Details

analyze480.0ms (7.7%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	167×	body	128	valid
8.0ms	32×	body	2048	valid
5.0ms	15×	body	4096	valid
4.0ms	23×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	18×	body	128	invalid
1.0ms	17×	body	128	nan
1.0ms	8×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify219.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_435`
13×	`*-un-lft-identity_binary64_414`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`add-cube-cbrt_binary64_446`
6×	`times-frac_binary64_420` `difference-of-squares_binary64_383` `sqrt-prod_binary64_429` `associate-/l*_binary64_361`
5×	`pow1_binary64_472`
4×	`flip3--_binary64_418` `flip--_binary64_389`
3×	`distribute-lft-out--_binary64_368`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `prod-exp_binary64_460` `frac-2neg_binary64_425` `pow1/2_binary64_491` `cbrt-unprod_binary64_444` `div-sub_binary64_419` `associate-/r*_binary64_360` `rem-sqrt-square_binary64_427`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series544.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
136.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune123.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 5.7b

Counts

83 → 10

Compiler

Compiled 2155 to 1298 computations (39.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite118.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_420`
438×	`add-sqr-sqrt_binary64_435`
363×	`*-un-lft-identity_binary64_414`
289×	`add-cube-cbrt_binary64_446`
74×	`difference-of-squares_binary64_383`
71×	`associate-/r*_binary64_360`
40×	`sqrt-prod_binary64_429`
37×	`distribute-lft-out--_binary64_368`
25×	`add-exp-log_binary64_449`
17×	`div-inv_binary64_411`
15×	`div-exp_binary64_462`
13×	`add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
6×	`pow1_binary64_472` `cbrt-undiv_binary64_445`
5×	`associate-/r/_binary64_362`
3×	`1-exp_binary64_455` `flip3--_binary64_418` `rec-exp_binary64_461` `flip--_binary64_389` `associate-/l*_binary64_361`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`clear-num_binary64_413` `inv-pow_binary64_496` `pow-flip_binary64_485` `sqrt-pow1_binary64_431` `frac-2neg_binary64_425` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 352

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series567.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

256.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify188.0ms (3%)

Algorithm

1×	egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5071	16279

prune811.0ms (13%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	360	4	364
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	363	11	374

Merged error: 5.6b

Counts

374 → 11

Compiler

Compiled 12760 to 7717 computations (39.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_435`
17×	`*-un-lft-identity_binary64_414`
13×	`add-cube-cbrt_binary64_446` `associate-r_binary64_356`
10×	`times-frac_binary64_420`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`pow1_binary64_472`
6×	`associate-l_binary64_357`
5×	`flip3--_binary64_418` `sqrt-prod_binary64_429` `flip--_binary64_389`
4×	`difference-of-squares_binary64_383`
2×	`distribute-lft-out--_binary64_368` `sqrt-div_binary64_430` `associate-*l/_binary64_359` `diff-log_binary64_503` `prod-exp_binary64_460` `sub-neg_binary64_407` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `frac-times_binary64_424`
1×	`div-inv_binary64_411` `-commutative_binary64_347` `sqrt-pow1_binary64_431` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `pow1/2_binary64_491` `associate-r/_binary64_358` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

4 → 79

Calls

4 calls:

17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series540.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4945	2222
1	4945	2222

prune108.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	92	10	102

Merged error: 5.6b

Counts

102 → 10

Compiler

Compiled 2308 to 1381 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.0b	(/.f64 1 (sqrt.f64 2))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_435`
22×	`*-un-lft-identity_binary64_414`
20×	`add-cube-cbrt_binary64_446`
18×	`times-frac_binary64_420`
16×	`sqrt-prod_binary64_429`
8×	`add-exp-log_binary64_449` `add-log-exp_binary64_450`
7×	`pow1_binary64_472`
6×	`add-cbrt-cube_binary64_447` `associate-/r*_binary64_360`
3×	`flip3--_binary64_418` `pow-flip_binary64_485` `flip--_binary64_389` `associate-/l*_binary64_361`
2×	`sqrt-div_binary64_430` `difference-of-squares_binary64_383` `diff-log_binary64_503` `sqrt-pow1_binary64_431` `sub-neg_binary64_407` `pow1/2_binary64_491` `div-exp_binary64_462`
1×	`1-exp_binary64_455` `clear-num_binary64_413` `distribute-lft-out--_binary64_368` `inv-pow_binary64_496` `div-inv_binary64_411` `cbrt-undiv_binary64_445` `rec-exp_binary64_461` `frac-2neg_binary64_425` `rem-sqrt-square_binary64_427`

Counts

4 → 85

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(/.f64 1 (sqrt.f64 2))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series312.0ms (5%)

Counts

4 → 10

Calls

4 calls:

123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0ms	(/.f64 1 (sqrt.f64 2))

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5033	1524

prune131.0ms (2.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	95	10	105

Merged error: 5.6b

Counts

105 → 10

Compiler

Compiled 2608 to 1834 computations (29.7% saved)

regimes182.0ms (2.9%)

Compiler: Compiled 510 to 441 computations (13.5% saved)

bsearch112.0ms (1.8%)

Steps

Iters	Range		Point
9	250566454504151.5	3.764613681933625e+19	7.957206871783919e+17
10	3.0752939460482864e-143	1.2187648676017627e-130	2.6856742787563955e-139
9	-1.1728433930348086e+159	-6.078197847532872e+152	-3.625373603204043e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	94
1	108	94

end0.0ms (0%)

sample1.4s (22.2%)

Algorithm

1×

intervals

Results

280.0ms	5217×	body	128	valid
279.0ms	1114×	body	2048	valid
137.0ms	719×	body	1024	valid
128.0ms	406×	body	4096	valid
53.0ms	371×	body	512	valid
34.0ms	695×	body	128	nan
20.0ms	397×	body	128	invalid
17.0ms	173×	body	256	valid

Compiler

Compiled 249 to 200 computations (19.7% saved)

Details

analyze480.0ms (7.7%)

sample40.0ms (0.6%)

simplify219.0ms (3.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite41.0ms (0.7%)

series544.0ms (8.7%)

simplify100.0ms (1.6%)

prune123.0ms (2%)

localize12.0ms (0.2%)

rewrite118.0ms (1.9%)

series567.0ms (9.1%)

simplify188.0ms (3%)

prune811.0ms (13%)

localize10.0ms (0.2%)

rewrite42.0ms (0.7%)

series540.0ms (8.6%)

simplify75.0ms (1.2%)

prune108.0ms (1.7%)

localize14.0ms (0.2%)

rewrite32.0ms (0.5%)

series312.0ms (5%)

simplify48.0ms (0.8%)

prune131.0ms (2.1%)

regimes182.0ms (2.9%)

bsearch112.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (22.2%)

Profiling