Details

analyze44.0ms

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

sample36.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5230	53

prune7.0ms

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: 56.0b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
36.8b	(/.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 2.0 i)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) 1.0))
47.6b	(/.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 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
58×	`times-frac_binary64`
54×	`flip3-+_binary64` `flip-+_binary64`
50×	`associate-/r/_binary64`
44×	`add-sqr-sqrt_binary64`
36×	`frac-times_binary64`
30×	`associate-*r/_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`cbrt-unprod_binary64` `prod-exp_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
18×	`associate-*l/_binary64`
16×	`pow1_binary64`
14×	`difference-of-squares_binary64` `associate-/l*_binary64`
9×	`associate-/l/_binary64`
7×	`div-inv_binary64`
6×	`associate-r_binary64`
5×	`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 → 200

Calls

4 calls:

17.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
41.0ms	(/.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 2.0 i)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) 1.0))
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 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))

series619.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i)))
49.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
467.0ms	(/.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 2.0 i)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2.0 i)) (+.f64 (+.f64 alpha beta) (.f64 2.0 i))) 1.0))
75.0ms	(/.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 2.0 i)) (+.f64 (+.f64 alpha beta) (*.f64 2.0 i))))

simplify117.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4999	10097
1	4999	10097

prune379.0ms

Filtered

151 candidates to 212 candidates (-40.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	204	8	212
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	8	213

Merged error: 35.7b

Counts

213 → 8

localize20.0ms

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 2.0))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0)))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0))))
35.9b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))
35.9b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac_binary64`
300×	`add-sqr-sqrt_binary64`
235×	`*-un-lft-identity_binary64`
155×	`add-cube-cbrt_binary64`
96×	`associate-r_binary64`
70×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
62×	`difference-of-squares_binary64`
44×	`associate-/r/_binary64`
42×	`associate-l_binary64`
33×	`cbrt-undiv_binary64` `div-exp_binary64`
31×	`distribute-lft-out--_binary64` `sqrt-prod_binary64`
22×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
19×	`associate-/l*_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`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 → 364

Calls

4 calls:

24.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0)))
104.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0))))
11.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))
13.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0)))
608.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)) (sqrt.f64 1.0))))
47.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))
21.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))

simplify120.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5005	18793

prune847.0ms

Filtered

251 candidates to 376 candidates (-49.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	372	4	376
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	376	8	384

Merged error: 35.7b

Counts

384 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))) (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))))
35.9b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))
35.9b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))
35.9b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod_binary64`
40×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
27×	`times-frac_binary64`
19×	`pow1_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`swap-sqr_binary64` `associate-/r/_binary64`
12×	`associate-r_binary64` `associate-l_binary64`
10×	`flip3-+_binary64` `flip-+_binary64`
9×	`associate-/r*_binary64`
8×	`pow1/2_binary64` `sqrt-pow1_binary64`
7×	`div-inv_binary64`
6×	`associate-/l/_binary64`
5×	`pow-prod-up_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/l_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `pow-sqr_binary64`
1×	`rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 151

Calls

4 calls:

31.0ms	(.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))) (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))))
12.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))
14.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))
14.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))) (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))))
35.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))
20.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))
21.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5279	3266

prune290.0ms

Filtered

115 candidates to 163 candidates (-41.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	163	8	171

Merged error: 35.7b

Counts

171 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0))))
0.5b	(.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))) (/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))))
0.5b	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0))))
35.9b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity_binary64`
117×	`times-frac_binary64`
106×	`add-sqr-sqrt_binary64`
76×	`add-cube-cbrt_binary64`
60×	`sqrt-prod_binary64`
39×	`distribute-lft-out_binary64`
36×	`associate-r_binary64`
24×	`associate-l_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`associate-/r*_binary64`
11×	`associate-/l*_binary64`
10×	`associate-/r/_binary64`
9×	`unswap-sqr_binary64`
8×	`sqrt-div_binary64`
7×	`flip3-+_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip-+_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 218

Calls

4 calls:

9.0ms	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0))))
42.0ms	(.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))) (/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))))
14.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0))))
12.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0))))
43.0ms	(.f64 (/.f64 i (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2.0)))) (/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))))
38.0ms	(/.f64 (+.f64 i (+.f64 alpha beta)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2.0))))
37.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 i (+.f64 alpha beta)))) (+.f64 (+.f64 alpha beta) (*.f64 i 2.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4965	5179
1	4965	5179

prune384.0ms

Filtered

146 candidates to 230 candidates (-57.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	227	3	230
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	231	7	238

Merged error: 2.7b

Counts

238 → 7

regimes242.0ms

Accuracy

25.6% (12.2b remaining)

Error of 14.7b against oracle of 2.5b and baseline of 18.9b

bsearch62.0ms

Steps

Iters	Range	Point
5	1.4214025905189597e+180	3.5038899697870747e+180	2.178716223398337e+180
8	4.425378108998965e+140	1.2196746002532731e+144	1.202295370415579e+144
9	1.5609937890440059e+111	5.040828458311111e+116	1.5824841192270528e+111

Iters

Range

Point

1.4214025905189597e+180

3.5038899697870747e+180

2.178716223398337e+180

4.425378108998965e+140

1.2196746002532731e+144

1.202295370415579e+144

1.5609937890440059e+111

5.040828458311111e+116

1.5824841192270528e+111

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	119
1	66	119

end0.0ms

sample1.0s

Algorithm

intervals

Results

653.0ms	8000×	body	80	valid
178.0ms	8000×	pre	80	true

Details

analyze44.0ms

sample36.0ms

simplify30.0ms

prune7.0ms

localize19.0ms

rewrite109.0ms

series619.0ms

simplify117.0ms

prune379.0ms

localize20.0ms

rewrite181.0ms

series749.0ms

simplify120.0ms

prune847.0ms

localize26.0ms

rewrite80.0ms

series113.0ms

simplify43.0ms

prune290.0ms

localize27.0ms

rewrite87.0ms

series154.0ms

simplify74.0ms

prune384.0ms

regimes242.0ms

bsearch62.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling