Details

analyze50.0ms (0.2%)

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 (0.2%)

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)

simplify134.0ms (0.6%)

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: 55.0b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize16.0ms (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))))
33.3b	(/.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))
47.5b	(/.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))))

rewrite168.0ms (0.7%)

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:

48.0ms	(/.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))
30.0ms	(/.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 (+.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))))

series11.6s (47.7%)

Counts

4 → 71

Calls

4 calls:

10.4s	(/.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))
578.0ms	(/.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))))
402.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
216.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 17504 to 12366 computations (29.4% saved)

simplify210.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5021	24958

prune1.1s (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	292	7	299
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	293	7	300

Merged error: 9.3b

Counts

300 → 7

Compiler

Compiled 23753 to 10021 computations (57.8% 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

prune10.0ms (0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Merged error: 9.3b

Counts

7 → 7

Compiler

Compiled 260 to 147 computations (43.5% saved)

localize157.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(/.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))
31.0b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
32.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite142.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_1789`
174×	`*-un-lft-identity_binary64_1783`
170×	`add-sqr-sqrt_binary64_1805`
106×	`add-cube-cbrt_binary64_1818`
34×	`associate-/r/_binary64_1729`
32×	`difference-of-squares_binary64_1752`
28×	`associate-/l*_binary64_1728`
25×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
18×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
17×	`div-inv_binary64_1780` `associate-/r*_binary64_1727`
16×	`difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735`
11×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
10×	`distribute-lft-out_binary64_1734`
6×	`associate-/l/_binary64_1730`
4×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `add-log-exp_binary64_1822` `pow1_binary64_1844`
2×	`associate-*r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
1×	`flip3--_binary64_1787` `flip--_binary64_1758`

Counts

4 → 268

Calls

4 calls:

24.0ms	(/.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))
24.0ms	(/.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))
15.0ms	(/.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)))

series4.1s (17%)

Counts

4 → 65

Calls

4 calls:

2.2s	(/.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))
1.4s	(/.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))
264.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
209.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 12721 to 8745 computations (31.3% saved)

simplify192.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5220	22449

prune1.3s (5.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	325	8	333
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	328	12	340

Merged error: 8.2b

Counts

340 → 12

Compiler

Compiled 27017 to 11658 computations (56.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
31.0b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
32.2b	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))
32.2b	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))

rewrite58.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

17.0ms	(/.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)))))

series1.4s (5.9%)

Counts

4 → 68

Calls

4 calls:

690.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta))))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
257.0ms	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))
250.0ms	(sqrt.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))))
225.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

Compiler

Compiled 10280 to 6154 computations (40.1% saved)

simplify108.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5004	7259

prune481.0ms (2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	167	11	178

Merged error: 8.2b

Counts

178 → 11

Compiler

Compiled 14204 to 5182 computations (63.5% saved)

regimes648.0ms (2.7%)

Compiler: Compiled 10660 to 5729 computations (46.3% saved)

bsearch31.0ms (0.1%)

Steps

Iters	Range		Point
6	3.2058810832883946e+132	3.1083454677953027e+133	3.0508630174715843e+133

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	111
1	47	111

end0.0ms (0%)

sample2.3s (9.3%)

Algorithm

1×

intervals

Results

627.0ms	8000×	body	128	valid
188.0ms	8000×	pre	128	true

Compiler

Compiled 2734 to 1465 computations (46.4% saved)

Details

analyze50.0ms (0.2%)

sample37.0ms (0.2%)

simplify134.0ms (0.6%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite168.0ms (0.7%)

series11.6s (47.7%)

simplify210.0ms (0.9%)

prune1.1s (4.6%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune10.0ms (0%)

localize157.0ms (0.6%)

rewrite142.0ms (0.6%)

series4.1s (17%)

simplify192.0ms (0.8%)

prune1.3s (5.2%)

localize21.0ms (0.1%)

rewrite58.0ms (0.2%)

series1.4s (5.9%)

simplify108.0ms (0.4%)

prune481.0ms (2%)

regimes648.0ms (2.7%)

bsearch31.0ms (0.1%)

simplify6.0ms (0%)

end0.0ms (0%)

sample2.3s (9.3%)

Profiling