Details

analyze46.0ms (0.4%)

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)

sample37.0ms (0.3%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify205.0ms (1.6%)

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

Merged error: 54.7b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize15.0ms (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))))
35.7b	(/.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))
47.0b	(/.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))))

rewrite157.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_1805`
66×	`associate-/r/_binary64_1745` `flip3-+_binary64_1802` `flip-+_binary64_1773`
61×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
46×	`add-sqr-sqrt_binary64_1821`
44×	`*-un-lft-identity_binary64_1799` `frac-times_binary64_1809`
34×	`associate-*r/_binary64_1741`
30×	`add-cube-cbrt_binary64_1834`
28×	`difference-of-squares_binary64_1768`
22×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `associate-*l/_binary64_1742`
19×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
16×	`pow1_binary64_1860`
14×	`associate-/l*_binary64_1744` `difference-of-sqr-1_binary64_1769`
9×	`associate-/l/_binary64_1746` `div-inv_binary64_1796`
7×	`associate-/r*_binary64_1743`
6×	`associate-r_binary64_1739`
4×	`add-log-exp_binary64_1838` `associate-l_binary64_1740` `pow-prod-down_binary64_1870`
3×	`swap-sqr_binary64_1766`
2×	`distribute-rgt-in_binary64_1749` `clear-num_binary64_1798` `distribute-lft-in_binary64_1748` `frac-2neg_binary64_1810` `*-commutative_binary64_1730`
1×	`pow2_binary64_1880` `pow-sqr_binary64_1772` `unswap-sqr_binary64_1767` `flip--_binary64_1774` `flip3--_binary64_1803` `pow-prod-up_binary64_1869` `pow-plus_binary64_1862`

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))
28.0ms	(/.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))))
15.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
14.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series3.6s (27.2%)

Counts

4 → 12

Calls

4 calls:

2.9s	(/.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))
406.0ms	(/.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))))
200.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
91.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify148.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5255	18181

prune854.0ms (6.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	233	7	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	234	7	241

Merged error: 33.1b

Counts

241 → 7

Compiler

Compiled 24365 to 9982 computations (59% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.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))
0.3b	(/.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))
35.0b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
35.7b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite133.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_1805`
174×	`*-un-lft-identity_binary64_1799`
170×	`add-sqr-sqrt_binary64_1821`
106×	`add-cube-cbrt_binary64_1834`
34×	`associate-/r/_binary64_1745`
32×	`difference-of-squares_binary64_1768`
28×	`associate-/l*_binary64_1744`
25×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
18×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
17×	`associate-/r*_binary64_1743` `div-inv_binary64_1796`
16×	`difference-of-sqr-1_binary64_1769` `distribute-lft-out--_binary64_1751`
11×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
10×	`distribute-lft-out_binary64_1750`
6×	`associate-/l/_binary64_1746`
4×	`pow1_binary64_1860` `clear-num_binary64_1798` `add-log-exp_binary64_1838` `frac-2neg_binary64_1810`
2×	`prod-exp_binary64_1848` `associate-*r/_binary64_1741` `cbrt-unprod_binary64_1832`
1×	`flip--_binary64_1774` `flip3--_binary64_1803`

Counts

4 → 268

Calls

4 calls:

26.0ms	(/.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))
23.0ms	(/.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))
14.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
12.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series929.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

374.0ms	(/.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))
216.0ms	(/.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))
214.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
125.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify159.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5138	16880

prune1.2s (9.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	274	6	280
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	278	9	287

Merged error: 33.1b

Counts

287 → 9

Compiler

Compiled 33839 to 15284 computations (54.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
35.0b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
35.5b	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))
35.5b	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))

rewrite54.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1821`
23×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
21×	`times-frac_binary64_1805`
18×	`sqrt-prod_binary64_1815`
11×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
7×	`associate-/l*_binary64_1744`
6×	`pow1_binary64_1860` `sqrt-div_binary64_1816` `associate-/r*_binary64_1743` `flip3-+_binary64_1802` `flip-+_binary64_1773`
4×	`add-log-exp_binary64_1838` `associate-/r/_binary64_1745` `associate-/l/_binary64_1746`
3×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `pow1/2_binary64_1879` `associate-*r/_binary64_1741` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`
1×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`

Counts

4 → 98

Calls

4 calls:

14.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
12.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))

series630.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

282.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
116.0ms	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))
116.0ms	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))
116.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4966	3606
1	4966	3606

prune344.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	110	9	119

Merged error: 33.1b

Counts

119 → 9

Compiler

Compiled 11693 to 4446 computations (62% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
0.5b	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
0.5b	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
35.7b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite162.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

427×	`*-un-lft-identity_binary64_1799`
351×	`times-frac_binary64_1805`
168×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
148×	`distribute-lft-out_binary64_1750`
105×	`sqrt-prod_binary64_1815`
47×	`associate-/l*_binary64_1744`
19×	`associate-/r*_binary64_1743`
18×	`associate-/r/_binary64_1745`
15×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
14×	`sqrt-div_binary64_1816`
11×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
9×	`div-inv_binary64_1796`
6×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833`
5×	`associate-/l/_binary64_1746`
4×	`pow1_binary64_1860` `clear-num_binary64_1798` `add-log-exp_binary64_1838` `frac-2neg_binary64_1810`

Counts

4 → 330

Calls

4 calls:

34.0ms	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
15.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.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)))
10.0ms	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))

series988.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

430.0ms	(/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
208.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
178.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
172.0ms	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))

simplify177.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5033	17017

prune1.6s (12%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	340	2	342
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	342	9	351

Merged error: 1.5b

Counts

351 → 9

Compiler

Compiled 29654 to 13597 computations (54.1% saved)

regimes132.0ms (1%)

Compiler: Compiled 1647 to 918 computations (44.3% saved)

bsearch34.0ms (0.3%)

Steps

Iters	Range		Point
6	3.447753342443552e+132	4.3975301478197423e+133	3.2748075795360256e+133

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	63	193
1	63	193

end0.0ms (0%)

sample1.4s (10.4%)

Algorithm

1×

intervals

Results

641.0ms	8000×	body	128	valid
180.0ms	8000×	pre	128	true

Compiler

Compiled 738 to 400 computations (45.8% saved)

Details

analyze46.0ms (0.4%)

sample37.0ms (0.3%)

simplify205.0ms (1.6%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite157.0ms (1.2%)

series3.6s (27.2%)

simplify148.0ms (1.1%)

prune854.0ms (6.5%)

localize18.0ms (0.1%)

rewrite133.0ms (1%)

series929.0ms (7.1%)

simplify159.0ms (1.2%)

prune1.2s (9.5%)

localize21.0ms (0.2%)

rewrite54.0ms (0.4%)

series630.0ms (4.8%)

simplify73.0ms (0.6%)

prune344.0ms (2.6%)

localize22.0ms (0.2%)

rewrite162.0ms (1.2%)

series988.0ms (7.6%)

simplify177.0ms (1.3%)

prune1.6s (12%)

regimes132.0ms (1%)

bsearch34.0ms (0.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4s (10.4%)

Profiling