Details

analyze7.0ms

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

sample27.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify196.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (193.0ms)

Iter	Nodes	Cost
0	4986	25
1	4986	25

prune9.0ms

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: 1.0b

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)))
6.5b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.7b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite92.0ms

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)))
26.0ms	(.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)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
22.0ms	(/.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)))
25.0ms	(.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)))

simplify45.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5330	2658

prune225.0ms

Filtered

111 candidates to 170 candidates (-53.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	159	11	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	161	11	172

Merged error: 0.0b

Counts

172 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
6.5b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

826×	`*-un-lft-identity_binary64`
508×	`times-frac_binary64`
374×	`distribute-lft-out_binary64`
191×	`add-sqr-sqrt_binary64`
182×	`add-cube-cbrt_binary64`
136×	`associate-r_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
31×	`associate-/l*_binary64`
30×	`associate-/r/_binary64`
20×	`flip3-+_binary64` `flip-+_binary64`
15×	`associate-/r*_binary64` `div-inv_binary64`
14×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`associate-/l/_binary64`
6×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 422

Calls

4 calls:

13.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
20.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
34.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
52.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
12.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
28.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
21.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

simplify97.0ms

Algorithm

egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4963	8383
1	4963	8383

prune349.0ms

Filtered

187 candidates to 434 candidates (-132.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	430	4	434
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	436	9	445

Merged error: 0.0b

Counts

445 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
0.2b	(/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
0.2b	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
0.5b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))

rewrite383.0ms

Algorithm

rewrite-expression-head

Rules

2378×	`*-un-lft-identity_binary64`
2005×	`times-frac_binary64`
1840×	`sqrt-prod_binary64`
907×	`distribute-lft-out_binary64`
818×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
502×	`associate-r_binary64`
94×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
70×	`associate-/l*_binary64`
42×	`associate-/r/_binary64` `sqrt-div_binary64`
38×	`cbrt-undiv_binary64` `div-exp_binary64`
30×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
21×	`associate-/r*_binary64` `div-inv_binary64`
18×	`frac-times_binary64` `associate-*l/_binary64`
14×	`associate-/l/_binary64`
9×	`pow1_binary64`
6×	`associate-*r/_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-l_binary64` `*-commutative_binary64`

Counts

4 → 1268

Calls

4 calls:

76.0ms	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
39.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
114.0ms	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
15.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
9.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
25.0ms	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
10.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))

simplify256.0ms

Algorithm

egg-herbie

Counts

1280 → 1280

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4955	34300
1	4955	34300

prune1.0s

Filtered

315 candidates to 1280 candidates (-306.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1279	1	1280
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	1281	8	1289

Merged error: 0b

Counts

1289 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.2b	(.f64 (/.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
0.5b	(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.5b	(/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

1751×	`*-un-lft-identity_binary64`
1312×	`times-frac_binary64`
799×	`sqrt-prod_binary64`
730×	`distribute-lft-out_binary64`
528×	`add-sqr-sqrt_binary64`
504×	`add-cube-cbrt_binary64`
334×	`associate-r_binary64`
74×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
49×	`associate-/l*_binary64`
44×	`associate-/r/_binary64`
32×	`cbrt-undiv_binary64` `div-exp_binary64`
25×	`flip3-+_binary64` `flip-+_binary64`
22×	`div-inv_binary64`
21×	`associate-/r*_binary64`
20×	`cbrt-unprod_binary64` `prod-exp_binary64`
14×	`associate-l_binary64`
10×	`sqrt-div_binary64`
8×	`associate-/l/_binary64`
7×	`unswap-sqr_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-*l/_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 888

Calls

4 calls:

12.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
146.0ms	(.f64 (/.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
23.0ms	(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
30.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
23.0ms	(.f64 (/.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
22.0ms	(/.f64 (*.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
16.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

simplify193.0ms

Algorithm

egg-herbie

Counts

900 → 900

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4980	27315
1	4980	27315

prune814.0ms

Filtered

264 candidates to 900 candidates (-240.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	900	0	900
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	900	8	908

Merged error: 0b

Counts

908 → 8

regimes109.0ms

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

sample765.0ms

Algorithm

intervals

Results

489.0ms	8000×	body	80	valid
135.0ms	8000×	pre	80	true

Details

analyze7.0ms

sample27.0ms

simplify196.0ms

prune9.0ms

localize12.0ms

rewrite92.0ms

series64.0ms

simplify45.0ms

prune225.0ms

localize15.0ms

rewrite151.0ms

series68.0ms

simplify97.0ms

prune349.0ms

localize23.0ms

rewrite383.0ms

series76.0ms

simplify256.0ms

prune1.0s

localize17.0ms

rewrite301.0ms

series69.0ms

simplify193.0ms

prune814.0ms

regimes109.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample765.0ms

Profiling