Details

analyze48.0ms (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)

sample44.0ms (0.1%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify145.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5395	79

prune7.0ms (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

54.5b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize24.0ms (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))))
37.1b	(/.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))
46.3b	(/.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))))

rewrite1.1s (1.8%)

Algorithm

1×	rewrite-expression-head

Error

39.7b

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:

47.0ms	(/.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))
32.0ms	(/.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)

series12.9s (21.3%)

Error

12.0b

Counts

4 → 105

Calls

4 calls:

10.5s	(/.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))
934.0ms	(/.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))))
590.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
301.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 27843 to 18912 computations (32.1% saved)

simplify259.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5361	27473

prune1.4s (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	325	8	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	326	8	334

Error

10.3b

Counts

334 → 8

Compiler

Compiled 26169 to 11767 computations (55% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

10.3b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 10.3b
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

prune15.0ms (0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

10.3b

Counts

8 → 8

Compiler

Compiled 366 to 219 computations (40.2% saved)

localize34.0ms (0.1%)

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)))
36.7b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
37.1b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite3.0s (4.9%)

Algorithm

1×	rewrite-expression-head

Error

10.3b

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:

179.0ms	(.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)))
22.0ms	(/.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))))
11.0ms	(/.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)

series13.8s (22.7%)

Error

10.1b

Counts

4 → 109

Calls

4 calls:

10.6s	(.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)))
1.6s	(/.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))
448.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
331.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 33744 to 23425 computations (30.6% saved)

simplify472.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

606 → 606

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5154	52588

prune3.9s (6.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	601	5	606
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	603	11	614

Error

10.0b

Counts

614 → 11

Compiler

Compiled 52800 to 25506 computations (51.7% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (-.f64 (+.f64 alpha (+.f64 beta (*.f64 2 i))) 1)))
36.7b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
37.0b	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))
37.0b	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))

rewrite809.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

10.0b

Rules

101×	`*-un-lft-identity_binary64_1783`
89×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
83×	`times-frac_binary64_1789`
56×	`associate-l_binary64_1724`
42×	`add-sqr-sqrt_binary64_1805`
38×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `distribute-lft-out_binary64_1734`
31×	`add-cube-cbrt_binary64_1818`
29×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
16×	`associate-/r/_binary64_1729`
14×	`associate-r_binary64_1723`
10×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
8×	`pow1_binary64_1844` `div-inv_binary64_1780`
6×	`sqrt-prod_binary64_1799`
4×	`add-log-exp_binary64_1822` `sqrt-div_binary64_1800` `associate-/r*_binary64_1727`
3×	`associate-*r/_binary64_1725`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `associate-/l/_binary64_1730` `unswap-sqr_binary64_1751` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
1×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-/l_binary64_1728` `pow-prod-down_binary64_1854` `frac-times_binary64_1793` `associate-l/_binary64_1726` `difference-of-sqr-1_binary64_1753` `flip3--_binary64_1787` `flip--_binary64_1758` `*-commutative_binary64_1714`

Counts

4 → 173

Calls

4 calls:

87.0ms	(.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 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (-.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))))
4.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))

Compiler

Compiled 17009 to 6857 computations (59.7% saved)

series11.9s (19.6%)

Error

10.0b

Counts

4 → 87

Calls

4 calls:

10.4s	(.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 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (-.f64 (+.f64 alpha (+.f64 beta (*.f64 2 i))) 1)))
307.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
295.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))
247.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))

Compiler

Compiled 28948 to 19295 computations (33.3% saved)

simplify232.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4973	20520
1	4973	20520

prune1.5s (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	260	11	271

Error

10.0b

Counts

271 → 11

Compiler

Compiled 22596 to 10907 computations (51.7% saved)

regimes2.3s (3.9%)

Accuracy

Total 4.7b remaining (38.6%)

Threshold costs 0b (0%)

Compiler

Compiled 32781 to 19145 computations (41.6% saved)

bsearch116.0ms (0.2%)

Steps

Iters	Range		Point
5	3.539975187025043e+119	8.562891752395168e+119	8.438851657495755e+119
7	1.3849747316643134e+77	1.345544305891266e+79	1.80215627512591e+78
7	2.1827669958294294e+57	2.760176186012631e+59	2.7053834425805328e+59

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	214
1	78	214

end0.0ms (0%)

sample6.5s (10.8%)

Algorithm

1×

intervals

Results

771.0ms	8000×	body	128	valid
224.0ms	8000×	pre	128	true

Compiler

Compiled 8307 to 4852 computations (41.6% saved)

Details

analyze48.0ms (0.1%)

sample44.0ms (0.1%)

simplify145.0ms (0.2%)

prune7.0ms (0%)

localize24.0ms (0%)

rewrite1.1s (1.8%)

series12.9s (21.3%)

simplify259.0ms (0.4%)

prune1.4s (2.4%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune15.0ms (0%)

localize34.0ms (0.1%)

rewrite3.0s (4.9%)

series13.8s (22.7%)

simplify472.0ms (0.8%)

prune3.9s (6.4%)

localize35.0ms (0.1%)

rewrite809.0ms (1.3%)

series11.9s (19.6%)

simplify232.0ms (0.4%)

prune1.5s (2.5%)

regimes2.3s (3.9%)

bsearch116.0ms (0.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.5s (10.8%)

Profiling