Details

analyze4.0ms (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)

sample29.0ms (0.1%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify424.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (256.0ms)

Iter	Nodes	Cost
0	5111	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: 1.0b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize13.0ms (0%)

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)))
7.6b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
9.0b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))

rewrite112.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1762`
34×	`distribute-lft-out_binary64_1715` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
24×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
21×	`add-sqr-sqrt_binary64_1783` `associate-r_binary64_1704`
18×	`associate-/r/_binary64_1710`
16×	`frac-times_binary64_1772`
15×	`add-cube-cbrt_binary64_1794`
14×	`times-frac_binary64_1768`
13×	`pow1_binary64_1820`
11×	`swap-sqr_binary64_1729`
10×	`prod-exp_binary64_1808` `associate-*l/_binary64_1707` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `cbrt-unprod_binary64_1792`
9×	`associate-l_binary64_1705`
8×	`associate-*r/_binary64_1706`
7×	`associate-/l/_binary64_1711`
6×	`associate-/r*_binary64_1708`
5×	`associate-/l*_binary64_1709`
4×	`add-log-exp_binary64_1798`
3×	`div-inv_binary64_1759` `unswap-sqr_binary64_1730`
2×	`frac-2neg_binary64_1773` `pow-prod-down_binary64_1830` `clear-num_binary64_1761` `*-commutative_binary64_1695`
1×	`pow-sqr_binary64_1735` `pow-prod-up_binary64_1829` `pow-plus_binary64_1822` `distribute-rgt-in_binary64_1714` `distribute-lft-in_binary64_1713` `pow2_binary64_1840`

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)))
26.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
18.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
16.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series543.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.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)))
196.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
93.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify104.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4939	3959
1	4939	3959

prune286.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	6	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

Compiler

Compiled 5231 to 3389 computations (35.2% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite115.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64_1762`
89×	`times-frac_binary64_1768`
82×	`distribute-lft-out_binary64_1715`
60×	`add-sqr-sqrt_binary64_1783`
48×	`add-cube-cbrt_binary64_1794`
38×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
26×	`associate-l_binary64_1705` `associate-r_binary64_1704`
15×	`associate-/r*_binary64_1708` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
10×	`associate-/r/_binary64_1710`
9×	`associate-/l*_binary64_1709`
8×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
7×	`associate-/l/_binary64_1711` `flip3-+_binary64_1765` `flip-+_binary64_1736`
6×	`pow1_binary64_1820`
5×	`div-inv_binary64_1759`
4×	`unswap-sqr_binary64_1730` `add-log-exp_binary64_1798`
3×	`frac-2neg_binary64_1773` `clear-num_binary64_1761`
2×	`frac-times_binary64_1772` `associate-l/_binary64_1707` `associate-r/_binary64_1706`
1×	`pow-prod-down_binary64_1830` `*-commutative_binary64_1695`

Counts

4 → 202

Calls

4 calls:

38.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
29.0ms	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))

series497.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
173.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
51.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
50.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))

simplify79.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5289	5499

prune359.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	216	5	221

Merged error: 0.0b

Counts

221 → 5

Compiler

Compiled 6972 to 4405 computations (36.8% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite1.5s (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

15581×	`*-un-lft-identity_binary64_1762`
12730×	`times-frac_binary64_1768`
6938×	`distribute-lft-out_binary64_1715`
3552×	`add-sqr-sqrt_binary64_1783` `add-cube-cbrt_binary64_1794`
587×	`associate-/r/_binary64_1710`
308×	`div-inv_binary64_1759`
282×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
171×	`associate-/r*_binary64_1708`
39×	`associate-/l*_binary64_1709`
34×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
20×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
7×	`associate-/l/_binary64_1711`
4×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `add-log-exp_binary64_1798` `pow1_binary64_1820`

Counts

4 → 3963

Calls

4 calls:

136.0ms	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))
32.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
12.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))

series424.0ms (1%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))
92.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
52.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))
51.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify2.1s (5%)

Algorithm

1×	egg-herbie

Counts

3975 → 3975

Iterations

Useful iterations: 0 (182.0ms)

Iter	Nodes	Cost
0	5539	269388

prune31.9s (75.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	3974	1	3975
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	3975	5	3980

Merged error: 0b

Counts

3980 → 5

Compiler

Compiled 186863 to 120277 computations (35.6% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
9.0b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))

rewrite139.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

133×	`*-un-lft-identity_binary64_1762`
103×	`add-exp-log_binary64_1797`
67×	`times-frac_binary64_1768`
61×	`add-cbrt-cube_binary64_1795`
54×	`add-sqr-sqrt_binary64_1783` `distribute-lft-out_binary64_1715`
42×	`prod-exp_binary64_1808`
37×	`add-cube-cbrt_binary64_1794`
35×	`div-exp_binary64_1810`
27×	`associate-r_binary64_1704`
25×	`associate-l_binary64_1705`
22×	`cbrt-unprod_binary64_1792`
19×	`frac-times_binary64_1772` `cbrt-undiv_binary64_1793`
13×	`associate-/l/_binary64_1711` `flip3-+_binary64_1765` `flip-+_binary64_1736` `associate-*r/_binary64_1706`
11×	`associate-*l/_binary64_1707` `pow1_binary64_1820`
10×	`associate-/r*_binary64_1708`
8×	`associate-/r/_binary64_1710`
6×	`unswap-sqr_binary64_1730` `1-exp_binary64_1803` `rec-exp_binary64_1809`
5×	`associate-/l*_binary64_1709`
4×	`pow-prod-down_binary64_1830` `div-inv_binary64_1759` `add-log-exp_binary64_1798`
2×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `*-commutative_binary64_1695`

Counts

4 → 212

Calls

4 calls:

34.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
32.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
30.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))
11.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series597.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
182.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))
153.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
52.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify112.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4947	5833
1	4947	5833

prune363.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	224	5	229

Merged error: 0b

Counts

229 → 5

Compiler

Compiled 7069 to 4573 computations (35.3% saved)

regimes337.0ms (0.8%)

Compiler: Compiled 4500 to 3461 computations (23.1% 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 (4.6%)

Algorithm

1×

intervals

Results

505.0ms	8000×	body	128	valid
145.0ms	8000×	pre	128	true

Compiler

Compiled 1507 to 1159 computations (23.1% saved)

Details

analyze4.0ms (0%)

sample29.0ms (0.1%)

simplify424.0ms (1%)

prune5.0ms (0%)

localize13.0ms (0%)

rewrite112.0ms (0.3%)

series543.0ms (1.3%)

simplify104.0ms (0.2%)

prune286.0ms (0.7%)

localize13.0ms (0%)

rewrite115.0ms (0.3%)

series497.0ms (1.2%)

simplify79.0ms (0.2%)

prune359.0ms (0.9%)

localize13.0ms (0%)

rewrite1.5s (3.7%)

series424.0ms (1%)

simplify2.1s (5%)

prune31.9s (75.8%)

localize14.0ms (0%)

rewrite139.0ms (0.3%)

series597.0ms (1.4%)

simplify112.0ms (0.3%)

prune363.0ms (0.9%)

regimes337.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (4.6%)

Profiling