Details

analyze4.0ms

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	80	valid
4.0ms	256×	pre	80	true

simplify193.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (190.0ms)

Iter	Nodes	Cost
0	4986	25
1	4986	25

prune12.0ms

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: 1.3b

Counts

2 → 2

localize14.0ms

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)))
7.4b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
11.4b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite95.0ms

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:

18.0ms	(*.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)))
24.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
18.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
23.0ms	(/.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)))
22.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

simplify52.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5330	2658

prune164.0ms

Filtered

111 candidates to 170 candidates (-53.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	160	10	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	10	172

Merged error: 0b

Counts

172 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64`
89×	`times-frac_binary64`
82×	`distribute-lft-out_binary64`
60×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`
38×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`associate-r_binary64` `associate-l_binary64`
15×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
10×	`associate-/r/_binary64`
9×	`associate-/l*_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 202

Calls

4 calls:

37.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
10.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
29.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
6.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
7.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
23.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

simplify53.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5409	3681

prune164.0ms

Filtered

130 candidates to 214 candidates (-64.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	212	2	214
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	215	9	224

Merged error: 0b

Counts

224 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
0.1b	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
0.2b	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

808×	`*-un-lft-identity_binary64`
627×	`times-frac_binary64`
352×	`sqrt-prod_binary64`
307×	`distribute-lft-out_binary64`
265×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
58×	`associate-/r*_binary64`
42×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
23×	`associate-/r/_binary64`
21×	`cbrt-undiv_binary64` `div-exp_binary64`
20×	`sqrt-div_binary64`
17×	`associate-/l*_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
9×	`associate-/l/_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 500

Calls

4 calls:

10.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
25.0ms	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
51.0ms	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
13.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
7.0ms	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
30.0ms	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
12.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))

simplify107.0ms

Algorithm

egg-herbie

Counts

512 → 512

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5120	10844

prune314.0ms

Filtered

181 candidates to 512 candidates (-182.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	512	0	512
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	512	9	521

Merged error: 0b

Counts

521 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 beta 1))
0.2b	(cbrt.f64 (+.f64 beta 1))
0.2b	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
7.4b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64` `add-exp-log_binary64`
32×	`cbrt-prod_binary64`
26×	`add-cbrt-cube_binary64`
23×	`add-sqr-sqrt_binary64`
16×	`cbrt-div_binary64` `pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
15×	`add-cube-cbrt_binary64`
13×	`frac-times_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`associate-l_binary64`
9×	`swap-sqr_binary64` `distribute-lft-out_binary64`
8×	`associate-r_binary64` `associate-*r/_binary64` `pow1/3_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
2×	`pow-prod-up_binary64` `pow-sqr_binary64` `*-commutative_binary64`
1×	`pow-plus_binary64` `pow2_binary64`

Counts

4 → 121

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 beta 1))
3.0ms	(cbrt.f64 (+.f64 beta 1))
11.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
37.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cbrt.f64 (+.f64 beta 1))
5.0ms	(cbrt.f64 (+.f64 beta 1))
7.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
22.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

simplify65.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4924	1729
1	4924	1729

prune118.0ms

Filtered

92 candidates to 133 candidates (-44.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	133	9	142

Merged error: 0b

Counts

142 → 9

regimes81.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	25
1	23	25

end0.0ms

sample756.0ms

Algorithm

intervals

Results

490.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true

Details

analyze4.0ms

sample26.0ms

simplify193.0ms

prune12.0ms

localize14.0ms

rewrite95.0ms

series63.0ms

simplify52.0ms

prune164.0ms

localize16.0ms

rewrite96.0ms

series58.0ms

simplify53.0ms

prune164.0ms

localize15.0ms

rewrite142.0ms

series56.0ms

simplify107.0ms

prune314.0ms

localize16.0ms

rewrite59.0ms

series39.0ms

simplify65.0ms

prune118.0ms

regimes81.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample756.0ms

Profiling