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

sample33.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify294.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (285.0ms)

Iter	Nodes	Cost
0	5024	37

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: 0.9b

Counts

2 → 2

localize22.0ms

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)))
7.8b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.7b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite91.0ms

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))
27.0ms	(/.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)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
124.0ms	(/.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)))
94.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
50.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

simplify105.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4942	3970
1	4942	3970

prune203.0ms

Filtered

111 candidates to 170 candidates (-53.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	9	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	162	10	172

Merged error: 0b

Counts

172 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

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:

11.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
10.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
33.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
31.0ms	(/.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)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
28.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
85.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
101.0ms	(/.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)))

simplify107.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4947	5499
1	4947	5499

prune200.0ms

Filtered

130 candidates to 214 candidates (-64.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	216	8	224

Merged error: 0b

Counts

224 → 8

localize17.0ms

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)))
7.8b	(.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))))

rewrite56.0ms

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)))
35.0ms	(.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))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt.f64 (+.f64 beta 1))
26.0ms	(cbrt.f64 (+.f64 beta 1))
26.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
97.0ms	(.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))))

simplify91.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4921	2606
1	4921	2606

prune174.0ms

Filtered

92 candidates to 133 candidates (-44.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	133	8	141

Merged error: 0b

Counts

141 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.1b	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
0.5b	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

1158×	`*-un-lft-identity_binary64`
821×	`times-frac_binary64`
492×	`distribute-lft-out_binary64`
343×	`add-sqr-sqrt_binary64`
306×	`add-cube-cbrt_binary64`
279×	`sqrt-prod_binary64`
214×	`associate-l_binary64`
61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
44×	`associate-/r/_binary64`
31×	`associate-/l*_binary64`
29×	`cbrt-undiv_binary64` `div-exp_binary64`
26×	`associate-r_binary64`
23×	`flip3-+_binary64` `flip-+_binary64`
22×	`div-inv_binary64`
21×	`associate-/r*_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`unswap-sqr_binary64`
6×	`associate-/l/_binary64` `pow1_binary64` `sqrt-div_binary64`
4×	`add-log-exp_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 → 624

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
50.0ms	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
110.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
25.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
96.0ms	(/.f64 (*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
101.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
49.0ms	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

simplify249.0ms

Algorithm

egg-herbie

Counts

636 → 636

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4980	25803
1	4980	25803

prune699.0ms

Filtered

251 candidates to 636 candidates (-153.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	636	0	636
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	636	8	644

Merged error: 0b

Counts

644 → 8

regimes41.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	37
1	25	37

end0.0ms

sample750.0ms

Algorithm

intervals

Results

480.0ms	8000×	body	80	valid
125.0ms	8000×	pre	80	true

Details

analyze4.0ms

sample33.0ms

simplify294.0ms

prune9.0ms

localize22.0ms

rewrite91.0ms

series285.0ms

simplify105.0ms

prune203.0ms

localize15.0ms

rewrite94.0ms

series242.0ms

simplify107.0ms

prune200.0ms

localize17.0ms

rewrite56.0ms

series174.0ms

simplify91.0ms

prune174.0ms

localize15.0ms

rewrite253.0ms

series271.0ms

simplify249.0ms

prune699.0ms

regimes41.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample750.0ms

Profiling