Details

analyze4.0ms (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)

sample29.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify331.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (232.0ms)

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

Error

1.3b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize14.0ms (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)))
7.5b	(.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)))

rewrite107.0ms (1.6%)

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:

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)))
24.0ms	(.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)))
15.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series276.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(/.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)))
101.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
50.0ms	(/.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))

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4964	3959
1	4964	3959

prune278.0ms (4.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	162	8	170
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	162	10	172

Error

0.0b

Counts

172 → 10

Compiler

Compiled 5306 to 3446 computations (35.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite109.0ms (1.6%)

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:

37.0ms	(*.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)))
10.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
10.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

series254.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.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)))
91.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
28.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
25.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))

simplify107.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4954	5499
1	4954	5499

prune389.0ms (5.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	4	4	8
Picked	1	0	1
Done	1	0	1
Total	216	8	224

Error

0.0b

Counts

224 → 8

Compiler

Compiled 7076 to 4485 computations (36.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite185.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

442×	`*-un-lft-identity_binary64_1783`
358×	`times-frac_binary64_1789`
184×	`add-sqr-sqrt_binary64_1805`
163×	`distribute-lft-out_binary64_1734`
151×	`add-cube-cbrt_binary64_1818`
123×	`add-exp-log_binary64_1821`
83×	`associate-l_binary64_1724`
65×	`div-exp_binary64_1834`
61×	`add-cbrt-cube_binary64_1819`
35×	`associate-/r*_binary64_1727`
29×	`cbrt-undiv_binary64_1817`
28×	`prod-exp_binary64_1832`
26×	`associate-r_binary64_1723`
22×	`associate-/r/_binary64_1729`
12×	`cbrt-unprod_binary64_1816` `div-inv_binary64_1780`
11×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
10×	`1-exp_binary64_1827` `unswap-sqr_binary64_1751` `rec-exp_binary64_1833`
9×	`associate-/l*_binary64_1728`
7×	`pow1_binary64_1844`
5×	`associate-/l/_binary64_1730`
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×	`inv-pow_binary64_1868` `pow-flip_binary64_1857` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854`

Counts

4 → 372

Calls

4 calls:

64.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
37.0ms	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
14.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 alpha)))
12.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 alpha))

series250.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
96.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
24.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 alpha)))
20.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 alpha))

simplify150.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

384 → 384

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5055	10763

prune911.0ms (13.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	383	1	384
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	385	7	392

Error

0.0b

Counts

392 → 7

Compiler

Compiled 13600 to 8912 computations (34.5% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite102.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

206×	`add-exp-log_binary64_1821`
101×	`div-exp_binary64_1834`
72×	`prod-exp_binary64_1832`
62×	`add-cbrt-cube_binary64_1819`
56×	`*-un-lft-identity_binary64_1783`
34×	`times-frac_binary64_1789`
33×	`add-sqr-sqrt_binary64_1805`
27×	`cbrt-undiv_binary64_1817`
26×	`add-cube-cbrt_binary64_1818` `1-exp_binary64_1827` `rec-exp_binary64_1833`
18×	`associate-r_binary64_1723`
16×	`distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816`
12×	`associate-/r/_binary64_1729`
10×	`associate-/r*_binary64_1727` `pow1_binary64_1844`
7×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `flip3-+_binary64_1786`
5×	`associate-l_binary64_1724` `associate-*l/_binary64_1726` `frac-times_binary64_1793`
4×	`div-inv_binary64_1780` `add-log-exp_binary64_1822`
3×	`associate-*r/_binary64_1725` `associate-/l/_binary64_1730` `pow-flip_binary64_1857` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `unswap-sqr_binary64_1751`
2×	`un-div-inv_binary64_1781` `inv-pow_binary64_1868` `pow-prod-down_binary64_1854`
1×	`*-commutative_binary64_1714`

Counts

4 → 196

Calls

4 calls:

35.0ms	(/.f64 (.f64 (/.f64 1 (.f64 (+.f64 (+.f64 alpha beta) 2) (/.f64 1 (+.f64 alpha 1)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
17.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (/.f64 1 (+.f64 alpha 1)))
14.0ms	(/.f64 1 (*.f64 (+.f64 (+.f64 alpha beta) 2) (/.f64 1 (+.f64 alpha 1))))
6.0ms	(/.f64 1 (+.f64 alpha 1))

series169.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(/.f64 (.f64 (/.f64 1 (.f64 (+.f64 (+.f64 alpha beta) 2) (/.f64 1 (+.f64 alpha 1)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
25.0ms	(/.f64 1 (*.f64 (+.f64 (+.f64 alpha beta) 2) (/.f64 1 (+.f64 alpha 1))))
21.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (/.f64 1 (+.f64 alpha 1)))
11.0ms	(/.f64 1 (+.f64 alpha 1))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5118	4556

prune493.0ms (7.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	208	7	215

Error

0.0b

Counts

215 → 7

Compiler

Compiled 6439 to 4181 computations (35.1% saved)

regimes340.0ms (5%)

Accuracy

Total 0.1b remaining (93.6%)

Threshold costs 0.1b (93.6%)

Compiler

Compiled 4671 to 3617 computations (22.6% 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 (30.2%)

Algorithm

1×

intervals

Results

534.0ms	8000×	body	128	valid
147.0ms	8000×	pre	128	true

Compiler

Compiled 1564 to 1211 computations (22.6% saved)

Details

analyze4.0ms (0.1%)

sample29.0ms (0.4%)

simplify331.0ms (4.9%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

rewrite107.0ms (1.6%)

series276.0ms (4.1%)

simplify91.0ms (1.3%)

prune278.0ms (4.1%)

localize15.0ms (0.2%)

rewrite109.0ms (1.6%)

series254.0ms (3.8%)

simplify107.0ms (1.6%)

prune389.0ms (5.8%)

localize15.0ms (0.2%)

rewrite185.0ms (2.7%)

series250.0ms (3.7%)

simplify150.0ms (2.2%)

prune911.0ms (13.5%)

localize19.0ms (0.3%)

rewrite102.0ms (1.5%)

series169.0ms (2.5%)

simplify76.0ms (1.1%)

prune493.0ms (7.3%)

regimes340.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (30.2%)

Profiling