Details

analyze5.0ms (0%)

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)

sample28.0ms (0.2%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify325.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (227.0ms)

Iter	Nodes	Cost
0	5023	37

prune5.0ms (0%)

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: 1.5b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize12.0ms (0.1%)

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)))
8.3b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.0b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite106.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1783`
34×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `distribute-lft-out_binary64_1734`
24×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
21×	`add-sqr-sqrt_binary64_1805` `associate-r_binary64_1723`
18×	`associate-/r/_binary64_1729`
16×	`frac-times_binary64_1793`
15×	`add-cube-cbrt_binary64_1818`
14×	`times-frac_binary64_1789`
13×	`pow1_binary64_1844`
11×	`swap-sqr_binary64_1750`
10×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `associate-*l/_binary64_1726` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
9×	`associate-l_binary64_1724`
8×	`associate-*r/_binary64_1725`
7×	`associate-/l/_binary64_1730`
6×	`associate-/r*_binary64_1727`
5×	`associate-/l*_binary64_1728`
4×	`add-log-exp_binary64_1822`
3×	`div-inv_binary64_1780` `unswap-sqr_binary64_1751`
2×	`*-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow-prod-down_binary64_1854`
1×	`distribute-lft-in_binary64_1732` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `distribute-rgt-in_binary64_1733` `pow2_binary64_1864`

Counts

4 → 158

Calls

4 calls:

32.0ms	(/.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)))
24.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
17.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
15.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series254.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(/.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)))
89.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
47.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
18.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify89.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4964	3959
1	4964	3959

prune286.0ms (2%)

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 5240 to 3402 computations (35.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite110.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64_1783`
89×	`times-frac_binary64_1789`
82×	`distribute-lft-out_binary64_1734`
60×	`add-sqr-sqrt_binary64_1805`
48×	`add-cube-cbrt_binary64_1818`
38×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
26×	`associate-l_binary64_1724` `associate-r_binary64_1723`
15×	`associate-/r*_binary64_1727` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
10×	`associate-/r/_binary64_1729`
9×	`associate-/l*_binary64_1728`
8×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
7×	`associate-/l/_binary64_1730` `flip-+_binary64_1757` `flip3-+_binary64_1786`
6×	`pow1_binary64_1844`
5×	`div-inv_binary64_1780`
4×	`unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`associate-r/_binary64_1725` `associate-l/_binary64_1726` `frac-times_binary64_1793`
1×	`*-commutative_binary64_1714` `pow-prod-down_binary64_1854`

Counts

4 → 202

Calls

4 calls:

34.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
28.0ms	(/.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)))
14.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
10.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))

series248.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.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)))
88.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
25.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
24.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))

simplify105.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4954	5499
1	4954	5499

prune322.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	214	7	221

Merged error: 0b

Counts

221 → 7

Compiler

Compiled 7003 to 4432 computations (36.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.1b	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
0.1b	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.5b	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

rewrite341.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

1158×	`*-un-lft-identity_binary64_1783`
821×	`times-frac_binary64_1789`
492×	`distribute-lft-out_binary64_1734`
343×	`add-sqr-sqrt_binary64_1805`
306×	`add-cube-cbrt_binary64_1818`
279×	`sqrt-prod_binary64_1799`
214×	`associate-l_binary64_1724`
61×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
44×	`associate-/r/_binary64_1729`
31×	`associate-/l*_binary64_1728`
29×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
26×	`associate-r_binary64_1723`
23×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
22×	`div-inv_binary64_1780`
21×	`associate-/r*_binary64_1727`
12×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
10×	`unswap-sqr_binary64_1751`
6×	`associate-/l/_binary64_1730` `sqrt-div_binary64_1800` `pow1_binary64_1844`
4×	`add-log-exp_binary64_1822`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`associate-r/_binary64_1725` `associate-l/_binary64_1726` `frac-times_binary64_1793`
1×	`*-commutative_binary64_1714` `pow-prod-down_binary64_1854`

Counts

4 → 624

Calls

4 calls:

128.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
53.0ms	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
23.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
13.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series273.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
94.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
44.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
26.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify252.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

636 → 636

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4995	25802
1	4995	25802

prune2.7s (18.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	636	0	636
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	636	7	643

Merged error: 0b

Counts

643 → 7

Compiler

Compiled 29821 to 19918 computations (33.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.1b	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
0.5b	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.5b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

rewrite926.0ms (6.4%)

Algorithm

1×	rewrite-expression-head

Rules

2156×	`*-un-lft-identity_binary64_1783`
1592×	`times-frac_binary64_1789`
917×	`distribute-lft-out_binary64_1734`
679×	`add-sqr-sqrt_binary64_1805`
569×	`add-cube-cbrt_binary64_1818`
550×	`sqrt-prod_binary64_1799`
214×	`associate-l_binary64_1724` `associate-r_binary64_1723`
78×	`associate-/r/_binary64_1729`
56×	`associate-/l*_binary64_1728`
52×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
40×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
39×	`div-inv_binary64_1780`
25×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `unswap-sqr_binary64_1751`
21×	`associate-/r*_binary64_1727`
9×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
8×	`sqrt-div_binary64_1800`
6×	`pow1_binary64_1844`
4×	`associate-/l/_binary64_1730` `add-log-exp_binary64_1822`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`associate-r/_binary64_1725` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `frac-times_binary64_1793` `pow-prod-down_binary64_1854`

Counts

4 → 1046

Calls

4 calls:

646.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
23.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
23.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
10.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series217.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
47.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
43.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
24.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify422.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1058 → 1058

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4969	48086
1	4969	48086

prune5.2s (35.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1058	0	1058
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	1058	7	1065

Merged error: 0b

Counts

1065 → 7

Compiler

Compiled 50602 to 33714 computations (33.4% saved)

regimes310.0ms (2.1%)

Compiler: Compiled 4263 to 3311 computations (22.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

end0.0ms (0%)

sample1.9s (13%)

Algorithm

1×

intervals

Results

491.0ms	8000×	body	128	valid
140.0ms	8000×	pre	128	true

Compiler

Compiled 1428 to 1109 computations (22.3% saved)

Details

analyze5.0ms (0%)

sample28.0ms (0.2%)

simplify325.0ms (2.2%)

prune5.0ms (0%)

localize12.0ms (0.1%)

rewrite106.0ms (0.7%)

series254.0ms (1.8%)

simplify89.0ms (0.6%)

prune286.0ms (2%)

localize15.0ms (0.1%)

rewrite110.0ms (0.8%)

series248.0ms (1.7%)

simplify105.0ms (0.7%)

prune322.0ms (2.2%)

localize15.0ms (0.1%)

rewrite341.0ms (2.4%)

series273.0ms (1.9%)

simplify252.0ms (1.7%)

prune2.7s (18.9%)

localize15.0ms (0.1%)

rewrite926.0ms (6.4%)

series217.0ms (1.5%)

simplify422.0ms (2.9%)

prune5.2s (35.8%)

regimes310.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (13%)

Profiling