft-out--_binary64`
89×	`add-sqr-sqrt_binary64`
50×	`frac-sub_binary64`
37×	`difference-of-squares_binary64`
28×	`add-cube-cbrt_binary64`
26×	`div-inv_binary64`
22×	`flip3--_binary64` `flip--_binary64`
18×	`frac-times_binary64`
17×	`associate-/l/_binary64`
16×	`associate-/r*_binary64`
14×	`cbrt-prod_binary64`
10×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `associate-r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l/_binary64`
5×	`associate-/r/_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`sub-neg_binary64`
2×	`pow1/3_binary64` `difference-of-sqr-1_binary64` `associate--l+_binary64`
1×	`diff-log_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`

Counts

4 → 186

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 x 1))
4.0ms	(cbrt.f64 (-.f64 x 1))
66.0ms	(-.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (*.f64 (-.f64 x 1) (cbrt.f64 (-.f64 x 1)))))
116.0ms	(/.f64 (-.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (*.f64 (-.f64 x 1) (cbrt.f64 (-.f64 x 1))))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))

series908.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(cbrt.f64 (-.f64 x 1))
215.0ms	(cbrt.f64 (-.f64 x 1))
241.0ms	(-.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (*.f64 (-.f64 x 1) (cbrt.f64 (-.f64 x 1)))))
234.0ms	(/.f64 (-.f64 (.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (*.f64 (-.f64 x 1) (cbrt.f64 (-.f64 x 1))))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4913	2410
1	4913	2410
0	4913	2410
1	4913	2410
0	1	3
1	1	3
0	4769	1990
1	4769	1990
0	4769	1990
1	4769	1990
0	1	3
1	1	3
0	57	1626
1	57	1626
0	57	1626
1	57	1626
0	5408	14
0	57	1626
1	57	1626
0	57	1626
1	57	1626
0	5408	14

simplify172.0ms

Counts

198 → 198

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5201	15408

prune810.0ms

Filtered

122 candidates to 198 candidates (-62.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	193	5	198
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	197	15	212

Merged error: 7.7b

Counts

212 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(*.f64 x (+.f64 1 x))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
20.5b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*r/_binary64`
40×	`*-un-lft-identity_binary64`
32×	`frac-add_binary64`
25×	`flip3--_binary64` `flip--_binary64`
21×	`times-frac_binary64`
20×	`flip3-+_binary64` `add-sqr-sqrt_binary64` `flip-+_binary64`
18×	`associate-/l/_binary64` `add-cube-cbrt_binary64`
16×	`frac-times_binary64`
9×	`distribute-lft-out_binary64`
8×	`add-log-exp_binary64` `distribute-rgt-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow3_binary64` `associate-*l/_binary64`
7×	`associate-/r*_binary64`
6×	`pow1_binary64`
4×	`associate-r_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `insert-posit16`
3×	`sub-neg_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64`
2×	`associate-+l+_binary64` `associate-/r/_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 132

Calls

4 calls:

4.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
8.0ms	(*.f64 x (+.f64 1 x))
27.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
14.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

series1.7s

Counts

4 → 12

Calls

4 calls:

491.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
246.0ms	(*.f64 x (+.f64 1 x))
272.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
644.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	2013	863
1	2013	863
0	2013	863
1	2013	863
0	5289	12
0	1143	1928
1	1143	1928
0	1143	1928
1	1143	1928
0	1	3
1	1	3
0	346	302
1	346	302
0	346	302
1	346	302
0	4984	15
1	4984	15
0	1688	177
1	1688	177
0	1688	177
1	1688	177
0	5110	15

simplify114.0ms

Counts

144 → 144

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	6220	5472

prune266.0ms

Filtered

117 candidates to 144 candidates (-23.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	142	17	159

Merged error: 7.7b

Counts

159 → 17

regimes124.0ms

Accuracy

94.4% (0.9b remaining)

Error of 10.0b against oracle of 9.0b and baseline of 25.7b

bsearch85.0ms

Steps

Iters	Range		Point
10	6.29677175524033e+138	2.639568132496066e+154	1.3274650429408704e+154
9	-2.589451850498077e+161	-4.133085746122108e+153	-1.3270199621315663e+154

simplify10.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	155	130
1	155	130

end0.0ms

sample1.0s

Algorithm

intervals

Results

376.0ms	1870×	body	640	valid
210.0ms	4095×	body	80	valid
153.0ms	996×	body	320	valid
143.0ms	562×	body	1280	valid
48.0ms	477×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze6.0ms

sample30.0ms

simplify30.0ms

prune3.0ms

localize9.0ms

rewrite89.0ms

series1.5s

simplify122.0ms

prune133.0ms

localize14.0ms

rewrite397.0ms

series1.2s

simplify294.0ms

prune1.4s

localize21.0ms

rewrite206.0ms

series908.0ms

simplify172.0ms

prune810.0ms

localize13.0ms

rewrite62.0ms

series1.7s

simplify114.0ms

prune266.0ms

regimes124.0ms

bsearch85.0ms

simplify10.0ms

end0.0ms

sample1.0s

Profiling