Details

analyze5.0ms

Algorithm

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

sample26.0ms

Algorithm

intervals

Results

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

simplify229.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (221.0ms)

Iter	Nodes	Cost
0	5022	37

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 0.6b

Counts

2 → 2

localize12.0ms

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)))
8.9b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.2b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
34×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`flip3-+_binary64` `flip-+_binary64`
21×	`associate-r_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r/_binary64`
16×	`frac-times_binary64`
15×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`
13×	`pow1_binary64`
11×	`swap-sqr_binary64`
10×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
9×	`associate-l_binary64`
8×	`associate-*r/_binary64`
7×	`associate-/l/_binary64`
6×	`associate-/r*_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`unswap-sqr_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 158

Calls

4 calls:

15.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
28.0ms	(/.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)))
28.0ms	(.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)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
220.0ms	(/.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)))
192.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
105.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

simplify86.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4939	3970
1	4939	3970

prune205.0ms

Filtered

111 candidates to 170 candidates (-53.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	6	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.1b	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
8.9b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

133×	`*-un-lft-identity_binary64`
82×	`add-exp-log_binary64`
67×	`times-frac_binary64`
61×	`add-cbrt-cube_binary64`
54×	`distribute-lft-out_binary64` `add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
32×	`prod-exp_binary64`
27×	`associate-r_binary64`
25×	`associate-l_binary64`
24×	`div-exp_binary64`
22×	`cbrt-unprod_binary64`
19×	`cbrt-undiv_binary64` `frac-times_binary64`
13×	`flip3-+_binary64` `associate-/l/_binary64` `associate-*r/_binary64` `flip-+_binary64`
11×	`pow1_binary64` `associate-*l/_binary64`
10×	`associate-/r*_binary64`
8×	`associate-/r/_binary64`
6×	`unswap-sqr_binary64` `rec-exp_binary64`
5×	`associate-/l*_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `div-inv_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 206

Calls

4 calls:

10.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
30.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
33.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
29.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))

series569.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
97.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
230.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
189.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))

simplify114.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4943	5666
1	4943	5666

prune223.0ms

Filtered

130 candidates to 218 candidates (-67.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	218	7	225

Merged error: 0b

Counts

225 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
0.4b	(*.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
8.9b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

480×	`*-un-lft-identity_binary64`
307×	`times-frac_binary64`
213×	`distribute-lft-out_binary64`
196×	`sqrt-prod_binary64`
156×	`add-sqr-sqrt_binary64`
155×	`associate-l_binary64`
113×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
30×	`associate-r_binary64`
19×	`frac-times_binary64`
18×	`associate-/r/_binary64`
17×	`flip3-+_binary64` `flip-+_binary64`
15×	`sqrt-div_binary64`
13×	`associate-*r/_binary64`
12×	`pow1_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
11×	`associate-/l/_binary64` `associate-*l/_binary64`
9×	`div-inv_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
2×	`rem-sqrt-square_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`

Counts

4 → 320

Calls

4 calls:

52.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
104.0ms	(*.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
46.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))))

series848.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))) (+.f64 alpha (+.f64 beta 3)))
83.0ms	(sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
120.0ms	(*.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
391.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))))

simplify133.0ms

Algorithm

egg-herbie

Counts

332 → 332

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5353	11497

prune404.0ms

Filtered

172 candidates to 332 candidates (-93.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	332	0	332
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	332	7	339

Merged error: 0b

Counts

339 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 1 alpha)) (/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1)))
0.7b	(pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4)
0.8b	(/.f64 1 (*.f64 (/.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 1 alpha)) (/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1))))
9.6b	(/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

202×	`*-un-lft-identity_binary64`
132×	`times-frac_binary64`
103×	`add-sqr-sqrt_binary64`
93×	`add-exp-log_binary64`
84×	`unpow-prod-down_binary64`
72×	`distribute-lft-out_binary64` `add-cube-cbrt_binary64`
54×	`associate-r_binary64`
52×	`sqrt-prod_binary64`
42×	`div-exp_binary64`
36×	`add-cbrt-cube_binary64`
26×	`associate-l_binary64`
24×	`prod-exp_binary64`
15×	`associate-/l*_binary64`
14×	`cbrt-undiv_binary64`
12×	`sqr-pow_binary64`
11×	`pow1_binary64`
10×	`unswap-sqr_binary64`
9×	`associate-/r/_binary64` `rec-exp_binary64`
8×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `pow-exp_binary64`
5×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `pow-pow_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-flip_binary64` `frac-times_binary64` `associate-l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow2_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `*-commutative_binary64`

Counts

4 → 265

Calls

4 calls:

48.0ms	(*.f64 (/.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 1 alpha)) (/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1)))
8.0ms	(pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4)
30.0ms	(/.f64 1 (*.f64 (/.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 1 alpha)) (/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1))))
14.0ms	(/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1))

series597.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(*.f64 (/.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 1 alpha)) (/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1)))
137.0ms	(pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4)
222.0ms	(/.f64 1 (*.f64 (/.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 1 alpha)) (/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1))))
56.0ms	(/.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)) 4) (+.f64 beta 1))

simplify144.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4960	8106
1	4960	8106

prune230.0ms

Filtered

139 candidates to 277 candidates (-99.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	277	7	284

Merged error: 0b

Counts

284 → 7

regimes44.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	40
1	25	40

end0.0ms

sample734.0ms

Algorithm

intervals

Results

464.0ms	8000×	body	128	valid
129.0ms	8000×	pre	128	true

Details

analyze5.0ms

sample26.0ms

simplify229.0ms

prune5.0ms

localize12.0ms

rewrite108.0ms

series552.0ms

simplify86.0ms

prune205.0ms

localize14.0ms

rewrite134.0ms

series569.0ms

simplify114.0ms

prune223.0ms

localize23.0ms

rewrite282.0ms

series848.0ms

simplify133.0ms

prune404.0ms

localize17.0ms

rewrite141.0ms

series597.0ms

simplify144.0ms

prune230.0ms

regimes44.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample734.0ms

Profiling