Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample31.0ms

Algorithm

intervals

Results

6.0ms	189×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	24×	body	1280	valid
3.0ms	24×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	7×	body	160	valid

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4804	19
1	4804	19

prune11.0ms

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: 15.8b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.1b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_3784`
26×	`add-sqr-sqrt_binary64_3769`
25×	`times-frac_binary64_3779`
19×	`distribute-lft-out_binary64_3828`
14×	`add-cube-cbrt_binary64_3755`
6×	`difference-of-squares_binary64_3813` `distribute-lft-out--_binary64_3829`
5×	`associate-/r_binary64_3847` `associate-/l_binary64_3848`
4×	`add-exp-log_binary64_3748` `add-log-exp_binary64_3749` `add-cbrt-cube_binary64_3756`
2×	`associate-/l/_binary64_3850` `pow1_binary64_3730` `div-sub_binary64_3778` `flip-+_binary64_3809` `flip3-+_binary64_3782` `associate-/r/_binary64_3849`
1×	`+-commutative_binary64_3851` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `associate-+l-_binary64_3838` `div-inv_binary64_3785` `flip3--_binary64_3783` `flip--_binary64_3810` `cbrt-undiv_binary64_3754` `div-exp_binary64_3737` `sum-log_binary64_3699`

Counts

2 → 65

Calls

2 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
23.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series73.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
46.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

simplify80.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5082	1488

prune280.0ms

Filtered

47 candidates to 71 candidates (-51.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 15.1b

Counts

72 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
2.1b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64_3784`
40×	`add-sqr-sqrt_binary64_3769`
34×	`times-frac_binary64_3779`
24×	`distribute-lft-out_binary64_3828` `add-cube-cbrt_binary64_3755`
11×	`add-log-exp_binary64_3749`
10×	`associate-/r*_binary64_3847`
8×	`add-exp-log_binary64_3748` `add-cbrt-cube_binary64_3756`
6×	`difference-of-squares_binary64_3813` `associate-/l*_binary64_3848`
4×	`pow1_binary64_3730` `distribute-lft-out--_binary64_3829` `diff-log_binary64_3700` `associate-/r/_binary64_3849`
3×	`flip3--_binary64_3783` `flip--_binary64_3810` `sub-neg_binary64_3788`
2×	`frac-sub_binary64_3775` `difference-of-sqr-1_binary64_3814` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `div-inv_binary64_3785` `cbrt-undiv_binary64_3754` `flip-+_binary64_3809` `div-exp_binary64_3737` `flip3-+_binary64_3782`
1×	`associate--r+_binary64_3839` `associate--r-_binary64_3842`

Counts

4 → 112

Calls

4 calls:

30.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
7.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
21.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

series149.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
26.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
27.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
55.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

simplify81.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6083	2582

prune489.0ms

Filtered

85 candidates to 124 candidates (-45.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	115	9	124
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Merged error: 3.5b

Counts

135 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.0b	(/.f64 (+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
0.1b	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
2.0b	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity_binary64_3784`
58×	`times-frac_binary64_3779`
47×	`add-sqr-sqrt_binary64_3769`
42×	`add-cube-cbrt_binary64_3755`
33×	`distribute-lft-out_binary64_3828`
21×	`cube-prod_binary64_3757` `associate-l_binary64_3844` `unpow-prod-down_binary64_3719`
14×	`add-exp-log_binary64_3748` `add-cbrt-cube_binary64_3756`
8×	`flip-+_binary64_3809` `flip3-+_binary64_3782` `associate-/r/_binary64_3849`
7×	`pow1_binary64_3730`
6×	`add-log-exp_binary64_3749`
4×	`div-inv_binary64_3785` `associate-/l_binary64_3848` `associate-r*_binary64_3843`
3×	`associate-/r*_binary64_3847` `pow-unpow_binary64_3717` `cbrt-undiv_binary64_3754` `div-exp_binary64_3737`
2×	`associate-/l/_binary64_3850` `cbrt-unprod_binary64_3753` `prod-exp_binary64_3735` `rem-cube-cbrt_binary64_3760` `frac-times_binary64_3776` `unswap-sqr_binary64_3812` `associate-*r/_binary64_3845` `pow-exp_binary64_3708`
1×	`+-commutative_binary64_3851` `-commutative_binary64_3852` `sqr-pow_binary64_3816` `clear-num_binary64_3787` `frac-2neg_binary64_3777` `associate-l/_binary64_3846` `pow-to-exp_binary64_3709` `pow-prod-down_binary64_3711` `distribute-lft-in_binary64_3826` `pow-pow_binary64_3712` `cube-div_binary64_3758` `unpow3_binary64_3728` `cube-mult_binary64_3759` `sum-log_binary64_3699` `distribute-rgt-in_binary64_3827`

Counts

4 → 156

Calls

4 calls:

25.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
24.0ms	(/.f64 (+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
10.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
26.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))

series329.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
136.0ms	(/.f64 (+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)) (+.f64 1 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
54.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
81.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))

simplify87.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5686	5333

prune859.0ms

Filtered

103 candidates to 168 candidates (-63.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	168	10	178

Merged error: 3.5b

Counts

178 → 10

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
2.0b	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
2.0b	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
2.0b	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64_3784`
30×	`times-frac_binary64_3779`
23×	`add-sqr-sqrt_binary64_3769` `add-cube-cbrt_binary64_3755`
21×	`cube-prod_binary64_3757` `distribute-lft-out_binary64_3828` `unpow-prod-down_binary64_3719`
10×	`add-log-exp_binary64_3749`
7×	`add-exp-log_binary64_3748` `add-cbrt-cube_binary64_3756`
5×	`pow1_binary64_3730` `flip-+_binary64_3809` `flip3-+_binary64_3782`
4×	`associate-/r/_binary64_3849`
3×	`+-commutative_binary64_3851` `pow-unpow_binary64_3717` `sum-log_binary64_3699`
2×	`div-inv_binary64_3785` `rem-cube-cbrt_binary64_3760` `pow-exp_binary64_3708`
1×	`sqr-pow_binary64_3816` `pow-to-exp_binary64_3709` `cbrt-undiv_binary64_3754` `pow-pow_binary64_3712` `div-exp_binary64_3737` `cube-div_binary64_3758` `unpow3_binary64_3728` `cube-mult_binary64_3759`

Counts

4 → 98

Calls

4 calls:

13.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
19.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
19.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
20.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))

series300.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
80.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
83.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))
83.0ms	(+.f64 -1 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3))

simplify101.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4948	2232
1	4948	2232

prune559.0ms

Filtered

63 candidates to 110 candidates (-74.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Merged error: 3.4b

Counts

120 → 10

regimes258.0ms

Accuracy

72.3% (3.4b remaining)

Error of 6.5b against oracle of 3.1b and baseline of 15.4b

bsearch29.0ms

Steps

Iters	Range		Point
8	65236927464182540817924096	1082748383432863404762024902656	6.629639534794314e+25

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	226	76
1	226	76

end0.0ms

sample797.0ms

Algorithm

intervals

Results

195.0ms	5879×	body	80	valid
135.0ms	8000×	pre	80	true
134.0ms	822×	body	1280	valid
93.0ms	738×	body	640	valid
33.0ms	350×	body	320	valid
13.0ms	211×	body	160	valid

Details

analyze2.0ms

sample31.0ms

simplify107.0ms

prune11.0ms

localize13.0ms

rewrite37.0ms

series73.0ms

simplify80.0ms

prune280.0ms

localize15.0ms

rewrite70.0ms

series149.0ms

simplify81.0ms

prune489.0ms

localize25.0ms

rewrite95.0ms

series329.0ms

simplify87.0ms

prune859.0ms

localize45.0ms

rewrite74.0ms

series300.0ms

simplify101.0ms

prune559.0ms

regimes258.0ms

bsearch29.0ms

simplify6.0ms

end0.0ms

sample797.0ms

Profiling