Details

analyze457.0ms (7.4%)

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	166×	body	128	valid
8.0ms	30×	body	2048	valid
5.0ms	24×	body	1024	valid
4.0ms	12×	body	4096	valid
2.0ms	16×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	10×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify223.0ms (3.6%)

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: 36.3b

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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (0.5%)

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-/l*_binary64_361`
3×	`sqrt-prod_binary64_429` `associate-/r*_binary64_360`
2×	`flip3--_binary64_418` `sqrt-div_binary64_430` `flip3-+_binary64_417` `flip-+_binary64_388` `flip--_binary64_389` `associate-/l/_binary64_363`
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 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series458.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
113.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5412	2012

prune127.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	9	84

Merged error: 6.5b

Counts

84 → 9

Compiler

Compiled 2178 to 1186 computations (45.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.4b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_420`
53×	`add-sqr-sqrt_binary64_435`
40×	`*-un-lft-identity_binary64_414`
28×	`add-cube-cbrt_binary64_446`
27×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
13×	`associate-/l*_binary64_361`
12×	`difference-of-squares_binary64_383`
10×	`associate-/r/_binary64_362` `cbrt-undiv_binary64_445` `div-exp_binary64_462`
9×	`sqrt-prod_binary64_429` `associate-/r*_binary64_360`
7×	`flip3--_binary64_418` `flip--_binary64_389`
6×	`distribute-lft-out--_binary64_368` `div-inv_binary64_411` `prod-exp_binary64_460` `add-log-exp_binary64_450` `cbrt-unprod_binary64_444`
5×	`pow1_binary64_472`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
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 → 127

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
13.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series925.0ms (15.1%)

Counts

4 → 12

Calls

4 calls:

415.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
330.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5440	4678

prune193.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 6.5b

Counts

148 → 8

Compiler

Compiled 4546 to 2412 computations (46.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_435`
26×	`*-un-lft-identity_binary64_414`
18×	`times-frac_binary64_420`
16×	`add-cube-cbrt_binary64_446`
10×	`difference-of-squares_binary64_383`
8×	`sqrt-prod_binary64_429` `add-log-exp_binary64_450`
6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `associate-/r*_binary64_360`
5×	`distribute-lft-out--_binary64_368` `pow1_binary64_472`
4×	`flip3--_binary64_418` `flip--_binary64_389`
3×	`associate-/l*_binary64_361`
2×	`associate-/r/_binary64_362` `sqrt-div_binary64_430` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `cbrt-undiv_binary64_445` `frac-2neg_binary64_425` `pow1/2_binary64_491` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series647.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

365.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
112.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
103.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5183	2447

prune121.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 6.5b

Counts

101 → 8

Compiler

Compiled 2819 to 1670 computations (40.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_420`
121×	`add-sqr-sqrt_binary64_435`
94×	`*-un-lft-identity_binary64_414`
68×	`add-cube-cbrt_binary64_446`
26×	`difference-of-squares_binary64_383`
22×	`associate-/r*_binary64_360`
16×	`sqrt-prod_binary64_429`
13×	`distribute-lft-out--_binary64_368`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
5×	`pow1_binary64_472` `div-inv_binary64_411`
3×	`flip3--_binary64_418` `cbrt-undiv_binary64_445` `flip--_binary64_389` `associate-/l*_binary64_361` `div-exp_binary64_462`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`associate-/r/_binary64_362` `clear-num_binary64_413` `sqrt-pow1_binary64_431` `frac-2neg_binary64_425` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 146

Calls

4 calls:

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

series565.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
125.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
67.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify104.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5045	5651

prune234.0ms (3.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	158	8	166

Merged error: 6.5b

Counts

166 → 8

Compiler

Compiled 5181 to 3004 computations (42% saved)

regimes102.0ms (1.7%)

Compiler: Compiled 474 to 378 computations (20.3% saved)

bsearch83.0ms (1.3%)

Steps

Iters	Range	Point
6	3.453198629799523e+50	2.437223188812816e+51	2.404688834790521e+51
5	1.4879601855401445e-294	4.1080958905033815e-294	3.0328686823891354e-294
8	-6.563919617033063e+159	-1.3263602242760849e+157	-1.338340640721482e+157

Iters

Range

Point

3.453198629799523e+50

2.437223188812816e+51

2.404688834790521e+51

1.4879601855401445e-294

4.1080958905033815e-294

3.0328686823891354e-294

-6.563919617033063e+159

-1.3263602242760849e+157

-1.338340640721482e+157

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	109	98
1	109	98

end0.0ms (0%)

sample1.4s (23.1%)

Algorithm

1×

intervals

Results

283.0ms	1092×	body	2048	valid
274.0ms	5243×	body	128	valid
142.0ms	719×	body	1024	valid
136.0ms	415×	body	4096	valid
54.0ms	369×	body	512	valid
36.0ms	684×	body	128	nan
20.0ms	392×	body	128	invalid
16.0ms	162×	body	256	valid

Compiler

Compiled 282 to 210 computations (25.5% saved)

Details

analyze457.0ms (7.4%)

sample38.0ms (0.6%)

simplify223.0ms (3.6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite31.0ms (0.5%)

series458.0ms (7.5%)

simplify71.0ms (1.2%)

prune127.0ms (2.1%)

localize12.0ms (0.2%)

rewrite56.0ms (0.9%)

series925.0ms (15.1%)

simplify66.0ms (1.1%)

prune193.0ms (3.2%)

localize16.0ms (0.3%)

rewrite34.0ms (0.6%)

series647.0ms (10.6%)

simplify69.0ms (1.1%)

prune121.0ms (2%)

localize13.0ms (0.2%)

rewrite51.0ms (0.8%)

series565.0ms (9.2%)

simplify104.0ms (1.7%)

prune234.0ms (3.8%)

regimes102.0ms (1.7%)

bsearch83.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (23.1%)

Profiling