Details

analyze459.0ms (7.3%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	18×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify221.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

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: 35.0b

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))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.0b	(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:

13.0ms	(/.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 (8.1%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune120.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 7.0b

Counts

83 → 9

Compiler

Compiled 2125 to 1274 computations (40% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.5b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
9.7b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
22×	`times-frac_binary64_420`
21×	`*-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` `distribute-lft-out_binary64_367` `associate-/r*_binary64_360`
4×	`flip3-+_binary64_417` `div-inv_binary64_411` `flip-+_binary64_388`
3×	`sqrt-prod_binary64_429`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
1×	`flip3--_binary64_418` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `pow1/2_binary64_491` `flip--_binary64_389` `associate-/l/_binary64_363` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 102

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))
14.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.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)))

series916.0ms (14.6%)

Counts

4 → 12

Calls

4 calls:

371.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
299.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
129.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4940	3121
1	4940	3121

prune144.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	116	7	123

Merged error: 6.9b

Counts

123 → 7

Compiler

Compiled 3262 to 1997 computations (38.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.6b	(.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
3.6b	(.f64 (/.f64 1 a) (.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) a))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite58.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-exp-log_binary64_449`
45×	`add-cbrt-cube_binary64_447`
41×	`prod-exp_binary64_460`
23×	`cbrt-unprod_binary64_444`
19×	`pow1_binary64_472`
15×	`*-un-lft-identity_binary64_414`
14×	`associate-l_binary64_357` `add-sqr-sqrt_binary64_435`
13×	`add-cube-cbrt_binary64_446` `div-exp_binary64_462`
9×	`times-frac_binary64_420` `pow-prod-down_binary64_482`
7×	`cbrt-undiv_binary64_445`
6×	`add-log-exp_binary64_450`
4×	`1-exp_binary64_455` `associate-l/_binary64_359` `rec-exp_binary64_461` `associate-r_binary64_356` `associate-r/_binary64_358`
3×	`sqrt-prod_binary64_429`
2×	`sqrt-div_binary64_430` `*-commutative_binary64_347`
1×	`flip3--_binary64_418` `flip3-+_binary64_417` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `flip-+_binary64_388` `distribute-lft-out_binary64_367` `pow1/2_binary64_491` `flip--_binary64_389` `frac-times_binary64_424` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 100

Calls

4 calls:

21.0ms	(.f64 (/.f64 1 a) (.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) a))
14.0ms	(.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
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)))

series945.0ms (15%)

Counts

4 → 12

Calls

4 calls:

407.0ms	(.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
309.0ms	(.f64 (/.f64 1 a) (.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) a))
117.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify95.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4919	2753
1	4919	2753

prune129.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	112	7	119

Merged error: 6.9b

Counts

119 → 7

Compiler

Compiled 2815 to 1724 computations (38.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_435`
10×	`*-un-lft-identity_binary64_414`
8×	`sqrt-prod_binary64_429` `add-log-exp_binary64_450`
6×	`pow1_binary64_472` `add-cube-cbrt_binary64_446`
4×	`flip3--_binary64_418` `sqrt-div_binary64_430` `difference-of-squares_binary64_383` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `flip--_binary64_389`
2×	`distribute-lft-out--_binary64_368` `diff-log_binary64_503` `sqrt-pow1_binary64_431` `sub-neg_binary64_407` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(-.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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series478.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
116.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4838	1536
1	4838	1536

prune109.0ms (1.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	70	7	77

Merged error: 6.9b

Counts

77 → 7

Compiler

Compiled 2644 to 1563 computations (40.9% saved)

regimes148.0ms (2.4%)

Compiler: Compiled 477 to 360 computations (24.5% saved)

bsearch93.0ms (1.5%)

Steps

Iters	Range		Point
8	5.047843856159705e+79	3.275486995190224e+82	4.1764143448038173e+80
7	5.04859006045966e-282	4.3005727715627705e-280	5.135816095786639e-282
8	-1.6249009059312762e+154	-3.534796202621665e+151	-2.598568989113781e+152

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	91
1	108	91

end0.0ms (0%)

sample1.4s (21.8%)

Algorithm

1×

intervals

Results

282.0ms	1134×	body	2048	valid
268.0ms	5060×	body	128	valid
155.0ms	792×	body	1024	valid
127.0ms	417×	body	4096	valid
60.0ms	403×	body	512	valid
32.0ms	666×	body	128	nan
19.0ms	380×	body	128	invalid
19.0ms	194×	body	256	valid

Compiler

Compiled 236 to 171 computations (27.5% saved)

Details

analyze459.0ms (7.3%)

sample38.0ms (0.6%)

simplify221.0ms (3.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series512.0ms (8.1%)

simplify97.0ms (1.5%)

prune120.0ms (1.9%)

localize15.0ms (0.2%)

rewrite54.0ms (0.9%)

series916.0ms (14.6%)

simplify86.0ms (1.4%)

prune144.0ms (2.3%)

localize15.0ms (0.2%)

rewrite58.0ms (0.9%)

series945.0ms (15%)

simplify95.0ms (1.5%)

prune129.0ms (2%)

localize13.0ms (0.2%)

rewrite33.0ms (0.5%)

series478.0ms (7.6%)

simplify88.0ms (1.4%)

prune109.0ms (1.7%)

regimes148.0ms (2.4%)

bsearch93.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (21.8%)

Profiling