Details

analyze44.0ms (0.1%)

Algorithm

1×

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

Compiler

Compiled 63 to 34 computations (46% saved)

sample46.0ms (0.1%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify125.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

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

52.0b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize15.0ms (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))))
34.9b	(/.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))
44.6b	(/.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))))

rewrite837.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

35.2b

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:

39.0ms	(/.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))
31.0ms	(/.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))))
14.0ms	(.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)

series9.0s (10.5%)

Error

10.3b

Counts

4 → 99

Calls

4 calls:

7.0s	(/.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))
876.0ms	(/.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))))
493.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
241.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 24735 to 16613 computations (32.8% saved)

simplify222.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

327 → 327

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4974	25841
1	4974	25841

prune1.2s (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	320	7	327
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	321	7	328

Error

6.7b

Counts

328 → 7

Compiler

Compiled 24861 to 10993 computations (55.8% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

6.7b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 6.7b
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

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

6.7b

Counts

7 → 7

Compiler

Compiled 202 to 122 computations (39.6% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.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))
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)))
31.6b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
32.8b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite2.7s (3.1%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

606×	`*-un-lft-identity_binary64_1783`
587×	`times-frac_binary64_1789`
379×	`add-sqr-sqrt_binary64_1805`
210×	`add-cube-cbrt_binary64_1818`
150×	`associate-r_binary64_1723`
129×	`distribute-lft-out_binary64_1734`
74×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
70×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
56×	`associate-l_binary64_1724`
54×	`associate-/r/_binary64_1729`
37×	`difference-of-sqr-1_binary64_1753`
33×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
27×	`div-inv_binary64_1780` `flip3-+_binary64_1786` `flip-+_binary64_1757`
22×	`associate-/l*_binary64_1728`
16×	`associate-/r*_binary64_1727` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
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`
2×	`flip3--_binary64_1787` `flip--_binary64_1758`
1×	`pow-prod-down_binary64_1854` `frac-times_binary64_1793` `associate-l/_binary64_1726` `-commutative_binary64_1714`

Counts

4 → 497

Calls

4 calls:

157.0ms	(.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)))
20.0ms	(/.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))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
10.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 41545 to 19607 computations (52.8% saved)

series16.1s (18.8%)

Error

5.9b

Counts

4 → 97

Calls

4 calls:

13.1s	(.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)))
1.4s	(/.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))
345.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
256.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 39648 to 28260 computations (28.7% saved)

simplify420.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

594 → 594

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5543	59125

prune4.0s (4.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	590	4	594
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	591	10	601

Error

5.9b

Counts

601 → 10

Compiler

Compiled 56630 to 28728 computations (49.3% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.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 1 (/.f64 (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))))))
31.6b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
32.8b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite11.5s (13.3%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

Rules

2691×	`times-frac_binary64_1789`
2087×	`*-un-lft-identity_binary64_1783`
1474×	`add-sqr-sqrt_binary64_1805`
917×	`add-cube-cbrt_binary64_1818`
452×	`associate-r_binary64_1723`
335×	`distribute-lft-out_binary64_1734`
252×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
220×	`add-exp-log_binary64_1821`
157×	`associate-/r*_binary64_1727`
137×	`associate-/r/_binary64_1729`
128×	`div-exp_binary64_1834`
126×	`difference-of-sqr-1_binary64_1753`
100×	`add-cbrt-cube_binary64_1819`
73×	`div-inv_binary64_1780`
66×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
56×	`associate-l_binary64_1724`
53×	`cbrt-undiv_binary64_1817`
51×	`prod-exp_binary64_1832`
21×	`cbrt-unprod_binary64_1816`
15×	`1-exp_binary64_1827` `rec-exp_binary64_1833`
14×	`unswap-sqr_binary64_1751`
7×	`pow1_binary64_1844` `associate-/l*_binary64_1728`
4×	`add-log-exp_binary64_1822` `associate-/l/_binary64_1730`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-*r/_binary64_1725`
1×	`pow-prod-down_binary64_1854` `frac-times_binary64_1793` `un-div-inv_binary64_1781` `associate-l/_binary64_1726` `-commutative_binary64_1714` `inv-pow_binary64_1868` `pow-flip_binary64_1857`

Counts

4 → 1277

Calls

4 calls:

403.0ms	(.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 1 (/.f64 (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))))))
45.0ms	(/.f64 1 (/.f64 (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i))))))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
11.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 114802 to 57544 computations (49.9% saved)

series16.2s (18.9%)

Error

5.9b

Counts

4 → 97

Calls

4 calls:

13.1s	(.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 1 (/.f64 (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))))))
1.4s	(/.f64 1 (/.f64 (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i))))))
353.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
263.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 39874 to 28486 computations (28.6% saved)

simplify904.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1374 → 1374

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5332	125534

prune15.5s (18.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1373	1	1374
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	1375	9	1384

Error

5.9b

Counts

1384 → 9

Compiler

Compiled 126438 to 63367 computations (49.9% saved)

regimes2.1s (2.4%)

Accuracy

Total 3.2b remaining (29.3%)

Threshold costs 0b (0%)

Compiler

Compiled 30876 to 17885 computations (42.1% saved)

bsearch38.0ms (0%)

Steps

Iters	Range		Point
6	9.664679637509052e+145	1.2605494832636703e+147	1.8720501362633033e+146

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	89
1	46	89

end0.0ms (0%)

sample4.9s (5.7%)

Algorithm

1×

intervals

Results

721.0ms	8000×	body	128	valid
171.0ms	8000×	pre	128	true

Compiler

Compiled 7733 to 4489 computations (42% saved)

Details

analyze44.0ms (0.1%)

sample46.0ms (0.1%)

simplify125.0ms (0.1%)

prune4.0ms (0%)

localize15.0ms (0%)

rewrite837.0ms (1%)

series9.0s (10.5%)

simplify222.0ms (0.3%)

prune1.2s (1.4%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune10.0ms (0%)

localize18.0ms (0%)

rewrite2.7s (3.1%)

series16.1s (18.8%)

simplify420.0ms (0.5%)

prune4.0s (4.6%)

localize20.0ms (0%)

rewrite11.5s (13.3%)

series16.2s (18.9%)

simplify904.0ms (1.1%)

prune15.5s (18.1%)

regimes2.1s (2.4%)

bsearch38.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.9s (5.7%)

Profiling