Details

analyze530.0ms (8.5%)

Algorithm

1×

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
2.0ms	24×	body	128	nan
1.0ms	15×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify252.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune8.0ms (0.1%)

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: 20.7b

Counts

2 → 1

Compiler

Compiled 148 to 102 computations (31.1% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_118` `*-un-lft-identity_binary64_79`
8×	`add-sqr-sqrt_binary64_101`
6×	`sqrt-prod_binary64_95` `add-cube-cbrt_binary64_114` `pow1_binary64_140`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `sqrt-div_binary64_96`
3×	`flip--_binary64_54` `flip3--_binary64_83`
2×	`sum-log_binary64_170` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `distribute-lft-out_binary64_30`
1×	`neg-sub0_binary64_74` `flip-+_binary64_53` `neg-log_binary64_172` `associate-+l-_binary64_14` `+-commutative_binary64_9` `distribute-rgt-neg-in_binary64_37` `diff-log_binary64_171` `cancel-sign-sub-inv_binary64_45` `flip3-+_binary64_82` `sub-neg_binary64_72`

Counts

4 → 57

Calls

4 calls:

9.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series423.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5933	1356

prune275.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	6	70

Merged error: 7.5b

Counts

70 → 6

Compiler

Compiled 6481 to 4084 computations (37% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.4b	(/.f64 (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) (*.f64 2 a))
6.0b	(/.f64 (*.f64 a c) b)
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_79`
14×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-sqr-sqrt_binary64_101`
9×	`times-frac_binary64_85` `add-cube-cbrt_binary64_114`
8×	`add-log-exp_binary64_118`
7×	`associate-/l*_binary64_24`
5×	`pow1_binary64_140`
4×	`associate-/r*_binary64_23` `cbrt-undiv_binary64_113` `div-exp_binary64_130` `distribute-lft-out--_binary64_31`
3×	`sqrt-prod_binary64_95` `distribute-rgt-neg-in_binary64_37`
2×	`div-inv_binary64_76` `sum-log_binary64_170` `flip--_binary64_54` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `sqrt-div_binary64_96` `difference-of-squares_binary64_48` `clear-num_binary64_78` `flip3--_binary64_83` `associate-/l/_binary64_26` `distribute-lft-out_binary64_30` `frac-2neg_binary64_90`
1×	`neg-sub0_binary64_74` `flip-+_binary64_53` `div-sub_binary64_84` `neg-log_binary64_172` `associate-+l-_binary64_14` `+-commutative_binary64_9` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `flip3-+_binary64_82`

Counts

4 → 81

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) (*.f64 2 a))
9.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series356.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
89.0ms	(/.f64 (-.f64 (neg.f64 b) (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) (*.f64 2 a))
35.0ms	(/.f64 (*.f64 a c) b)

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5085	1697

prune334.0ms (5.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	90	9	99

Merged error: 6.6b

Counts

99 → 9

Compiler

Compiled 8348 to 5122 computations (38.6% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_79`
10×	`add-log-exp_binary64_118`
9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-sqr-sqrt_binary64_101`
7×	`add-cube-cbrt_binary64_114`
6×	`distribute-lft-out_binary64_30`
5×	`associate-/r*_binary64_23` `times-frac_binary64_85` `pow1_binary64_140`
3×	`sqrt-prod_binary64_95` `distribute-rgt-neg-in_binary64_37`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `flip-+_binary64_53` `sum-log_binary64_170` `flip--_binary64_54` `associate-/r/_binary64_25` `sqrt-div_binary64_96` `flip3--_binary64_83` `flip3-+_binary64_82`
1×	`neg-sub0_binary64_74` `div-inv_binary64_76` `neg-log_binary64_172` `associate-/l*_binary64_24` `associate-+l-_binary64_14` `+-commutative_binary64_9` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `diff-log_binary64_171` `clear-num_binary64_78` `pow1/2_binary64_159` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

4 → 69

Calls

4 calls:

15.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
9.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series686.0ms (11%)

Counts

4 → 12

Calls

4 calls:

403.0ms	(/.f64 (.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))
119.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
104.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
59.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4971	1756
1	4971	1756

prune358.0ms (5.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	81	9	90

Merged error: 6.3b

Counts

90 → 9

Compiler

Compiled 8652 to 5416 computations (37.4% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 2 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) c))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_85`
122×	`add-sqr-sqrt_binary64_101`
95×	`*-un-lft-identity_binary64_79`
69×	`add-cube-cbrt_binary64_114`
26×	`difference-of-squares_binary64_48`
22×	`associate-/r*_binary64_23`
16×	`sqrt-prod_binary64_95`
13×	`distribute-lft-out--_binary64_31`
9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-log-exp_binary64_118`
5×	`div-inv_binary64_76` `pow1_binary64_140`
4×	`cancel-sign-sub-inv_binary64_45`
3×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `associate-/l*_binary64_24` `flip--_binary64_54` `flip3--_binary64_83`
2×	`sqrt-div_binary64_96` `diff-log_binary64_171` `sub-neg_binary64_72`
1×	`associate-/r/_binary64_25` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `frac-2neg_binary64_90`

Counts

4 → 150

Calls

4 calls:

13.0ms	(/.f64 2 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series540.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(/.f64 2 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) c))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
112.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify110.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5239	5736

prune305.0ms (4.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	163	8	171

Merged error: 5.1b

Counts

171 → 8

Compiler

Compiled 7511 to 3920 computations (47.8% saved)

regimes183.0ms (2.9%)

Compiler: Compiled 1270 to 890 computations (29.9% saved)

bsearch74.0ms (1.2%)

Steps

Iters	Range		Point
8	4.128312546146331e+96	1.9135304727080364e+99	1.2920436183135944e+99
9	-2.4536555793202624e+100	-3.0730103674035083e+94	-2.4202304013350694e+100

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	127	92
1	127	92

end0.0ms (0%)

sample1.3s (21.5%)

Algorithm

1×

intervals

Results

736.0ms	8000×	body	128	valid
62.0ms	704×	body	128	nan
33.0ms	375×	body	128	invalid

Compiler

Compiled 397 to 275 computations (30.7% saved)

Details

analyze530.0ms (8.5%)

sample36.0ms (0.6%)

simplify252.0ms (4%)

prune8.0ms (0.1%)

localize24.0ms (0.4%)

rewrite25.0ms (0.4%)

series423.0ms (6.8%)

simplify79.0ms (1.3%)

prune275.0ms (4.4%)

localize29.0ms (0.5%)

rewrite33.0ms (0.5%)

series356.0ms (5.7%)

simplify44.0ms (0.7%)

prune334.0ms (5.4%)

localize23.0ms (0.4%)

rewrite37.0ms (0.6%)

series686.0ms (11%)

simplify58.0ms (0.9%)

prune358.0ms (5.7%)

localize26.0ms (0.4%)

rewrite42.0ms (0.7%)

series540.0ms (8.7%)

simplify110.0ms (1.8%)

prune305.0ms (4.9%)

regimes183.0ms (2.9%)

bsearch74.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (21.5%)

Profiling