Details

analyze793.0ms

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

sample66.0ms

Algorithm

intervals

Results

12.0ms	34×	body	640	valid
12.0ms	166×	body	80	valid
8.0ms	24×	body	1280	valid
5.0ms	18×	body	640	nan
4.0ms	22×	body	320	valid
4.0ms	11×	body	1280	nan
3.0ms	49×	body	80	nan
3.0ms	17×	body	320	nan
1.0ms	10×	body	160	valid
0.0ms	2×	body	160	nan

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5004	27

prune3.0ms

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: 44.5b

Counts

2 → 1

localize16.0ms

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)
13.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
22.9b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite58.0ms

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)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.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)
68.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
241.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

simplify63.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4974	2007
1	4974	2007

prune155.0ms

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: 6.3b

Counts

92 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

3.2b	(+.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)
10.4b	(/.f64 (*.f64 t t) x)
28.5b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite29.0ms

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)))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
4.0ms	(/.f64 (*.f64 l l) x)
4.0ms	(/.f64 (*.f64 t t) x)
34.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

simplify28.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5022	1324

prune124.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 3.2b

Counts

91 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
3.2b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
10.4b	(/.f64 (*.f64 t t) x)
28.5b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite29.0ms

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 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))))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
22.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
4.0ms	(/.f64 (*.f64 t t) x)
31.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

simplify28.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5126	1346

prune121.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	74	14	88

Merged error: 3.1b

Counts

88 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

10.4b	(/.f64 (*.f64 t t) x)
28.5b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))) (sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))))))
28.5b	(sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
28.5b	(sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-div_binary64`
18×	`associate-*r/_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
8×	`frac-add_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `times-frac_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

7.0ms	(/.f64 (*.f64 t t) x)
11.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))) (sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))))))
5.0ms	(sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
5.0ms	(sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/.f64 (*.f64 t t) x)
31.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (.f64 (sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))) (sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))))))
18.0ms	(sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))
18.0ms	(sqrt.f64 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4961	1589
1	4961	1589

prune88.0ms

Filtered

67 candidates to 86 candidates (-28.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	88	12	100

Merged error: 3.1b

Counts

100 → 12

regimes645.0ms

Accuracy

76.9% (5.6b remaining)

Error of 9.7b against oracle of 4.1b and baseline of 28.2b

bsearch477.0ms

Steps

Iters	Range		Point
8	6.906509369204707e+85	1.408300421472565e+89	1.38095966045702e+89
4	1.0034994831809399e-153	1.9855364651192827e-153	1.0218099834270248e-153
8	4.754042215846116e-224	1.293032107623262e-219	1.2726627814772679e-219
5	-9.547773202688461e-257	-2.612893485181745e-257	-9.353770347627324e-257
7	-1.4977081677011302e-198	-1.3050808961173902e-200	-1.3384093830115906e-200
10	-1.027771339857061e+129	-2.939521704848395e+114	-6.947129452840641e+124

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	165	246
1	165	246

end0.0ms

sample2.0s

Algorithm

intervals

Results

372.0ms	5082×	body	80	valid
296.0ms	871×	body	1280	valid
277.0ms	1034×	body	640	valid
210.0ms	617×	body	1280	nan
161.0ms	599×	body	640	nan
134.0ms	663×	body	320	valid
99.0ms	1416×	body	80	nan
74.0ms	383×	body	320	nan
47.0ms	350×	body	160	valid
25.0ms	189×	body	160	nan

Details

analyze793.0ms

sample66.0ms

simplify62.0ms

prune3.0ms

localize16.0ms

rewrite58.0ms

series429.0ms

simplify63.0ms

prune155.0ms

localize15.0ms

rewrite29.0ms

series60.0ms

simplify28.0ms

prune124.0ms

localize17.0ms

rewrite29.0ms

series68.0ms

simplify28.0ms

prune121.0ms

localize17.0ms

rewrite30.0ms

series71.0ms

simplify46.0ms

prune88.0ms

regimes645.0ms

bsearch477.0ms

simplify4.0ms

end0.0ms

sample2.0s

Profiling