Details

analyze173.0ms (0.5%)

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)

sample48.0ms (0.1%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify43.0ms (0.1%)

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

52.0b

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))))
35.9b	(/.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))
44.0b	(/.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))))

rewrite926.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

37.9b

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:

44.0ms	(/.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))
26.0ms	(/.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)))
14.0ms	(.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)

series10.7s (29.5%)

Error

8.1b

Counts

4 → 96

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))
765.0ms	(/.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))))
448.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
243.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 27012 to 18309 computations (32.2% saved)

simplify230.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

324 → 324

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5420	27149

prune1.3s (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	318	6	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	319	6	325

Error

7.0b

Counts

325 → 6

Compiler

Compiled 25559 to 11427 computations (55.3% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

7.0b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 7.0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (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

7.0b

Counts

6 → 6

Compiler

Compiled 205 to 123 computations (40% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.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)))))
0.3b	(/.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))
34.9b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
35.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite1.4s (3.8%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

376×	`*-un-lft-identity_binary64_1783`
342×	`times-frac_binary64_1789`
205×	`add-sqr-sqrt_binary64_1805`
129×	`add-cube-cbrt_binary64_1818`
91×	`distribute-lft-out_binary64_1734`
38×	`associate-/r/_binary64_1729` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
32×	`associate-/l*_binary64_1728`
25×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
21×	`associate-/r*_binary64_1727`
20×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
19×	`div-inv_binary64_1780` `difference-of-sqr-1_binary64_1753`
11×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
6×	`associate-/l/_binary64_1730`
4×	`pow1_binary64_1844` `add-log-exp_binary64_1822` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-*r/_binary64_1725`
1×	`flip3--_binary64_1787` `flip--_binary64_1758`

Counts

4 → 333

Calls

4 calls:

21.0ms	(/.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))
20.0ms	(/.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)))))
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 26191 to 12414 computations (52.6% saved)

series5.3s (14.5%)

Error

6.7b

Counts

4 → 97

Calls

4 calls:

2.5s	(/.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))
1.7s	(/.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)))))
351.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
238.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 25962 to 17557 computations (32.4% saved)

simplify256.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5377	30455

prune2.0s (5.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	427	3	430
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	428	8	436

Error

6.7b

Counts

436 → 8

Compiler

Compiled 35075 to 16880 computations (51.9% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.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)))))
0.3b	(/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
34.9b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
35.4b	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

rewrite1.2s (3.4%)

Algorithm

1×	rewrite-expression-head

Error

6.7b

Rules

315×	`*-un-lft-identity_binary64_1783`
252×	`times-frac_binary64_1789`
105×	`add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805`
101×	`distribute-lft-out_binary64_1734`
31×	`associate-/r/_binary64_1729` `associate-/r*_binary64_1727`
25×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
19×	`associate-/l*_binary64_1728` `distribute-lft-out--_binary64_1735`
18×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
16×	`div-inv_binary64_1780`
11×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
7×	`associate-/l/_binary64_1730`
4×	`pow1_binary64_1844` `add-log-exp_binary64_1822` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-*r/_binary64_1725`
1×	`associate-+r-_binary64_1717` `div-sub_binary64_1788`

Counts

4 → 277

Calls

4 calls:

20.0ms	(/.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)))))
20.0ms	(/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
11.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

Compiler

Compiled 21811 to 10599 computations (51.4% saved)

series4.1s (11.4%)

Error

6.7b

Counts

4 → 97

Calls

4 calls:

1.7s	(/.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)))))
1.4s	(/.f64 (+.f64 alpha (-.f64 (+.f64 beta (.f64 i 2)) 1)) (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha)))
362.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
247.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 24151 to 15813 computations (34.5% saved)

simplify270.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4968	23694
1	4968	23694

prune1.9s (5.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	374	0	374
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	374	8	382

Error

6.7b

Counts

382 → 8

Compiler

Compiled 29394 to 14243 computations (51.5% saved)

regimes1.7s (4.6%)

Accuracy

Total 4.3b remaining (36.6%)

Threshold costs 0b (0%)

Compiler

Compiled 26524 to 14977 computations (43.5% saved)

bsearch102.0ms (0.3%)

Steps

Iters	Range		Point
7	4.840321972178979e+108	1.5011517721087707e+110	7.847732791584524e+108
6	1.6434036971327238e+86	6.855295510350113e+86	6.775388124021871e+86
6	6.998718286987994e+59	5.088469909752467e+60	7.266231672116392e+59

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify18.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	196
1	78	196

Compiler

Compiled 264 to 162 computations (38.6% saved)

end0.0ms (0%)

sample4.5s (12.4%)

Algorithm

1×

intervals

Results

674.0ms	8000×	body	128	valid
173.0ms	8000×	pre	128	true

Compiler

Compiled 6758 to 3823 computations (43.4% saved)

Details

analyze173.0ms (0.5%)

sample48.0ms (0.1%)

simplify43.0ms (0.1%)

prune4.0ms (0%)

localize16.0ms (0%)

rewrite926.0ms (2.6%)

series10.7s (29.5%)

simplify230.0ms (0.6%)

prune1.3s (3.6%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0%)

prune10.0ms (0%)

localize20.0ms (0.1%)

rewrite1.4s (3.8%)

series5.3s (14.5%)

simplify256.0ms (0.7%)

prune2.0s (5.5%)

localize32.0ms (0.1%)

rewrite1.2s (3.4%)

series4.1s (11.4%)

simplify270.0ms (0.7%)

prune1.9s (5.2%)

regimes1.7s (4.6%)

bsearch102.0ms (0.3%)

simplify18.0ms (0%)

end0.0ms (0%)

sample4.5s (12.4%)

Profiling