Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	61×	body	1024	valid
5.0ms	131×	body	128	valid
4.0ms	37×	body	512	valid
2.0ms	11×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify171.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune2.0ms (0.1%)

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: 31.0b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
3.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite69.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_5193`
88×	`times-frac_binary64_5199`
85×	`add-sqr-sqrt_binary64_5215`
37×	`add-cube-cbrt_binary64_5228`
34×	`cancel-sign-sub-inv_binary64_5159`
27×	`distribute-lft-out_binary64_5144`
22×	`distribute-lft-out--_binary64_5145` `difference-of-squares_binary64_5162`
11×	`associate-/r*_binary64_5137`
9×	`difference-of-sqr-1_binary64_5163`
7×	`add-cbrt-cube_binary64_5229` `associate-/l*_binary64_5138` `add-exp-log_binary64_5231`
6×	`associate-/r/_binary64_5139`
5×	`add-log-exp_binary64_5232`
3×	`flip3--_binary64_5197` `flip--_binary64_5168` `div-inv_binary64_5190` `pow1_binary64_5254`
2×	`flip-+_binary64_5167` `cbrt-undiv_binary64_5227` `clear-num_binary64_5192` `flip3-+_binary64_5196` `div-exp_binary64_5244` `associate-/l/_binary64_5140` `frac-2neg_binary64_5204`
1×	`sub-neg_binary64_5186` `frac-sub_binary64_5202` `diff-log_binary64_5285`

Counts

3 → 147

Calls

3 calls:

39.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 x (+.f64 x 1))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

series60.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

36.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
12.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
12.0ms	(/.f64 x (+.f64 x 1))

simplify78.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5658	2774

prune192.0ms (5.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	152	4	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	4	157

Merged error: 0.0b

Counts

157 → 4

Compiler

Compiled 3066 to 2163 computations (29.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 -1 (*.f64 x x))
0.4b	(/.f64 3 (pow.f64 x 3))
7.2b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite61.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64_5193` `times-frac_binary64_5199`
39×	`add-sqr-sqrt_binary64_5215`
35×	`add-cube-cbrt_binary64_5228`
13×	`cancel-sign-sub-inv_binary64_5159` `add-exp-log_binary64_5231` `associate-/r*_binary64_5137`
12×	`cube-prod_binary64_5221` `unpow-prod-down_binary64_5272`
10×	`add-cbrt-cube_binary64_5229`
9×	`unpow3_binary64_5259`
8×	`add-log-exp_binary64_5232`
6×	`associate-/l*_binary64_5138` `distribute-lft-out_binary64_5144`
5×	`div-exp_binary64_5244`
4×	`distribute-rgt-out_binary64_5146` `div-inv_binary64_5190` `cube-mult_binary64_5223` `sqr-pow_binary64_5165`
3×	`cbrt-undiv_binary64_5227` `frac-sub_binary64_5202` `pow1_binary64_5254`
2×	`distribute-lft-out--_binary64_5145` `clear-num_binary64_5192` `difference-of-squares_binary64_5162` `diff-log_binary64_5285` `frac-2neg_binary64_5204`
1×	`flip3--_binary64_5197` `sub-neg_binary64_5186` `flip--_binary64_5168` `frac-add_binary64_5201` `distribute-rgt1-in_binary64_5149` `sum-log_binary64_5284` `flip-+_binary64_5167` `associate--r+_binary64_5129` `flip3-+_binary64_5196` `pow-to-exp_binary64_5262` `prod-exp_binary64_5242` `cbrt-unprod_binary64_5226` `pow-exp_binary64_5261`

Counts

3 → 119

Calls

3 calls:

41.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
5.0ms	(/.f64 3 (pow.f64 x 3))
4.0ms	(/.f64 -1 (*.f64 x x))

series55.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

22.0ms	(/.f64 3 (pow.f64 x 3))
17.0ms	(/.f64 -1 (*.f64 x x))
16.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify70.0ms (2%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5011	2076

prune146.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	128	4	132

Merged error: 0.0b

Counts

132 → 4

Compiler

Compiled 2677 to 1857 computations (30.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
3.3b	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
3.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite123.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

235×	`*-un-lft-identity_binary64_5193`
136×	`times-frac_binary64_5199`
128×	`add-sqr-sqrt_binary64_5215`
68×	`cancel-sign-sub-inv_binary64_5159`
52×	`add-cube-cbrt_binary64_5228`
42×	`distribute-lft-out_binary64_5144`
39×	`distribute-lft-out--_binary64_5145`
38×	`log-prod_binary64_5279`
35×	`exp-sum_binary64_5239`
34×	`difference-of-squares_binary64_5162`
17×	`log-pow_binary64_5282`
16×	`exp-prod_binary64_5245`
13×	`difference-of-sqr-1_binary64_5163`
11×	`associate-/r*_binary64_5137`
8×	`add-cbrt-cube_binary64_5229` `add-exp-log_binary64_5231` `associate-/r/_binary64_5139`
7×	`associate-/l*_binary64_5138`
6×	`add-log-exp_binary64_5232`
5×	`pow1_binary64_5254`
4×	`flip3--_binary64_5197` `flip--_binary64_5168` `div-inv_binary64_5190`
2×	`sub-neg_binary64_5186` `flip-+_binary64_5167` `cbrt-undiv_binary64_5227` `clear-num_binary64_5192` `flip3-+_binary64_5196` `div-exp_binary64_5244` `associate-/l/_binary64_5140` `frac-2neg_binary64_5204`
1×	`rem-log-exp_binary64_5234` `frac-sub_binary64_5202` `diff-log_binary64_5285` `exp-diff_binary64_5241` `log-div_binary64_5280`

Counts

4 → 211

Calls

4 calls:

46.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series123.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
45.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
13.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
13.0ms	(/.f64 x (+.f64 x 1))

simplify119.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5134	4217

prune271.0ms (7.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	223	4	227

Merged error: 0.0b

Counts

227 → 4

Compiler

Compiled 4643 to 3376 computations (27.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
0.1b	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
8.6b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

rewrite51.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_5215`
69×	`*-un-lft-identity_binary64_5193`
56×	`times-frac_binary64_5199`
37×	`add-cube-cbrt_binary64_5228`
27×	`associate-r_binary64_5133`
19×	`add-exp-log_binary64_5231`
14×	`difference-of-squares_binary64_5162`
13×	`add-cbrt-cube_binary64_5229`
11×	`associate-/r*_binary64_5137`
7×	`distribute-lft-out--_binary64_5145` `difference-of-sqr-1_binary64_5163` `pow1_binary64_5254`
6×	`associate-/l*_binary64_5138` `add-log-exp_binary64_5232` `frac-sub_binary64_5202` `associate-/r/_binary64_5139`
5×	`flip-+_binary64_5167` `distribute-lft-out_binary64_5144` `flip3-+_binary64_5196` `div-exp_binary64_5244`
4×	`associate-l_binary64_5134` `associate-*l/_binary64_5136` `frac-times_binary64_5203` `prod-exp_binary64_5242`
3×	`flip3--_binary64_5197` `flip--_binary64_5168` `div-inv_binary64_5190` `cbrt-undiv_binary64_5227` `unswap-sqr_binary64_5161`
2×	`un-div-inv_binary64_5191` `clear-num_binary64_5192` `1-exp_binary64_5237` `rec-exp_binary64_5243` `associate-*r/_binary64_5135` `cbrt-unprod_binary64_5226` `frac-2neg_binary64_5204`
1×	`pow-prod-down_binary64_5264` `sub-neg_binary64_5186` `*-commutative_binary64_5124` `cancel-sign-sub-inv_binary64_5159` `diff-log_binary64_5285` `pow-flip_binary64_5267` `inv-pow_binary64_5278`

Counts

4 → 155

Calls

4 calls:

15.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
11.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series72.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
17.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
13.0ms	(/.f64 x (+.f64 x 1))
9.0ms	(/.f64 1 (-.f64 x 1))

simplify81.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5801	2543

prune183.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	167	4	171

Merged error: 0.0b

Counts

171 → 4

Compiler

Compiled 3487 to 2527 computations (27.5% saved)

regimes143.0ms (4.1%)

Compiler: Compiled 1395 to 1065 computations (23.7% saved)

bsearch44.0ms (1.3%)

Steps

Iters	Range		Point
10	6603.38036270437	5.116023299066326e+18	13924.25804052536
10	-689321.1803201769	-0.0001079610384995891	-14488.508192621899

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	94	64
1	94	64

end0.0ms (0%)

sample1.3s (37.1%)

Algorithm

1×

intervals

Results

262.0ms	2020×	body	1024	valid
153.0ms	4285×	body	128	valid
103.0ms	995×	body	512	valid
40.0ms	228×	body	2048	valid
31.0ms	472×	body	256	valid

Compiler

Compiled 677 to 516 computations (23.8% saved)

Details

analyze4.0ms (0.1%)

sample24.0ms (0.7%)

simplify171.0ms (4.9%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite69.0ms (2%)

series60.0ms (1.7%)

simplify78.0ms (2.3%)

prune192.0ms (5.5%)

localize9.0ms (0.3%)

rewrite61.0ms (1.8%)

series55.0ms (1.6%)

simplify70.0ms (2%)

prune146.0ms (4.2%)

localize10.0ms (0.3%)

rewrite123.0ms (3.5%)

series123.0ms (3.5%)

simplify119.0ms (3.4%)

prune271.0ms (7.8%)

localize8.0ms (0.2%)

rewrite51.0ms (1.5%)

series72.0ms (2.1%)

simplify81.0ms (2.3%)

prune183.0ms (5.3%)

regimes143.0ms (4.1%)

bsearch44.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (37.1%)

Profiling