Details

analyze46.0ms (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)

sample36.0ms (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)

simplify198.0ms (0.9%)

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))))

rewrite169.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_1768`
66×	`associate-/r/_binary64_1710` `flip3-+_binary64_1765` `flip-+_binary64_1736`
61×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
46×	`add-sqr-sqrt_binary64_1783`
44×	`frac-times_binary64_1772` `*-un-lft-identity_binary64_1762`
34×	`associate-*r/_binary64_1706`
30×	`add-cube-cbrt_binary64_1794`
28×	`difference-of-squares_binary64_1731`
22×	`prod-exp_binary64_1808` `associate-*l/_binary64_1707` `cbrt-unprod_binary64_1792`
19×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
16×	`pow1_binary64_1820`
14×	`difference-of-sqr-1_binary64_1732` `associate-/l*_binary64_1709`
9×	`associate-/l/_binary64_1711` `div-inv_binary64_1759`
7×	`associate-/r*_binary64_1708`
6×	`associate-r_binary64_1704`
4×	`pow-prod-down_binary64_1830` `add-log-exp_binary64_1798` `associate-l_binary64_1705`
3×	`swap-sqr_binary64_1729`
2×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `distribute-rgt-in_binary64_1714` `*-commutative_binary64_1695` `distribute-lft-in_binary64_1713`
1×	`pow-sqr_binary64_1735` `flip3--_binary64_1766` `pow-prod-up_binary64_1829` `pow-plus_binary64_1822` `unswap-sqr_binary64_1730` `flip--_binary64_1737` `pow2_binary64_1840`

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))
29.0ms	(/.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))))

series3.6s (15.5%)

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))
391.0ms	(/.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))))
204.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
97.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify155.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5228	18186

prune612.0ms (2.7%)

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 17671 to 6645 computations (62.4% 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)))

rewrite138.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_1768`
174×	`*-un-lft-identity_binary64_1762`
170×	`add-sqr-sqrt_binary64_1783`
106×	`add-cube-cbrt_binary64_1794`
34×	`associate-/r/_binary64_1710`
32×	`difference-of-squares_binary64_1731`
28×	`associate-/l*_binary64_1709`
25×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
18×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
17×	`associate-/r*_binary64_1708` `div-inv_binary64_1759`
16×	`difference-of-sqr-1_binary64_1732` `distribute-lft-out--_binary64_1716`
11×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
10×	`distribute-lft-out_binary64_1715`
6×	`associate-/l/_binary64_1711`
4×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `add-log-exp_binary64_1798` `pow1_binary64_1820`
2×	`prod-exp_binary64_1808` `associate-*r/_binary64_1706` `cbrt-unprod_binary64_1792`
1×	`flip3--_binary64_1766` `flip--_binary64_1737`

Counts

4 → 268

Calls

4 calls:

27.0ms	(/.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))
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))
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)))

series990.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

400.0ms	(/.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))
229.0ms	(/.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))
224.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
136.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify165.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5091	16880

prune819.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	275	5	280
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	278	9	287

Merged error: 33.1b

Counts

287 → 9

Compiler

Compiled 21336 to 8711 computations (59.2% saved)

localize25.0ms (0.1%)

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)))

rewrite158.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

427×	`*-un-lft-identity_binary64_1762`
351×	`times-frac_binary64_1768`
168×	`add-sqr-sqrt_binary64_1783` `add-cube-cbrt_binary64_1794`
148×	`distribute-lft-out_binary64_1715`
105×	`sqrt-prod_binary64_1777`
47×	`associate-/l*_binary64_1709`
19×	`associate-/r*_binary64_1708`
18×	`associate-/r/_binary64_1710`
15×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
14×	`sqrt-div_binary64_1778`
11×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
9×	`div-inv_binary64_1759`
6×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
5×	`associate-/l/_binary64_1711`
4×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `add-log-exp_binary64_1798` `pow1_binary64_1820`

Counts

4 → 330

Calls

4 calls:

32.0ms	(/.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))
16.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.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)))
9.0ms	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))

series1.0s (4.4%)

Counts

4 → 12

Calls

4 calls:

449.0ms	(/.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))
217.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
191.0ms	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
168.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))

simplify164.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5096	17020

prune1.4s (6.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	339	3	342
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	342	9	351

Merged error: 1.5b

Counts

351 → 9

Compiler

Compiled 28444 to 12929 computations (54.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite314.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

729×	`*-un-lft-identity_binary64_1762`
647×	`times-frac_binary64_1768`
325×	`add-sqr-sqrt_binary64_1783`
278×	`add-cube-cbrt_binary64_1794`
256×	`distribute-lft-out_binary64_1715`
181×	`sqrt-prod_binary64_1777`
150×	`associate-r_binary64_1704`
44×	`associate-/l*_binary64_1709`
34×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
28×	`associate-/r/_binary64_1710`
24×	`sqrt-div_binary64_1778` `associate-l_binary64_1705`
16×	`associate-/r*_binary64_1708`
15×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
14×	`div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
12×	`unswap-sqr_binary64_1730`
6×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792` `pow1_binary64_1820`
4×	`add-log-exp_binary64_1798`
3×	`frac-2neg_binary64_1773` `associate-/l/_binary64_1711` `clear-num_binary64_1761`
1×	`frac-times_binary64_1772` `pow-prod-down_binary64_1830` `associate-l/_binary64_1707` `associate-r/_binary64_1706` `*-commutative_binary64_1695`

Counts

4 → 509

Calls

4 calls:

112.0ms	(.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (/.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)))
31.0ms	(/.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))
18.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
9.0ms	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))

series1.2s (5.1%)

Counts

4 → 12

Calls

4 calls:

448.0ms	(/.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))
373.0ms	(.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (/.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)))
179.0ms	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))
163.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2))))

simplify241.0ms (1%)

Algorithm

1×	egg-herbie

Counts

521 → 521

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5057	26763

prune2.9s (12.8%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	510	11	521
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	512	18	530

Merged error: 1.1b

Counts

530 → 18

Compiler

Compiled 38125 to 20246 computations (46.9% saved)

regimes2.4s (10.5%)

Compiler: Compiled 41412 to 23545 computations (43.1% saved)

bsearch47.0ms (0.2%)

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	61	174
1	61	174

end0.0ms (0%)

sample6.2s (26.8%)

Algorithm

1×

intervals

Results

653.0ms	8000×	body	128	valid
179.0ms	8000×	pre	128	true

Compiler

Compiled 10464 to 5947 computations (43.2% saved)

Details

analyze46.0ms (0.2%)

sample36.0ms (0.2%)

simplify198.0ms (0.9%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite169.0ms (0.7%)

series3.6s (15.5%)

simplify155.0ms (0.7%)

prune612.0ms (2.7%)

localize18.0ms (0.1%)

rewrite138.0ms (0.6%)

series990.0ms (4.3%)

simplify165.0ms (0.7%)

prune819.0ms (3.6%)

localize25.0ms (0.1%)

rewrite158.0ms (0.7%)

series1.0s (4.4%)

simplify164.0ms (0.7%)

prune1.4s (6.1%)

localize20.0ms (0.1%)

rewrite314.0ms (1.4%)

series1.2s (5.1%)

simplify241.0ms (1%)

prune2.9s (12.8%)

regimes2.4s (10.5%)

bsearch47.0ms (0.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.2s (26.8%)

Profiling