Details

analyze92.0ms (0.6%)

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)

sample68.0ms (0.4%)

Algorithm

1×

intervals

Results

39.0ms	256×	body	128	valid
11.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify202.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

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

Error

52.5b

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))))
36.1b	(/.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))
44.8b	(/.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))))

rewrite205.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`times-frac_binary64_766`
66×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `flip-+_binary64_734`
61×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
46×	`add-sqr-sqrt_binary64_782`
44×	`*-un-lft-identity_binary64_760` `frac-times_binary64_770`
34×	`associate-*r/_binary64_702`
30×	`add-cube-cbrt_binary64_795`
28×	`difference-of-squares_binary64_729`
22×	`associate-*l/_binary64_703` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
19×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
16×	`pow1_binary64_821`
14×	`associate-/l*_binary64_705` `difference-of-sqr-1_binary64_730`
9×	`associate-/l/_binary64_707` `div-inv_binary64_757`
7×	`associate-/r*_binary64_704`
6×	`associate-r_binary64_700`
4×	`add-log-exp_binary64_799` `associate-l_binary64_701` `pow-prod-down_binary64_831`
3×	`swap-sqr_binary64_727`
2×	`frac-2neg_binary64_771` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `clear-num_binary64_759` `*-commutative_binary64_691`
1×	`pow2_binary64_841` `unswap-sqr_binary64_728` `pow-sqr_binary64_733` `pow-plus_binary64_823` `pow-prod-up_binary64_830` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 228

Calls

4 calls:

45.0ms	(/.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))
27.0ms	(/.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))))
20.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

series2.6s (16.2%)

Counts

4 → 12

Calls

4 calls:

2.0s	(/.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))
344.0ms	(/.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))))
154.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
89.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify381.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5261	18181

prune992.0ms (6.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	233	7	240
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	233	8	241

Error

34.2b

Counts

241 → 8

Compiler

Compiled 17724 to 6652 computations (62.5% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.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))
0.5b	(/.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))
36.2b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite195.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_766`
174×	`*-un-lft-identity_binary64_760`
170×	`add-sqr-sqrt_binary64_782`
106×	`add-cube-cbrt_binary64_795`
34×	`associate-/r/_binary64_706`
32×	`difference-of-squares_binary64_729`
28×	`associate-/l*_binary64_705`
25×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
18×	`flip3-+_binary64_763` `flip-+_binary64_734`
17×	`associate-/r*_binary64_704` `div-inv_binary64_757`
16×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`
11×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
10×	`distribute-lft-out_binary64_711`
6×	`associate-/l/_binary64_707`
4×	`frac-2neg_binary64_771` `add-log-exp_binary64_799` `pow1_binary64_821` `clear-num_binary64_759`
2×	`prod-exp_binary64_809` `associate-*r/_binary64_702` `cbrt-unprod_binary64_793`
1×	`flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 268

Calls

4 calls:

38.0ms	(/.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))
25.0ms	(/.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))
19.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
17.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

series669.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

308.0ms	(/.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))
140.0ms	(/.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))
117.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
104.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify249.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4952	16880
1	4952	16880

prune1.2s (7.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	275	5	280
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	279	9	288

Error

34.2b

Counts

288 → 9

Compiler

Compiled 21323 to 8688 computations (59.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.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))
0.5b	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
36.2b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.4b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite142.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_766`
174×	`*-un-lft-identity_binary64_760`
170×	`add-sqr-sqrt_binary64_782`
106×	`add-cube-cbrt_binary64_795`
33×	`associate-/r/_binary64_706`
32×	`difference-of-squares_binary64_729`
25×	`add-exp-log_binary64_798` `associate-/r*_binary64_704` `add-cbrt-cube_binary64_796`
20×	`associate-/l*_binary64_705`
18×	`flip3-+_binary64_763` `flip-+_binary64_734`
17×	`div-inv_binary64_757`
16×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`
11×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
10×	`distribute-lft-out_binary64_711`
7×	`associate-/l/_binary64_707`
4×	`frac-2neg_binary64_771` `add-log-exp_binary64_799` `pow1_binary64_821` `clear-num_binary64_759`
2×	`prod-exp_binary64_809` `associate-*r/_binary64_702` `cbrt-unprod_binary64_793`
1×	`div-sub_binary64_765` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 269

Calls

4 calls:

22.0ms	(/.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))
22.0ms	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
13.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.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)))

series733.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

328.0ms	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
183.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))
133.0ms	(/.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))
89.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify258.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5192	17021

prune1.2s (7.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	281	9	290

Error

34.0b

Counts

290 → 9

Compiler

Compiled 21872 to 9177 computations (58% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.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))
0.5b	(/.f64 (.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
36.2b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.5b	(.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2))))

rewrite175.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`times-frac_binary64_766`
63×	`*-un-lft-identity_binary64_760`
51×	`add-sqr-sqrt_binary64_782`
42×	`add-exp-log_binary64_798`
36×	`add-cube-cbrt_binary64_795`
32×	`add-cbrt-cube_binary64_796`
18×	`associate-/r/_binary64_706`
16×	`div-exp_binary64_811`
15×	`associate-r_binary64_700`
14×	`associate-/r*_binary64_704`
13×	`flip3-+_binary64_763` `flip-+_binary64_734`
12×	`cbrt-undiv_binary64_794`
11×	`associate-/l*_binary64_705`
10×	`distribute-lft-out_binary64_711` `prod-exp_binary64_809`
9×	`associate-/l/_binary64_707` `div-inv_binary64_757`
6×	`cbrt-unprod_binary64_793` `pow1_binary64_821`
4×	`associate-l/_binary64_703` `add-log-exp_binary64_799` `difference-of-squares_binary64_729` `frac-times_binary64_770` `associate-r/_binary64_702`
3×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `associate-l_binary64_701` `clear-num_binary64_759`
2×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712` `rec-exp_binary64_810` `un-div-inv_binary64_758` `1-exp_binary64_804`
1×	`pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 176

Calls

4 calls:

49.0ms	(/.f64 (.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
28.0ms	(.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2))))
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 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

series620.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(/.f64 (.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2)))) (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
142.0ms	(.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 1 (+.f64 (+.f64 alpha beta) (.f64 i 2))))
118.0ms	(/.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))
114.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))

simplify219.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5046	7816

prune659.0ms (4.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	188	9	197

Error

34.0b

Counts

197 → 9

Compiler

Compiled 12677 to 5350 computations (57.8% saved)

regimes1.0s (6.5%)

Accuracy

Total 2.5b remaining (6.9%)

Threshold costs 0b (0%)

Compiler

Compiled 15508 to 7765 computations (49.9% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 53 to 27 computations (49.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	164
1	44	164

end0.0ms (0%)

sample3.9s (24.6%)

Algorithm

1×

intervals

Results

852.0ms	8000×	body	128	valid
240.0ms	8000×	pre	128	true

Compiler

Compiled 3982 to 1989 computations (50.1% saved)

Details

analyze92.0ms (0.6%)

sample68.0ms (0.4%)

simplify202.0ms (1.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite205.0ms (1.3%)

series2.6s (16.2%)

simplify381.0ms (2.4%)

prune992.0ms (6.3%)

localize29.0ms (0.2%)

rewrite195.0ms (1.2%)

series669.0ms (4.2%)

simplify249.0ms (1.6%)

prune1.2s (7.7%)

localize19.0ms (0.1%)

rewrite142.0ms (0.9%)

series733.0ms (4.6%)

simplify258.0ms (1.6%)

prune1.2s (7.4%)

localize35.0ms (0.2%)

rewrite175.0ms (1.1%)

series620.0ms (3.9%)

simplify219.0ms (1.4%)

prune659.0ms (4.2%)

regimes1.0s (6.5%)

bsearch8.0ms (0.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (24.6%)

Profiling