Details

analyze820.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample74.0ms

Algorithm

intervals

Results

12.0ms	162×	body	80	valid
11.0ms	30×	body	1280	valid
9.0ms	33×	body	640	valid
7.0ms	22×	body	1280	nan
6.0ms	24×	body	640	nan
4.0ms	18×	body	320	valid
3.0ms	42×	body	80	nan
2.0ms	12×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	6×	body	160	nan

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5619	41

prune5.0ms

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: 41.4b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.5b	(*.f64 (sqrt.f64 2) t)
14.0b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
18.1b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

20.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
5.0ms	(*.f64 (sqrt.f64 2) t)
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
15.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

series1.4s

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
27.0ms	(*.f64 (sqrt.f64 2) t)
185.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
765.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify81.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5015	3136

prune316.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 6.9b

Counts

92 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

3.3b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
7.6b	(/.f64 (*.f64 l l) x)
9.9b	(/.f64 (*.f64 t t) x)
23.7b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
17.0ms	(/.f64 (*.f64 l l) x)
14.0ms	(/.f64 (*.f64 t t) x)
91.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5098	1977

prune307.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	81	9	90

Merged error: 3.3b

Counts

90 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
3.3b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
9.9b	(/.f64 (*.f64 t t) x)
23.7b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `associate-*r/_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 64

Calls

4 calls:

9.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
5.0ms	(/.f64 (*.f64 t t) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
47.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
13.0ms	(/.f64 (*.f64 t t) x)
99.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5079	2011

prune290.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	74	11	85

Merged error: 3.3b

Counts

85 → 11

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
3.3b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
9.9b	(/.f64 (*.f64 t t) x)
23.7b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `associate-*r/_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 64

Calls

4 calls:

5.0ms	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
5.0ms	(/.f64 (*.f64 t t) x)
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
61.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
13.0ms	(/.f64 (*.f64 t t) x)
103.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

simplify85.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5100	2756

prune245.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	76	11	87

Merged error: 3.3b

Counts

87 → 11

regimes795.0ms

Accuracy

76.7% (5.5b remaining)

Error of 9.5b against oracle of 4.0b and baseline of 27.6b

bsearch142.0ms

Steps

Iters	Range	Point
7	2974852220661734812024155254206981675538609928211526424442567448449041614857579459044590941877829632	78748982520585484392207179779351855520035333309576731986455825441592238245618253829796635506477367296	7.744619413220778e+100
8	-1869068666331476538581696554508265724266108753546651966814935054509416553716294206236267138927498102422593290700089982976	-5295997076727627242348001860181944625269574016304936772170817746101251367341097167482424898452824441082528981965602816	-1.8055396062121203e+120

Iters

Range

Point

2974852220661734812024155254206981675538609928211526424442567448449041614857579459044590941877829632

78748982520585484392207179779351855520035333309576731986455825441592238245618253829796635506477367296

7.744619413220778e+100

-1869068666331476538581696554508265724266108753546651966814935054509416553716294206236267138927498102422593290700089982976

-5295997076727627242348001860181944625269574016304936772170817746101251367341097167482424898452824441082528981965602816

-1.8055396062121203e+120

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	207	168
1	207	168

end0.0ms

sample2.1s

Algorithm

intervals

Results

387.0ms	5047×	body	80	valid
316.0ms	868×	body	1280	valid
297.0ms	1073×	body	640	valid
214.0ms	589×	body	1280	nan
158.0ms	578×	body	640	nan
142.0ms	654×	body	320	valid
110.0ms	1492×	body	80	nan
75.0ms	365×	body	320	nan
51.0ms	358×	body	160	valid
28.0ms	204×	body	160	nan

Details

analyze820.0ms

sample74.0ms

simplify112.0ms

prune5.0ms

localize27.0ms

rewrite57.0ms

series1.4s

simplify81.0ms

prune316.0ms

localize29.0ms

rewrite28.0ms

series168.0ms

simplify74.0ms

prune307.0ms

localize26.0ms

rewrite33.0ms

series190.0ms

simplify62.0ms

prune290.0ms

localize38.0ms

rewrite28.0ms

series217.0ms

simplify85.0ms

prune245.0ms

regimes795.0ms

bsearch142.0ms

simplify7.0ms

end0.0ms

sample2.1s

Profiling