Details

analyze778.0ms

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

sample59.0ms

Algorithm

intervals

Results

12.0ms	179×	body	128	valid
9.0ms	33×	body	1024	valid
8.0ms	22×	body	1024	nan
5.0ms	27×	body	512	nan
5.0ms	25×	body	512	valid
4.0ms	62×	body	128	nan
2.0ms	15×	body	256	valid
1.0ms	4×	body	2048	valid
1.0ms	7×	body	256	nan

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5188	41

prune2.0ms

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: 42.7b

Counts

2 → 1

localize17.0ms

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))))
0.4b	(*.f64 (sqrt.f64 2) t)
12.0b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.7b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite75.0ms

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:

23.0ms	(/.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)
20.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
17.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

826.0ms	(/.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))))
47.0ms	(*.f64 (sqrt.f64 2) t)
334.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
1.6s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify50.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5200	3052

prune161.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	5	92

Merged error: 6.2b

Counts

92 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

2.4b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.5b	(/.f64 (*.f64 l l) x)
11.0b	(/.f64 (*.f64 t t) x)
27.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite38.0ms

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:

10.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
6.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
23.0ms	(/.f64 (*.f64 l l) x)
24.0ms	(/.f64 (*.f64 t t) x)
176.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5094	1977

prune112.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 3.7b

Counts

91 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
2.4b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
11.0b	(/.f64 (*.f64 t t) x)
27.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite45.0ms

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:

14.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
10.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
6.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
88.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
24.0ms	(/.f64 (*.f64 t t) x)
183.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5556	2011

prune95.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	76	10	86

Merged error: 3.7b

Counts

86 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

11.0b	(/.f64 (*.f64 t t) x)
11.0b	(/.f64 (*.f64 t t) x)
27.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
27.8b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64` `sqrt-div_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `times-frac_binary64` `sqrt-prod_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_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 → 76

Calls

4 calls:

6.0ms	(/.f64 (*.f64 t t) x)
6.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/.f64 (*.f64 t t) x)
23.0ms	(/.f64 (*.f64 t t) x)
174.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
161.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5045	2092

prune122.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	88	10	98

Merged error: 3.7b

Counts

98 → 10

regimes365.0ms

Accuracy

75.8% (5.8b remaining)

Error of 9.8b against oracle of 4.0b and baseline of 27.8b

bsearch468.0ms

Steps

Iters	Range		Point
7	2.1946163447053796e+48	1.1089481570130598e+50	1.0881803445765273e+50
4	8.002023907450636e-191	1.4495807641258422e-190	8.153802402658137e-191
10	5.675501349958206e-275	8.899859996089583e-265	8.817897027101529e-265
6	-6.070314333612724e-255	-1.1906185304380097e-255	-5.993496914647807e-255
8	-2.6388454601179834e-217	-1.3456202284215646e-220	-1.3645280228316457e-220
7	-6.777044855912082e+154	-1.6799548218599265e+153	-2.5410633816086304e+153

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	167	312
1	167	312

end0.0ms

sample1.7s

Algorithm

intervals

Results

374.0ms	5358×	body	128	valid
307.0ms	1126×	body	1024	valid
209.0ms	788×	body	1024	nan
184.0ms	905×	body	512	valid
100.0ms	1497×	body	128	nan
99.0ms	488×	body	512	nan
77.0ms	540×	body	256	valid
37.0ms	277×	body	256	nan
25.0ms	71×	body	2048	valid

Details

analyze778.0ms

sample59.0ms

simplify83.0ms

prune2.0ms

localize17.0ms

rewrite75.0ms

series2.8s

simplify50.0ms

prune161.0ms

localize16.0ms

rewrite38.0ms

series312.0ms

simplify47.0ms

prune112.0ms

localize16.0ms

rewrite45.0ms

series351.0ms

simplify47.0ms

prune95.0ms

localize24.0ms

rewrite42.0ms

series381.0ms

simplify42.0ms

prune122.0ms

regimes365.0ms

bsearch468.0ms

simplify6.0ms

end0.0ms

sample1.7s

Profiling