Details

analyze48.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample112.0ms (0.1%)

Algorithm

1×

intervals

Results

40.0ms	195×	body	128	valid
19.0ms	256×	pre	128	true
11.0ms	28×	body	1024	valid
5.0ms	22×	body	512	valid
1.0ms	10×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify813.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (542.0ms)

Iter	Nodes	Cost
0	5018	19

prune11.0ms (0%)

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: 15.2b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize17.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.7b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite64.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_760`
26×	`add-sqr-sqrt_binary64_782`
25×	`times-frac_binary64_766`
19×	`distribute-lft-out_binary64_711`
14×	`add-cube-cbrt_binary64_795`
6×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712`
5×	`associate-/r_binary64_704` `associate-/l_binary64_705`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
2×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `div-sub_binary64_765` `pow1_binary64_821`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-+l-_binary64_695` `div-exp_binary64_811` `clear-num_binary64_759` `flip--_binary64_735` `flip3--_binary64_764`

Counts

2 → 65

Calls

2 calls:

34.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
20.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series269.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

142.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
127.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify193.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	6172	1488

prune958.0ms (0.9%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	38	33	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	34	72

Merged error: 14.5b

Counts

72 → 34

Compiler

Compiled 2286 to 1363 computations (40.4% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
1.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite223.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64_760`
54×	`add-sqr-sqrt_binary64_782`
37×	`times-frac_binary64_766`
27×	`add-cube-cbrt_binary64_795`
24×	`distribute-lft-out_binary64_711`
16×	`cancel-sign-sub-inv_binary64_726`
11×	`add-log-exp_binary64_799`
10×	`associate-/r*_binary64_704` `difference-of-squares_binary64_729`
8×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
6×	`associate-/l*_binary64_705`
5×	`distribute-lft-out--_binary64_712`
4×	`diff-log_binary64_852` `associate-/r/_binary64_706` `difference-of-sqr-1_binary64_730` `associate--r+_binary64_696` `pow1_binary64_821`
3×	`sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`
2×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734` `frac-sub_binary64_769` `div-exp_binary64_811` `clear-num_binary64_759`
1×	`associate--r-_binary64_699`

Counts

4 → 128

Calls

4 calls:

107.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
28.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
23.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
15.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

series542.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
164.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
102.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
101.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify261.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4935	2917
1	4935	2917

prune2.6s (2.5%)

Pruning

87 alts after pruning (85 fresh and 2 done)

	Pruned	Kept	Total
New	78	62	140
Fresh	9	23	32
Picked	0	1	1
Done	0	1	1
Total	87	87	174

Merged error: 3.3b

Counts

174 → 87

Compiler

Compiled 6199 to 3933 computations (36.6% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.3b	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha))
1.7b	(-.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)) 1)

rewrite183.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`*-un-lft-identity_binary64_760`
165×	`times-frac_binary64_766`
113×	`add-sqr-sqrt_binary64_782`
81×	`add-cube-cbrt_binary64_795`
60×	`distribute-lft-out_binary64_711`
27×	`associate-/r*_binary64_704`
19×	`add-exp-log_binary64_798`
13×	`add-cbrt-cube_binary64_796`
11×	`associate-/l*_binary64_705`
10×	`difference-of-squares_binary64_729`
9×	`div-exp_binary64_811`
8×	`div-inv_binary64_757`
6×	`add-log-exp_binary64_799`
5×	`cbrt-undiv_binary64_794` `difference-of-sqr-1_binary64_730` `pow1_binary64_821`
3×	`frac-2neg_binary64_771` `associate-/r/_binary64_706` `cancel-sign-sub-inv_binary64_726` `clear-num_binary64_759`
2×	`flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `distribute-lft-out--_binary64_712` `rec-exp_binary64_810` `1-exp_binary64_804`
1×	`diff-log_binary64_852` `inv-pow_binary64_845` `sub-neg_binary64_753` `flip--_binary64_735` `pow-flip_binary64_834` `flip3--_binary64_764`

Counts

4 → 205

Calls

4 calls:

82.0ms	(-.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)) 1)
21.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha))
15.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
15.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)

series529.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
166.0ms	(-.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)) 1)
107.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha))
45.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)

simplify213.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4942	4159
1	4942	4159

prune4.6s (4.4%)

Pruning

129 alts after pruning (126 fresh and 3 done)

	Pruned	Kept	Total
New	167	50	217
Fresh	8	76	84
Picked	0	1	1
Done	0	2	2
Total	175	129	304

Merged error: 3.3b

Counts

304 → 129

Compiler

Compiled 10002 to 6433 computations (35.7% saved)

localize98.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)
0.0b	(/.f64 (neg.f64 beta) (-.f64 -2 (+.f64 alpha beta)))
0.3b	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha))
1.7b	(-.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)) 1)

rewrite398.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

252×	`*-un-lft-identity_binary64_760`
210×	`times-frac_binary64_766`
157×	`add-sqr-sqrt_binary64_782`
103×	`add-cube-cbrt_binary64_795`
59×	`distribute-lft-out_binary64_711`
28×	`associate-/r*_binary64_704`
24×	`distribute-lft-out--_binary64_712`
21×	`distribute-lft-neg-in_binary64_717` `difference-of-squares_binary64_729` `distribute-rgt-neg-in_binary64_718`
19×	`add-exp-log_binary64_798`
18×	`associate-/l*_binary64_705`
13×	`add-cbrt-cube_binary64_796`
9×	`div-exp_binary64_811`
8×	`div-inv_binary64_757`
7×	`neg-mul-1_binary64_756`
6×	`add-log-exp_binary64_799`
5×	`cbrt-undiv_binary64_794` `difference-of-sqr-1_binary64_730` `pow1_binary64_821`
3×	`frac-2neg_binary64_771` `associate-/r/_binary64_706` `cancel-sign-sub-inv_binary64_726` `clear-num_binary64_759`
2×	`associate-/l/_binary64_707` `rec-exp_binary64_810` `1-exp_binary64_804` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `flip3-+_binary64_763` `distribute-frac-neg_binary64_723` `neg-sub0_binary64_755` `inv-pow_binary64_845` `flip-+_binary64_734` `div-sub_binary64_765` `sub-neg_binary64_753` `pow-flip_binary64_834`

Counts

4 → 260

Calls

4 calls:

143.0ms	(-.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)) 1)
55.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha))
39.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)
37.0ms	(/.f64 (neg.f64 beta) (-.f64 -2 (+.f64 alpha beta)))

series411.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(/.f64 (neg.f64 beta) (-.f64 -2 (+.f64 alpha beta)))
112.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha))
107.0ms	(-.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)) 1)
72.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) alpha)

simplify561.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 0 (269.0ms)

Iter	Nodes	Cost
0	4966	5545
1	4966	5545

prune6.7s (6.5%)

Pruning

173 alts after pruning (169 fresh and 4 done)

	Pruned	Kept	Total
New	214	58	272
Fresh	14	111	125
Picked	0	1	1
Done	0	3	3
Total	228	173	401

Merged error: 3.3b

Counts

401 → 173

Compiler

Compiled 7964 to 4613 computations (42.1% saved)

regimes11.5s (11.1%)

Compiler: Compiled 51949 to 37570 computations (27.7% saved)

bsearch43.4s (42.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify50.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	260	86
1	260	86

end0.0ms (0%)

sample28.3s (27.5%)

Algorithm

1×

intervals

Results

401.0ms	5930×	body	128	valid
297.0ms	1053×	body	1024	valid
270.0ms	8000×	pre	128	true
111.0ms	581×	body	512	valid
44.0ms	329×	body	256	valid
38.0ms	107×	body	2048	valid

Compiler

Compiled 11086 to 7977 computations (28% saved)

Pareto

0.586956588195476

Details

analyze48.0ms (0%)

sample112.0ms (0.1%)

simplify813.0ms (0.8%)

prune11.0ms (0%)

localize17.0ms (0%)

rewrite64.0ms (0.1%)

series269.0ms (0.3%)

simplify193.0ms (0.2%)

prune958.0ms (0.9%)

localize28.0ms (0%)

rewrite223.0ms (0.2%)

series542.0ms (0.5%)

simplify261.0ms (0.3%)

prune2.6s (2.5%)

localize59.0ms (0.1%)

rewrite183.0ms (0.2%)

series529.0ms (0.5%)

simplify213.0ms (0.2%)

prune4.6s (4.4%)

localize98.0ms (0.1%)

rewrite398.0ms (0.4%)

series411.0ms (0.4%)

simplify561.0ms (0.5%)

prune6.7s (6.5%)

regimes11.5s (11.1%)

bsearch43.4s (42.1%)

simplify50.0ms (0%)

end0.0ms (0%)

sample28.3s (27.5%)

Profiling