Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample32.0ms (0.1%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify324.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (226.0ms)

Iter	Nodes	Cost
0	5023	37

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

1.8b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
8.8b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.6b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite413.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

77×	`*-un-lft-identity_binary64_1783`
34×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `distribute-lft-out_binary64_1734`
24×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
21×	`add-sqr-sqrt_binary64_1805` `associate-r_binary64_1723`
18×	`associate-/r/_binary64_1729`
16×	`frac-times_binary64_1793`
15×	`add-cube-cbrt_binary64_1818`
14×	`times-frac_binary64_1789`
13×	`pow1_binary64_1844`
11×	`swap-sqr_binary64_1750`
10×	`prod-exp_binary64_1832` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `cbrt-unprod_binary64_1816` `associate-*l/_binary64_1726`
9×	`associate-l_binary64_1724`
8×	`associate-*r/_binary64_1725`
7×	`associate-/l/_binary64_1730`
6×	`associate-/r*_binary64_1727`
5×	`associate-/l*_binary64_1728`
4×	`add-log-exp_binary64_1822`
3×	`div-inv_binary64_1780` `unswap-sqr_binary64_1751`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `*-commutative_binary64_1714`
1×	`pow2_binary64_1864` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `pow-sqr_binary64_1756` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732`

Counts

4 → 158

Calls

4 calls:

31.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
24.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
17.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
16.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 6017 to 3676 computations (38.9% saved)

series2.6s (6.9%)

Error

0.3b

Counts

4 → 89

Calls

4 calls:

1.1s	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
516.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
380.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
119.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 16683 to 13250 computations (20.6% saved)

simplify136.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5352	14087

prune842.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	237	10	247
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	238	11	249

Error

0.0b

Counts

249 → 11

Compiler

Compiled 13008 to 8758 computations (32.7% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))
0.1b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
8.8b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))

rewrite1.3s (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

826×	`*-un-lft-identity_binary64_1783`
508×	`times-frac_binary64_1789`
374×	`distribute-lft-out_binary64_1734`
191×	`add-sqr-sqrt_binary64_1805`
182×	`add-cube-cbrt_binary64_1818`
136×	`associate-r_binary64_1723`
34×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
31×	`associate-/l*_binary64_1728`
30×	`associate-/r/_binary64_1729`
20×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
15×	`div-inv_binary64_1780` `associate-/r*_binary64_1727`
14×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
8×	`associate-/l/_binary64_1730`
6×	`pow1_binary64_1844` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
4×	`add-log-exp_binary64_1822` `frac-times_binary64_1793` `associate-l/_binary64_1726` `associate-l*_binary64_1724`
3×	`unswap-sqr_binary64_1751` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`associate-*r/_binary64_1725`
1×	`pow-prod-down_binary64_1854` `*-commutative_binary64_1714`

Counts

4 → 422

Calls

4 calls:

59.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
36.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
22.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
10.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 16960 to 11567 computations (31.8% saved)

series2.8s (7.3%)

Error

0.0b

Counts

4 → 95

Calls

4 calls:

1.1s	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
538.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2)))
401.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta))) (+.f64 (+.f64 alpha beta) 2))
172.0ms	(/.f64 (+.f64 1 beta) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 18149 to 14328 computations (21.1% saved)

simplify215.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

517 → 517

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5591	23834

prune1.8s (4.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	515	2	517
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	518	10	528

Error

0.0b

Counts

528 → 10

Compiler

Compiled 24126 to 16569 computations (31.3% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

8.8b	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
8.8b	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
18.8b	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))
18.8b	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))

rewrite2.4s (6.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

738×	`*-un-lft-identity_binary64_1783`
476×	`times-frac_binary64_1789`
334×	`distribute-lft-out_binary64_1734`
272×	`associate-r_binary64_1723`
184×	`add-sqr-sqrt_binary64_1805`
164×	`add-cube-cbrt_binary64_1818`
28×	`associate-/r/_binary64_1729`
22×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `sqrt-prod_binary64_1799`
18×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
14×	`div-inv_binary64_1780`
10×	`pow1_binary64_1844`
8×	`associate-l_binary64_1724`
6×	`div-exp_binary64_1834` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `cbrt-undiv_binary64_1817` `unswap-sqr_binary64_1751`
4×	`add-log-exp_binary64_1822` `frac-times_binary64_1793` `associate-*l/_binary64_1726`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `sqrt-div_binary64_1800` `rem-sqrt-square_binary64_1796` `pow-prod-down_binary64_1854` `associate-r/_binary64_1725` `-commutative_binary64_1714`

Counts

4 → 370

Calls

4 calls:

60.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
56.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
36.0ms	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))
32.0ms	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))

Compiler

Compiled 25668 to 18419 computations (28.2% saved)

series12.1s (31.6%)

Error

Counts

4 → 94

Calls

4 calls:

4.2s	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))
4.2s	(sqrt.f64 (/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha))) (+.f64 alpha (+.f64 beta 3))))
544.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))
541.0ms	(*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta 2) alpha)) (+.f64 (+.f64 beta 2) alpha)))

Compiler

Compiled 53404 to 42733 computations (20% saved)

simplify327.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

464 → 464

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5023	41862

prune5.4s (14.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	462	2	464
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	464	10	474

Error

Counts

474 → 10

Compiler

Compiled 49081 to 35322 computations (28% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 1 beta))
0.2b	(cbrt.f64 (+.f64 1 beta))
0.2b	(*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta)))
8.8b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta))) (+.f64 alpha (+.f64 2 beta))) (/.f64 (cbrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))

rewrite343.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

35×	`add-exp-log_binary64_1821` `*-un-lft-identity_binary64_1783`
32×	`cbrt-prod_binary64_1814`
26×	`add-cbrt-cube_binary64_1819`
23×	`add-sqr-sqrt_binary64_1805`
16×	`pow1_binary64_1844` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `cbrt-div_binary64_1815`
15×	`add-cube-cbrt_binary64_1818`
13×	`frac-times_binary64_1793`
12×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
11×	`associate-l_binary64_1724`
9×	`distribute-lft-out_binary64_1734` `swap-sqr_binary64_1750`
8×	`associate-r/_binary64_1725` `associate-r*_binary64_1723` `pow1/3_binary64_1865`
7×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `associate-*l/_binary64_1726`
5×	`pow-prod-down_binary64_1854`
4×	`add-log-exp_binary64_1822` `unswap-sqr_binary64_1751`
2×	`*-commutative_binary64_1714` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846`

Counts

4 → 121

Calls

4 calls:

32.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta))) (+.f64 alpha (+.f64 2 beta))) (/.f64 (cbrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))
12.0ms	(*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta)))
3.0ms	(cbrt.f64 (+.f64 1 beta))
3.0ms	(cbrt.f64 (+.f64 1 beta))

Compiler

Compiled 5698 to 4215 computations (26% saved)

series889.0ms (2.3%)

Error

Counts

4 → 54

Calls

4 calls:

536.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta))) (+.f64 alpha (+.f64 2 beta))) (/.f64 (cbrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))))
67.0ms	(*.f64 (cbrt.f64 (+.f64 1 beta)) (cbrt.f64 (+.f64 1 beta)))
56.0ms	(cbrt.f64 (+.f64 1 beta))
53.0ms	(cbrt.f64 (+.f64 1 beta))

Compiler

Compiled 7494 to 5893 computations (21.4% saved)

simplify100.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4958	6022
1	4958	6022

prune467.0ms (1.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	175	10	185

Error

Counts

185 → 10

Compiler

Compiled 8056 to 5667 computations (29.7% saved)

regimes1.0s (2.7%)

Accuracy

Total 0.1b remaining (94.6%)

Threshold costs 0.1b (94.6%)

Compiler

Compiled 16520 to 12296 computations (25.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

end0.0ms (0%)

sample4.5s (11.8%)

Algorithm

1×

intervals

Results

492.0ms	8000×	body	128	valid
140.0ms	8000×	pre	128	true

Compiler

Compiled 5549 to 4129 computations (25.6% saved)

Details

analyze4.0ms (0%)

sample32.0ms (0.1%)

simplify324.0ms (0.8%)

prune5.0ms (0%)

localize13.0ms (0%)

rewrite413.0ms (1.1%)

series2.6s (6.9%)

simplify136.0ms (0.4%)

prune842.0ms (2.2%)

localize16.0ms (0%)

rewrite1.3s (3.5%)

series2.8s (7.3%)

simplify215.0ms (0.6%)

prune1.8s (4.7%)

localize16.0ms (0%)

rewrite2.4s (6.3%)

series12.1s (31.6%)

simplify327.0ms (0.9%)

prune5.4s (14.3%)

localize20.0ms (0.1%)

rewrite343.0ms (0.9%)

series889.0ms (2.3%)

simplify100.0ms (0.3%)

prune467.0ms (1.2%)

regimes1.0s (2.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.5s (11.8%)

Profiling