Details

analyze73.0ms

Algorithm

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

sample34.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5396	79

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 57.0b

Counts

2 → 1

localize17.0ms

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))))
38.3b	(/.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))
48.7b	(/.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))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

86×	`times-frac_binary64`
66×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64` `frac-times_binary64`
34×	`associate-*r/_binary64`
30×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`
22×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-*l/_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
16×	`pow1_binary64`
14×	`difference-of-sqr-1_binary64` `associate-/l*_binary64`
9×	`associate-/l/_binary64` `div-inv_binary64`
7×	`associate-/r*_binary64`
6×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l_binary64`
3×	`swap-sqr_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 228

Calls

4 calls:

13.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
18.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
43.0ms	(/.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))))

series1.9s

Counts

4 → 12

Calls

4 calls:

45.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
96.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
1.5s	(/.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))
202.0ms	(/.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))))

simplify153.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5235	18189

prune414.0ms

Filtered

152 candidates to 240 candidates (-57.9%)

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: 35.9b

Counts

241 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.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))
0.1b	(.f64 (/.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)) (/.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)))
36.4b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
37.6b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

414×	`times-frac_binary64`
314×	`add-sqr-sqrt_binary64`
280×	`*-un-lft-identity_binary64`
169×	`add-cube-cbrt_binary64`
111×	`associate-r_binary64`
70×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
62×	`difference-of-squares_binary64`
48×	`associate-/r/_binary64`
42×	`associate-l_binary64`
33×	`cbrt-undiv_binary64` `div-exp_binary64`
31×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
24×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
19×	`associate-/l*_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
13×	`associate-/r*_binary64`
9×	`distribute-lft-out_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64`
5×	`associate-/l/_binary64`
4×	`add-log-exp_binary64`
3×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3--_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 395

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))
111.0ms	(.f64 (/.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)) (/.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)))
14.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.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))
1.4s	(.f64 (/.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)) (/.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)))
54.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
101.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify237.0ms

Algorithm

egg-herbie

Counts

407 → 407

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5152	30005

prune888.0ms

Filtered

266 candidates to 407 candidates (-53.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	401	6	407
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	405	9	414

Merged error: 35.8b

Counts

414 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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)))
0.2b	(.f64 (.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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))) (/.f64 1 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
36.4b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
37.6b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

220×	`add-exp-log_binary64`
136×	`add-cbrt-cube_binary64`
94×	`times-frac_binary64`
91×	`div-exp_binary64`
87×	`prod-exp_binary64`
77×	`*-un-lft-identity_binary64`
74×	`add-sqr-sqrt_binary64`
69×	`associate-r_binary64`
54×	`cbrt-undiv_binary64`
50×	`add-cube-cbrt_binary64`
49×	`cbrt-unprod_binary64`
18×	`associate-/r/_binary64`
16×	`associate-l_binary64`
11×	`pow1_binary64`
10×	`flip3-+_binary64` `flip-+_binary64`
9×	`distribute-lft-out_binary64` `1-exp_binary64` `rec-exp_binary64` `div-inv_binary64`
6×	`associate-/r_binary64` `associate-r/_binary64` `difference-of-squares_binary64` `frac-times_binary64` `associate-*l/_binary64`
4×	`pow-prod-down_binary64` `associate-/l/_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
3×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `un-div-inv_binary64` `flip--_binary64`

Counts

4 → 245

Calls

4 calls:

45.0ms	(.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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)))
51.0ms	(.f64 (.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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))) (/.f64 1 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

529.0ms	(.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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)))
412.0ms	(.f64 (.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (/.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))) (/.f64 1 (-.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1)))
62.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
102.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify177.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5041	15900

prune386.0ms

Filtered

153 candidates to 257 candidates (-68.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	256	1	257
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	257	9	266

Merged error: 35.8b

Counts

266 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

36.4b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.4b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.4b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
37.6b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
12×	`associate-/r*_binary64`
8×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `flip-+_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-r/_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64`

Counts

4 → 106

Calls

4 calls:

17.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
14.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
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)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
56.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
65.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
104.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

simplify85.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5121	3285

prune284.0ms

Filtered

94 candidates to 118 candidates (-25.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	117	10	127

Merged error: 35.8b

Counts

127 → 10

regimes124.0ms

Accuracy

37.2% (2.4b remaining)

Error of 35.9b against oracle of 33.5b and baseline of 37.3b

bsearch12.0ms

Steps

Iters	Range		Point
3	4.0619906387723585e+206	5.4905178624345144e+206	4.151273590251243e+206

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	92
1	46	92

end0.0ms

sample1.0s

Algorithm

intervals

Results

657.0ms	8000×	body	80	valid
168.0ms	8000×	pre	80	true

Details

analyze73.0ms

sample34.0ms

simplify56.0ms

prune4.0ms

localize17.0ms

rewrite116.0ms

series1.9s

simplify153.0ms

prune414.0ms

localize18.0ms

rewrite189.0ms

series1.7s

simplify237.0ms

prune888.0ms

localize19.0ms

rewrite140.0ms

series1.1s

simplify177.0ms

prune386.0ms

localize23.0ms

rewrite59.0ms

series282.0ms

simplify85.0ms

prune284.0ms

regimes124.0ms

bsearch12.0ms

simplify4.0ms

end0.0ms

sample1.0s

Profiling