Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample34.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify273.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (266.0ms)

Iter	Nodes	Cost
0	5110	37

prune8.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 1.2b

Counts

2 → 2

Compiler

Compiled 145 to 102 computations (29.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
5.7b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.7b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite119.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
34×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`flip3-+_binary64` `flip-+_binary64`
21×	`associate-r_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r/_binary64`
16×	`frac-times_binary64`
15×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`
13×	`pow1_binary64`
11×	`swap-sqr_binary64`
10×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
9×	`associate-l_binary64`
8×	`associate-*r/_binary64`
7×	`associate-/l/_binary64`
6×	`associate-/r*_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`unswap-sqr_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 158

Calls

4 calls:

31.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
31.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
19.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
17.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series535.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
179.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
105.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
33.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4981	3959
1	4981	3959

prune694.0ms (9.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	7	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

Compiler

Compiled 14314 to 10205 computations (28.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
0.0b	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

rewrite121.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64`
89×	`times-frac_binary64`
82×	`distribute-lft-out_binary64`
60×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`
38×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`associate-r_binary64` `associate-l_binary64`
15×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
10×	`associate-/r/_binary64`
9×	`associate-/l*_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 202

Calls

4 calls:

37.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
13.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))

series536.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
192.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
62.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
55.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4952	5499
1	4952	5499

prune589.0ms (7.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	214	7	221

Merged error: 0b

Counts

221 → 7

Compiler

Compiled 9153 to 6006 computations (34.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
0.1b	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))

rewrite246.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

899×	`*-un-lft-identity_binary64`
549×	`times-frac_binary64`
405×	`distribute-lft-out_binary64`
221×	`add-sqr-sqrt_binary64`
200×	`add-cube-cbrt_binary64`
136×	`associate-r_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
32×	`associate-/r/_binary64`
26×	`associate-l_binary64`
18×	`flip3-+_binary64` `flip-+_binary64`
16×	`div-inv_binary64`
15×	`associate-/r*_binary64`
14×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow1_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
5×	`associate-/l/_binary64`
4×	`add-log-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 460

Calls

4 calls:

112.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))
23.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))

series454.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3))))
108.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 alpha (+.f64 beta 3)))
59.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))
52.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify187.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

472 → 472

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4971	15573
1	4971	15573

prune1.2s (15.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	472	0	472
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	472	7	479

Merged error: 0b

Counts

479 → 7

Compiler

Compiled 17678 to 11297 computations (36.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))))
0.2b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)))))

rewrite124.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`*-un-lft-identity_binary64`
101×	`times-frac_binary64`
70×	`add-exp-log_binary64`
60×	`distribute-lft-out_binary64`
51×	`add-cbrt-cube_binary64`
49×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
35×	`div-exp_binary64`
26×	`cbrt-undiv_binary64`
23×	`associate-/r*_binary64`
20×	`associate-/r/_binary64`
16×	`associate-/l*_binary64`
12×	`prod-exp_binary64`
8×	`cbrt-unprod_binary64` `div-inv_binary64`
6×	`associate-/l/_binary64` `rec-exp_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `associate-r/_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64`
4×	`add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 208

Calls

4 calls:

35.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)))))
32.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))))
12.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series520.0ms (7%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)))))
187.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))))
62.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
49.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2))

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4946	6833
1	4946	6833

prune429.0ms (5.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	220	7	227

Merged error: 0b

Counts

227 → 7

Compiler

Compiled 8088 to 5302 computations (34.4% saved)

regimes45.0ms (0.6%)

Compiler: Compiled 512 to 378 computations (26.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	37
1	23	37

end0.0ms (0%)

sample1.0s (13.9%)

Algorithm

1×

intervals

Results

501.0ms	8000×	body	128	valid
152.0ms	8000×	pre	128	true

Compiler

Compiled 321 to 234 computations (27.1% saved)

Details

analyze5.0ms (0.1%)

sample34.0ms (0.5%)

simplify273.0ms (3.7%)

prune8.0ms (0.1%)

localize12.0ms (0.2%)

rewrite119.0ms (1.6%)

series535.0ms (7.2%)

simplify84.0ms (1.1%)

prune694.0ms (9.3%)

localize15.0ms (0.2%)

rewrite121.0ms (1.6%)

series536.0ms (7.2%)

simplify102.0ms (1.4%)

prune589.0ms (7.9%)

localize15.0ms (0.2%)

rewrite246.0ms (3.3%)

series454.0ms (6.1%)

simplify187.0ms (2.5%)

prune1.2s (15.5%)

localize16.0ms (0.2%)

rewrite124.0ms (1.7%)

series520.0ms (7%)

simplify102.0ms (1.4%)

prune429.0ms (5.8%)

regimes45.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (13.9%)

Profiling