Details

analyze6.0ms (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)

sample53.0ms (0.5%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify391.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (272.0ms)

Iter	Nodes	Cost
0	5023	37

prune5.0ms (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: 1.5b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize13.0ms (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)))
7.0b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.1b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite138.0ms (1.4%)

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:

39.0ms	(/.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))))
30.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
14.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series320.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.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)))
109.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
69.0ms	(/.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))

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4964	3959
1	4964	3959

prune342.0ms (3.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	158	12	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	160	12	172

Merged error: 0.0b

Counts

172 → 12

Compiler

Compiled 5408 to 3518 computations (34.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
7.0b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite253.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

826×	`*-un-lft-identity_binary64_1783`
508×	`times-frac_binary64_1789`
374×	`distribute-lft-out_binary64_1734`
191×	`add-sqr-sqrt_binary64_1805`
182×	`add-cube-cbrt_binary64_1818`
136×	`associate-r_binary64_1723`
34×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
31×	`associate-/l*_binary64_1728`
30×	`associate-/r/_binary64_1729`
20×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
15×	`div-inv_binary64_1780` `associate-/r*_binary64_1727`
14×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
8×	`associate-/l/_binary64_1730`
6×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow1_binary64_1844`
4×	`associate-l_binary64_1724` `associate-*l/_binary64_1726` `frac-times_binary64_1793` `add-log-exp_binary64_1822`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `unswap-sqr_binary64_1751`
2×	`associate-*r/_binary64_1725`
1×	`*-commutative_binary64_1714` `pow-prod-down_binary64_1854`

Counts

4 → 422

Calls

4 calls:

65.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
43.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
21.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
16.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

series465.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

285.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
100.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
49.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
30.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

simplify157.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5106	12598

prune1.3s (13.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	430	4	434
Fresh	7	4	11
Picked	0	1	1
Done	0	0	0
Total	437	9	446

Merged error: 0b

Counts

446 → 9

Compiler

Compiled 15548 to 9835 computations (36.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite162.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`*-un-lft-identity_binary64_1783`
110×	`times-frac_binary64_1789`
92×	`distribute-lft-out_binary64_1734`
68×	`sqrt-prod_binary64_1799`
64×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
58×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
41×	`associate-r_binary64_1723`
20×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
19×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
18×	`frac-times_binary64_1793`
15×	`associate-/l/_binary64_1730` `associate-/l_binary64_1728` `associate-/r_binary64_1727`
14×	`flip-+_binary64_1757` `associate-*l/_binary64_1726` `flip3-+_binary64_1786`
10×	`associate-*r/_binary64_1725`
9×	`pow1_binary64_1844`
8×	`associate-/r/_binary64_1729`
4×	`div-inv_binary64_1780` `sqrt-div_binary64_1800` `add-log-exp_binary64_1822`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow-prod-down_binary64_1854`
1×	`associate-l_binary64_1724` `*-commutative_binary64_1714`

Counts

4 → 249

Calls

4 calls:

40.0ms	(/.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (+.f64 1 alpha)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
36.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (+.f64 1 alpha)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
23.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
13.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

series302.0ms (3%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(/.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (+.f64 1 alpha)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
90.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (+.f64 1 alpha)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
31.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

simplify151.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4958	7229
1	4958	7229

prune667.0ms (6.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	261	9	270

Merged error: 0b

Counts

270 → 9

Compiler

Compiled 9677 to 6438 computations (33.5% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.6b	(/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
2.7b	(*.f64 (/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite414.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

892×	`*-un-lft-identity_binary64_1783`
567×	`times-frac_binary64_1789`
396×	`distribute-lft-out_binary64_1734`
241×	`add-sqr-sqrt_binary64_1805`
208×	`add-cube-cbrt_binary64_1818`
136×	`associate-r_binary64_1723`
61×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
58×	`sqrt-prod_binary64_1799`
38×	`associate-l_binary64_1724`
32×	`associate-/r/_binary64_1729`
31×	`associate-/l*_binary64_1728`
29×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
21×	`associate-/r*_binary64_1727`
17×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
16×	`div-inv_binary64_1780`
12×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
9×	`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 → 491

Calls

4 calls:

186.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
78.0ms	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
31.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
20.0ms	(/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

series386.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
112.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
78.0ms	(/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
52.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

simplify263.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4965	17926
1	4965	17926

prune1.7s (17.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	503	0	503
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	503	9	512

Merged error: 0b

Counts

512 → 9

Compiler

Compiled 21847 to 14334 computations (34.4% saved)

regimes349.0ms (3.5%)

Compiler: Compiled 4449 to 3431 computations (22.9% 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%)

sample2.0s (19.6%)

Algorithm

1×

intervals

Results

490.0ms	8000×	body	128	valid
147.0ms	8000×	pre	128	true

Compiler

Compiled 1490 to 1149 computations (22.9% saved)

Details

analyze6.0ms (0.1%)

sample53.0ms (0.5%)

simplify391.0ms (3.9%)

prune5.0ms (0.1%)

localize13.0ms (0.1%)

rewrite138.0ms (1.4%)

series320.0ms (3.2%)

simplify88.0ms (0.9%)

prune342.0ms (3.4%)

localize17.0ms (0.2%)

rewrite253.0ms (2.5%)

series465.0ms (4.6%)

simplify157.0ms (1.6%)

prune1.3s (13.4%)

localize18.0ms (0.2%)

rewrite162.0ms (1.6%)

series302.0ms (3%)

simplify151.0ms (1.5%)

prune667.0ms (6.6%)

localize26.0ms (0.3%)

rewrite414.0ms (4.1%)

series386.0ms (3.8%)

simplify263.0ms (2.6%)

prune1.7s (17.4%)

regimes349.0ms (3.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (19.6%)

Profiling