Details

analyze318.0ms (0.7%)

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)

sample87.0ms (0.2%)

Algorithm

1×

intervals

Results

39.0ms	256×	body	128	valid
10.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify79.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5395	79

prune8.0ms (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

52.3b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize35.0ms (0.1%)

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))))
36.9b	(/.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))
44.3b	(/.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))))

rewrite1.4s (3.2%)

Algorithm

1×	rewrite-expression-head

Error

38.7b

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:

82.0ms	(/.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))
52.0ms	(/.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))))
35.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
26.0ms	(.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)

series18.0s (41.2%)

Error

9.4b

Counts

4 → 82

Calls

4 calls:

15.2s	(/.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))
962.0ms	(/.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))))
808.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
442.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 23383 to 15686 computations (32.9% saved)

simplify392.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5586	24522

prune1.8s (4.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	306	4	310
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	307	4	311

Error

7.7b

Counts

311 → 4

Compiler

Compiled 23625 to 10430 computations (55.9% saved)

localize1.0ms (0%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series1.0ms (0%)

Error: 7.7b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune9.0ms (0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

7.7b

Counts

4 → 4

Compiler

Compiled 87 to 57 computations (34.5% saved)

localize37.0ms (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))
35.9b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
36.1b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite2.2s (5%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

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:

43.0ms	(/.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))
39.0ms	(/.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)))))
28.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
20.0ms	(/.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)

series3.5s (8.1%)

Error

7.7b

Counts

4 → 59

Calls

4 calls:

2.1s	(/.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))
573.0ms	(/.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)))))
331.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
243.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 11896 to 7825 computations (34.2% saved)

simplify429.0ms (1%)

Algorithm

1×	egg-herbie

Counts

392 → 392

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4975	23598
1	4975	23598

prune2.4s (5.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	390	2	392
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	390	6	396

Error

7.7b

Counts

396 → 6

Compiler

Compiled 28986 to 13695 computations (52.8% saved)

localize55.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
35.9b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
35.9b	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))
35.9b	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))

rewrite567.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

Rules

43×	`*-un-lft-identity_binary64_1783`
28×	`times-frac_binary64_1789`
27×	`add-sqr-sqrt_binary64_1805`
25×	`add-cube-cbrt_binary64_1818`
21×	`sqrt-prod_binary64_1799`
11×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
9×	`distribute-lft-out_binary64_1734`
8×	`associate-/r*_binary64_1727`
7×	`associate-/l*_binary64_1728`
6×	`pow1_binary64_1844` `flip3-+_binary64_1786` `sqrt-div_binary64_1800` `flip-+_binary64_1757`
4×	`add-log-exp_binary64_1822` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729`
3×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `associate-*r/_binary64_1725`
1×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`

Counts

4 → 107

Calls

4 calls:

22.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
19.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
7.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))

Compiler

Compiled 9064 to 3357 computations (63% saved)

series1.7s (4%)

Error

7.7b

Counts

4 → 51

Calls

4 calls:

658.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta))))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
337.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))
313.0ms	(sqrt.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))))
253.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 11348 to 6693 computations (41% saved)

simplify128.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5493	3999

prune639.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	158	6	164

Error

7.7b

Counts

164 → 6

Compiler

Compiled 11613 to 4679 computations (59.7% saved)

regimes2.0s (4.7%)

Accuracy

Total 3.7b remaining (32.8%)

Threshold costs 0b (0%)

Compiler

Compiled 21660 to 12037 computations (44.4% saved)

bsearch54.0ms (0.1%)

Steps

Iters	Range		Point
6	1.1328725160429732e+123	5.478276028333073e+123	4.280023215608894e+123

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%)

sample7.6s (17.5%)

Algorithm

1×

intervals

Results

1.3s	8000×	body	128	valid
299.0ms	8000×	pre	128	true

Compiler

Compiled 5462 to 3042 computations (44.3% saved)

Details

analyze318.0ms (0.7%)

sample87.0ms (0.2%)

simplify79.0ms (0.2%)

prune8.0ms (0%)

localize35.0ms (0.1%)

rewrite1.4s (3.2%)

series18.0s (41.2%)

simplify392.0ms (0.9%)

prune1.8s (4.2%)

localize1.0ms (0%)

rewrite1.0ms (0%)

series1.0ms (0%)

simplify12.0ms (0%)

prune9.0ms (0%)

localize37.0ms (0.1%)

rewrite2.2s (5%)

series3.5s (8.1%)

simplify429.0ms (1%)

prune2.4s (5.6%)

localize55.0ms (0.1%)

rewrite567.0ms (1.3%)

series1.7s (4%)

simplify128.0ms (0.3%)

prune639.0ms (1.5%)

regimes2.0s (4.7%)

bsearch54.0ms (0.1%)

simplify20.0ms (0%)

end0.0ms (0%)

sample7.6s (17.5%)

Profiling