Details

analyze222.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample68.0ms

Algorithm

intervals

Results

28.0ms	54×	body	1280	valid
13.0ms	33×	body	640	valid
10.0ms	137×	body	80	valid
5.0ms	24×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	4×	body	80	invalid
0.0ms	4×	body	80	overflowed
0.0ms	1×	body	160	invalid

simplify90.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5488	41

prune6.0ms

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: 28.6b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.3b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
78×	`exp-neg_binary64`
76×	`frac-times_binary64`
59×	`neg-sub0_binary64` `exp-diff_binary64`
38×	`associate-r/_binary64` `associate-l/_binary64`
31×	`flip3--_binary64` `flip--_binary64`
27×	`flip3-+_binary64` `flip-+_binary64`
25×	`add-sqr-sqrt_binary64`
19×	`un-div-inv_binary64`
17×	`*-un-lft-identity_binary64`
14×	`associate-l_binary64`
12×	`exp-prod_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `times-frac_binary64`
5×	`add-exp-log_binary64`
4×	`rem-exp-log_binary64` `insert-posit16`
3×	`associate-r_binary64` `difference-of-sqr-1_binary64`
2×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 168

Calls

4 calls:

19.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
4.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
26.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series3.0s

Counts

4 → 12

Calls

4 calls:

1.2s	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
105.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
91.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
1.6s	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	25547	9
0	25547	9
0	1	3
1	1	3
0	409	9
1	409	9
0	409	9
1	409	9
0	1	3
1	1	3
0	576	9
1	576	9
0	576	9
1	576	9
0	1	3
1	1	3
0	44055	9
0	44055	9
0	1	3
1	1	3

simplify169.0ms

Counts

180 → 180

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5182	8714

prune283.0ms

Filtered

98 candidates to 180 candidates (-83.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	163	17	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	17	182

Merged error: 27.9b

Counts

182 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))
0.3b	(cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))
0.3b	(.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))))
19.7b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps)))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

766×	`times-frac_binary64`
706×	`add-sqr-sqrt_binary64`
576×	`cbrt-prod_binary64`
552×	`*-un-lft-identity_binary64`
216×	`exp-sum_binary64`
210×	`difference-of-squares_binary64`
152×	`add-cube-cbrt_binary64`
137×	`swap-sqr_binary64`
120×	`difference-of-sqr-1_binary64`
114×	`cbrt-div_binary64`
108×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
100×	`distribute-lft-out--_binary64`
77×	`associate-r_binary64` `associate-l_binary64`
74×	`frac-times_binary64`
63×	`frac-sub_binary64`
60×	`associate-*l/_binary64`
56×	`div-inv_binary64`
42×	`associate-*r/_binary64`
28×	`exp-neg_binary64`
21×	`flip3-+_binary64` `neg-sub0_binary64` `exp-diff_binary64` `flip-+_binary64`
11×	`pow1_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1/3_binary64`
7×	`un-div-inv_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `insert-posit16`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `flip--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 565

Calls

4 calls:

15.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))
16.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))
126.0ms	(.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))))
23.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps)))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))))

series2.2s

Counts

4 → 12

Calls

4 calls:

52.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))
52.0ms	(cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))
55.0ms	(.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))))
2.0s	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (.f64 x (+.f64 1 eps)))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	30042	9
0	30042	9
0	1	3
1	1	3
0	158	9
1	158	9
0	158	9
1	158	9
0	1	3
1	1	3
0	87	9
1	87	9
0	87	9
1	87	9
0	1	3
1	1	3
0	87	9
1	87	9
0	87	9
1	87	9
0	1	3
1	1	3

simplify305.0ms

Counts

577 → 577

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5243	34134

prune1.6s

Filtered

235 candidates to 577 candidates (-145.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	562	15	577
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	566	28	594

Merged error: 27.8b

Counts

594 → 28

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (-.f64 (/.f64 1 eps) 1))
0.4b	(*.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))
0.4b	(*.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))
21.7b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1))))) (.f64 (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (exp.f64 (.f64 x (+.f64 1 eps))))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))))

rewrite3.0s

Algorithm

rewrite-expression-head

Rules

34694×	`cbrt-div_binary64`
21073×	`frac-times_binary64`
10271×	`associate-*l/_binary64`
7790×	`flip3--_binary64` `flip--_binary64`
5987×	`associate-*r/_binary64`
5823×	`frac-sub_binary64`
2588×	`exp-neg_binary64`
1941×	`flip3-+_binary64` `neg-sub0_binary64` `exp-diff_binary64` `flip-+_binary64`
647×	`un-div-inv_binary64`
204×	`add-sqr-sqrt_binary64`
182×	`cbrt-prod_binary64`
154×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
66×	`difference-of-squares_binary64`
58×	`swap-sqr_binary64`
39×	`difference-of-sqr-1_binary64`
34×	`associate-r_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
21×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
17×	`div-inv_binary64`
13×	`pow1/3_binary64`
8×	`add-exp-log_binary64` `unswap-sqr_binary64`
6×	`add-log-exp_binary64`
4×	`pow-prod-down_binary64` `pow-prod-up_binary64` `add-cbrt-cube_binary64` `pow-sqr_binary64` `insert-posit16`
2×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64`

Counts

4 → 6048

Calls

4 calls:

9.0ms	(cbrt.f64 (-.f64 (/.f64 1 eps) 1))
30.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))
33.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))
396.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1))))) (.f64 (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (exp.f64 (.f64 x (+.f64 1 eps))))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt.f64 (-.f64 (/.f64 1 eps) 1))
72.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))
74.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))
2.1s	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1)))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (cbrt.f64 (-.f64 (/.f64 1 eps) 1))))) (.f64 (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (exp.f64 (.f64 x (+.f64 1 eps))))) (cbrt.f64 (/.f64 (cbrt.f64 (-.f64 (/.f64 1 eps) 1)) (exp.f64 (.f64 x (+.f64 1 eps))))))) (cbrt.f64 (/.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	30129	9
0	30129	9
0	1	3
1	1	3
0	591	9
1	591	9
0	591	9
1	591	9
0	1	3
1	1	3
0	591	9
1	591	9
0	591	9
1	591	9
0	1	3
1	1	3
0	51	9
1	51	9
0	51	9
1	51	9
0	1	3
1	1	3

simplify11.6s

Counts

6060 → 6060

Iterations

Useful iterations: 0 (309.0ms)

Iter	Nodes	Cost
0	13462	1820816

prune2.1min

Filtered: 5961 candidates to 6060 candidates (-1.7%)

Details

analyze222.0ms

sample68.0ms

simplify90.0ms

prune6.0ms

localize17.0ms

rewrite68.0ms

series3.0s

simplify169.0ms

prune283.0ms

localize21.0ms

rewrite262.0ms

series2.2s

simplify305.0ms

prune1.6s

localize36.0ms

rewrite3.0s

series2.3s

simplify11.6s

prune2.1min

Profiling