Details

analyze248.0ms (0.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5646	316
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Symmetry

(sort alpha beta)

Compiler

Compiled 63 to 34 computations (46% saved)

sample56.0ms (0.1%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5395	79

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

54.7b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
40.1b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
46.2b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite1.2s (3%)

Algorithm

1×	rewrite-expression-head

Error

40.7b

Rules

86×	`times-frac_binary64_1789`
66×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/r/_binary64_1729`
61×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
46×	`add-sqr-sqrt_binary64_1805`
44×	`*-un-lft-identity_binary64_1783` `frac-times_binary64_1793`
34×	`associate-*r/_binary64_1725`
30×	`add-cube-cbrt_binary64_1818`
28×	`difference-of-squares_binary64_1752`
22×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-*l/_binary64_1726`
19×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
16×	`pow1_binary64_1844`
14×	`associate-/l*_binary64_1728` `difference-of-sqr-1_binary64_1753`
9×	`div-inv_binary64_1780` `associate-/l/_binary64_1730`
7×	`associate-/r*_binary64_1727`
6×	`associate-r_binary64_1723`
4×	`add-log-exp_binary64_1822` `pow-prod-down_binary64_1854` `associate-l_binary64_1724`
3×	`swap-sqr_binary64_1750`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `*-commutative_binary64_1714`
1×	`flip3--_binary64_1787` `flip--_binary64_1758` `pow2_binary64_1864` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `pow-sqr_binary64_1756` `unswap-sqr_binary64_1751`

Counts

4 → 228

Calls

4 calls:

58.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
27.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
18.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

Compiler

Compiled 19221 to 7168 computations (62.7% saved)

series12.1s (30.3%)

Error

10.5b

Counts

4 → 82

Calls

4 calls:

10.2s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
659.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
528.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
316.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 23053 to 15464 computations (32.9% saved)

simplify238.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5545	24303

prune1.3s (3.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	304	6	310
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	305	6	311

Error

8.8b

Counts

311 → 6

Compiler

Compiled 23539 to 10347 computations (56% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

8.8b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 8.8b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune10.0ms (0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	0	0
Total	6	6

Error

8.8b

Counts

6 → 6

Compiler

Compiled 231 to 139 computations (39.8% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
37.4b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
38.1b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite2.6s (6.6%)

Algorithm

1×	rewrite-expression-head

Error

8.8b

Rules

437×	`*-un-lft-identity_binary64_1783`
409×	`times-frac_binary64_1789`
235×	`add-sqr-sqrt_binary64_1805`
150×	`associate-r_binary64_1723`
142×	`add-cube-cbrt_binary64_1818`
122×	`distribute-lft-out_binary64_1734`
74×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
56×	`associate-l_binary64_1724`
48×	`associate-/r/_binary64_1729`
36×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
35×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
25×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
24×	`div-inv_binary64_1780`
18×	`difference-of-sqr-1_binary64_1753`
17×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
14×	`associate-/l*_binary64_1728`
13×	`associate-/r*_binary64_1727`
6×	`pow1_binary64_1844` `unswap-sqr_binary64_1751`
5×	`associate-/l/_binary64_1730`
4×	`add-log-exp_binary64_1822`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-*r/_binary64_1725`
1×	`pow-prod-down_binary64_1854` `frac-times_binary64_1793` `associate-l/_binary64_1726` `flip3--_binary64_1787` `flip--_binary64_1758` `-commutative_binary64_1714`

Counts

4 → 394

Calls

4 calls:

200.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
30.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
23.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
19.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 32200 to 15467 computations (52% saved)

series9.7s (24.3%)

Error

8.1b

Counts

4 → 66

Calls

4 calls:

8.1s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
791.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
291.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
197.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 20776 to 14299 computations (31.2% saved)

simplify389.0ms (1%)

Algorithm

1×	egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5379	33092

prune2.6s (6.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	456	4	460
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	458	8	466

Error

8.1b

Counts

466 → 8

Compiler

Compiled 35807 to 17560 computations (51% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha)))) (/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
37.4b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
38.0b	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha))))
38.0b	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha))))

rewrite467.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

8.1b

Rules

43×	`add-sqr-sqrt_binary64_1805`
41×	`*-un-lft-identity_binary64_1783`
32×	`times-frac_binary64_1789`
30×	`associate-r_binary64_1723`
26×	`sqrt-prod_binary64_1799`
25×	`add-cube-cbrt_binary64_1818`
14×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
8×	`pow1_binary64_1844` `sqrt-div_binary64_1800` `distribute-lft-out_binary64_1734`
7×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
6×	`unswap-sqr_binary64_1751` `associate-l_binary64_1724`
4×	`add-log-exp_binary64_1822` `associate-/r/_binary64_1729` `associate-/r*_binary64_1727`
3×	`prod-exp_binary64_1832` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `cbrt-unprod_binary64_1816` `associate-*r/_binary64_1725`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `div-inv_binary64_1780` `associate-/l/_binary64_1730` `frac-times_binary64_1793` `associate-*l/_binary64_1726`
1×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-/l_binary64_1728` `pow-prod-down_binary64_1854` `-commutative_binary64_1714`

Counts

4 → 117

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha)))) (/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
18.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
4.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha))))
4.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha))))

Compiler

Compiled 10255 to 3696 computations (64% saved)

series982.0ms (2.5%)

Error

8.1b

Counts

4 → 55

Calls

4 calls:

273.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha)))) (/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
202.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
196.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha))))
195.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 i beta) alpha))))

Compiler

Compiled 10382 to 6097 computations (41.3% saved)

simplify105.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5010	4213

prune413.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	172	8	180

Error

8.1b

Counts

180 → 8

Compiler

Compiled 12081 to 5027 computations (58.4% saved)

regimes1.6s (4.1%)

Accuracy

Total 3.5b remaining (31.7%)

Threshold costs 0b (0%)

Compiler

Compiled 21524 to 12193 computations (43.4% saved)

bsearch51.0ms (0.1%)

Steps

Iters	Range		Point
7	1.7314361485825164e+121	2.882623618781556e+123	2.3338299766876374e+122

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify20.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	77
1	43	77

Compiler

Compiled 104 to 70 computations (32.7% saved)

end0.0ms (0%)

sample5.6s (13.9%)

Algorithm

1×

intervals

Results

905.0ms	8000×	body	128	valid
241.0ms	8000×	pre	128	true

Compiler

Compiled 5428 to 3081 computations (43.2% saved)

Details

analyze248.0ms (0.6%)

sample56.0ms (0.1%)

simplify64.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0%)

rewrite1.2s (3%)

series12.1s (30.3%)

simplify238.0ms (0.6%)

prune1.3s (3.3%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune10.0ms (0%)

localize38.0ms (0.1%)

rewrite2.6s (6.6%)

series9.7s (24.3%)

simplify389.0ms (1%)

prune2.6s (6.6%)

localize38.0ms (0.1%)

rewrite467.0ms (1.2%)

series982.0ms (2.5%)

simplify105.0ms (0.3%)

prune413.0ms (1%)

regimes1.6s (4.1%)

bsearch51.0ms (0.1%)

simplify20.0ms (0%)

end0.0ms (0%)

sample5.6s (13.9%)

Profiling