Details

analyze457.0ms (8.1%)

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 (0.7%)

Algorithm

1×

intervals

Results

11.0ms	171×	body	128	valid
9.0ms	40×	body	2048	valid
4.0ms	19×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	23×	body	128	nan
1.0ms	17×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify222.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 32.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (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))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite37.0ms (0.6%)

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:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 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)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series512.0ms (9%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
120.0ms	(-.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)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify102.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune127.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 6.0b

Counts

83 → 7

Compiler

Compiled 2052 to 1229 computations (40.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
9.6b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
22×	`times-frac_binary64_420`
19×	`*-un-lft-identity_binary64_414`
17×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
13×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
12×	`add-sqr-sqrt_binary64_435`
11×	`add-cube-cbrt_binary64_446` `associate-/l*_binary64_361`
6×	`associate-/r/_binary64_362` `add-log-exp_binary64_450`
5×	`pow1_binary64_472` `associate-/r*_binary64_360`
4×	`div-inv_binary64_411` `distribute-lft-out_binary64_367`
3×	`flip3-+_binary64_417` `sqrt-prod_binary64_429` `flip-+_binary64_388`
2×	`flip3--_binary64_418` `clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425` `flip--_binary64_389`
1×	`diff-log_binary64_503` `sqrt-pow1_binary64_431` `sub-neg_binary64_407` `pow1/2_binary64_491` `associate-/l/_binary64_363` `rem-sqrt-square_binary64_427`

Counts

4 → 101

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.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)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series853.0ms (15.1%)

Counts

4 → 12

Calls

4 calls:

367.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
310.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4960	3052
1	4960	3052

prune150.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	113	7	120

Merged error: 6.0b

Counts

120 → 7

Compiler

Compiled 3191 to 1961 computations (38.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_414`
15×	`add-sqr-sqrt_binary64_435`
14×	`add-cube-cbrt_binary64_446`
12×	`times-frac_binary64_420`
8×	`add-log-exp_binary64_450`
6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
5×	`pow1_binary64_472` `distribute-lft-out_binary64_367`
4×	`associate-/r*_binary64_360`
3×	`sqrt-prod_binary64_429` `associate-/l*_binary64_361`
2×	`associate-/r/_binary64_362` `flip3--_binary64_418` `sqrt-div_binary64_430` `flip3-+_binary64_417` `flip-+_binary64_388` `flip--_binary64_389`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `frac-2neg_binary64_425` `pow1/2_binary64_491` `sum-log_binary64_502` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

4 → 71

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.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)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series656.0ms (11.6%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
127.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4931	1962
1	4931	1962

prune105.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	83	7	90

Merged error: 6.0b

Counts

90 → 7

Compiler

Compiled 2194 to 1358 computations (38.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_450` `add-sqr-sqrt_binary64_435`
6×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `sqrt-prod_binary64_429` `*-un-lft-identity_binary64_414`
4×	`flip3--_binary64_418` `sqrt-div_binary64_430` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `flip--_binary64_389`
2×	`diff-log_binary64_503` `sqrt-pow1_binary64_431` `sub-neg_binary64_407` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 52

Calls

4 calls:

5.0ms	(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))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series361.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5020	1222

prune101.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	64	7	71

Merged error: 6.0b

Counts

71 → 7

Compiler

Compiled 2386 to 1421 computations (40.4% saved)

regimes107.0ms (1.9%)

Compiler: Compiled 357 to 297 computations (16.8% saved)

bsearch83.0ms (1.5%)

Steps

Iters	Range		Point
8	2.3396116861752783e+67	5.903799506100967e+70	5.781577797177691e+70
5	2.359896871153042e-296	5.74600834268242e-296	3.843995825405104e-296
6	-2.3677179713659354e+154	-2.465565162145652e+153	-2.5949872779844862e+153

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	113	88
1	113	88

end0.0ms (0%)

sample1.4s (24%)

Algorithm

1×

intervals

Results

277.0ms	5232×	body	128	valid
267.0ms	1074×	body	2048	valid
144.0ms	739×	body	1024	valid
128.0ms	408×	body	4096	valid
52.0ms	363×	body	512	valid
36.0ms	697×	body	128	nan
20.0ms	391×	body	128	invalid
18.0ms	184×	body	256	valid

Compiler

Compiled 194 to 149 computations (23.2% saved)

Details

analyze457.0ms (8.1%)

sample40.0ms (0.7%)

simplify222.0ms (3.9%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite37.0ms (0.6%)

series512.0ms (9%)

simplify102.0ms (1.8%)

prune127.0ms (2.2%)

localize15.0ms (0.3%)

rewrite53.0ms (0.9%)

series853.0ms (15.1%)

simplify93.0ms (1.6%)

prune150.0ms (2.7%)

localize14.0ms (0.2%)

rewrite31.0ms (0.6%)

series656.0ms (11.6%)

simplify71.0ms (1.3%)

prune105.0ms (1.9%)

localize13.0ms (0.2%)

rewrite25.0ms (0.4%)

series361.0ms (6.4%)

simplify55.0ms (1%)

prune101.0ms (1.8%)

regimes107.0ms (1.9%)

bsearch83.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (24%)

Profiling