Details

analyze40.0ms (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)

sample35.0ms (0.1%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify131.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

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

54.2b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize16.0ms (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))))
36.2b	(/.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))
46.1b	(/.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))))

rewrite150.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 228

Calls

4 calls:

43.0ms	(/.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))))
13.0ms	(.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))))

series10.4s (22%)

Counts

4 → 101

Calls

4 calls:

8.7s	(/.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))
945.0ms	(/.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))))
491.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
257.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 19119 to 13484 computations (29.5% saved)

simplify239.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5670	28252

prune1.4s (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	320	9	329
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	321	9	330

Error

7.3b

Counts

330 → 9

Compiler

Compiled 26788 to 11480 computations (57.1% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune18.0ms (0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

7.3b

Counts

9 → 9

Compiler

Compiled 535 to 275 computations (48.6% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)))
36.7b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
37.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite248.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

414×	`times-frac_binary64_1789`
314×	`add-sqr-sqrt_binary64_1805`
280×	`*-un-lft-identity_binary64_1783`
169×	`add-cube-cbrt_binary64_1818`
111×	`associate-r_binary64_1723`
70×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
62×	`difference-of-squares_binary64_1752`
48×	`associate-/r/_binary64_1729`
42×	`associate-l_binary64_1724`
33×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
31×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
24×	`flip-+_binary64_1757` `div-inv_binary64_1780` `flip3-+_binary64_1786`
19×	`associate-/l*_binary64_1728`
16×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
13×	`associate-/r*_binary64_1727`
9×	`distribute-lft-out_binary64_1734`
6×	`unswap-sqr_binary64_1751` `pow1_binary64_1844`
5×	`associate-/l/_binary64_1730`
4×	`add-log-exp_binary64_1822`
3×	`associate-*r/_binary64_1725` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`flip3--_binary64_1787` `flip--_binary64_1758`
1×	`associate-l/_binary64_1726` `-commutative_binary64_1714` `frac-times_binary64_1793` `pow-prod-down_binary64_1854`

Counts

4 → 395

Calls

4 calls:

116.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)))
21.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
13.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
10.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series9.7s (20.6%)

Counts

4 → 103

Calls

4 calls:

6.8s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)))
2.4s	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
300.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
227.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 20939 to 14768 computations (29.5% saved)

simplify350.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

498 → 498

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5056	48418

prune2.7s (5.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	494	4	498
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	500	7	507

Error

7.0b

Counts

507 → 7

Compiler

Compiled 46692 to 20753 computations (55.6% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)) (/.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))))
36.7b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
37.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite603.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

1927×	`times-frac_binary64_1789`
1182×	`add-sqr-sqrt_binary64_1805`
1048×	`*-un-lft-identity_binary64_1783`
709×	`add-cube-cbrt_binary64_1818`
335×	`associate-r_binary64_1723`
220×	`add-exp-log_binary64_1821`
210×	`difference-of-squares_binary64_1752`
128×	`div-exp_binary64_1834`
121×	`associate-/r/_binary64_1729`
116×	`associate-/r*_binary64_1727`
105×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
100×	`add-cbrt-cube_binary64_1819`
65×	`div-inv_binary64_1780`
58×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
53×	`cbrt-undiv_binary64_1817`
51×	`prod-exp_binary64_1832`
42×	`associate-l_binary64_1724`
21×	`cbrt-unprod_binary64_1816`
15×	`1-exp_binary64_1827` `rec-exp_binary64_1833`
14×	`unswap-sqr_binary64_1751`
9×	`distribute-lft-out_binary64_1734`
7×	`associate-/l*_binary64_1728` `pow1_binary64_1844`
4×	`associate-/l/_binary64_1730` `add-log-exp_binary64_1822`
3×	`associate-*r/_binary64_1725` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`un-div-inv_binary64_1781` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `associate-l/_binary64_1726` `-commutative_binary64_1714` `frac-times_binary64_1793` `pow-prod-down_binary64_1854`

Counts

4 → 984

Calls

4 calls:

269.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)) (/.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))))
34.0ms	(/.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))))
13.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
11.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series9.8s (20.8%)

Counts

4 → 103

Calls

4 calls:

6.9s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1)) (/.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))))
2.4s	(/.f64 1 (/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))))
315.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
242.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 21059 to 14888 computations (29.3% saved)

simplify733.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1087 → 1087

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4983	97597
1	4983	97597

prune6.9s (14.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1087	0	1087
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	1087	7	1094

Error

7.0b

Counts

1094 → 7

Compiler

Compiled 98432 to 43849 computations (55.5% saved)

regimes1.0s (2.2%)

Accuracy

Total 4.5b remaining (35.5%)

Threshold costs 0b (0%)

Compiler

Compiled 13540 to 7381 computations (45.5% saved)

bsearch72.0ms (0.2%)

Steps

Iters	Range		Point
3	7.007489079512985e+127	8.099426250272751e+127	8.031180177100264e+127
8	1.0072100280244118e+89	6.451845993839612e+91	1.6993400429866966e+89
6	2.1078652346646506e+30	1.1340348220796297e+31	1.1145808839945072e+31

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	59	217
1	59	217

end0.0ms (0%)

sample2.6s (5.5%)

Algorithm

1×

intervals

Results

632.0ms	8000×	body	128	valid
185.0ms	8000×	pre	128	true

Compiler

Compiled 3526 to 1916 computations (45.7% saved)

Details

analyze40.0ms (0.1%)

sample35.0ms (0.1%)

simplify131.0ms (0.3%)

prune4.0ms (0%)

localize16.0ms (0%)

rewrite150.0ms (0.3%)

series10.4s (22%)

simplify239.0ms (0.5%)

prune1.4s (2.9%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune18.0ms (0%)

localize18.0ms (0%)

rewrite248.0ms (0.5%)

series9.7s (20.6%)

simplify350.0ms (0.7%)

prune2.7s (5.7%)

localize19.0ms (0%)

rewrite603.0ms (1.3%)

series9.8s (20.8%)

simplify733.0ms (1.5%)

prune6.9s (14.7%)

regimes1.0s (2.2%)

bsearch72.0ms (0.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.6s (5.5%)

Profiling