Details

analyze2.2s

Algorithm

Search

True	Other	False	Iter
0%	99.5%	0.5%	0
0%	99.5%	0.5%	1
0%	99.5%	0.5%	2
0%	99.5%	0.5%	3
0%	99.5%	0.5%	4
0%	99.5%	0.5%	5
0%	99.5%	0.5%	6
0%	99.5%	0.5%	7
0%	99.5%	0.5%	8
0%	99.5%	0.5%	9
0%	99.5%	0.5%	10
0%	99.5%	0.5%	11
0%	99.5%	0.5%	12
0%	99.5%	0.5%	13
0%	99.5%	0.5%	14

sample82.0ms

Algorithm

intervals

Results

25.0ms	233×	body	80	invalid
22.0ms	256×	body	80	valid

simplify324.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (321.0ms)

Iter	Nodes	Cost
0	3063	29
1	3063	29

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 5.3b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x 18) y)
0.2b	(.f64 (.f64 j 27) k)
2.4b	(.f64 t (-.f64 (.f64 (.f64 (.f64 x 18) y) z) (*.f64 a 4)))
6.5b	(.f64 (.f64 (*.f64 x 18) y) z)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-r_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip--_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(.f64 (.f64 x 18) y)
8.0ms	(.f64 (.f64 j 27) k)
11.0ms	(.f64 t (-.f64 (.f64 (.f64 (.f64 x 18) y) z) (*.f64 a 4)))
7.0ms	(.f64 (.f64 (*.f64 x 18) y) z)

series42.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 x 18) y)
4.0ms	(.f64 (.f64 j 27) k)
27.0ms	(.f64 t (-.f64 (.f64 (.f64 (.f64 x 18) y) z) (*.f64 a 4)))
7.0ms	(.f64 (.f64 (*.f64 x 18) y) z)

simplify46.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5163	786

prune130.0ms

Filtered

51 candidates to 91 candidates (-78.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	81	10	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 2.4b

Counts

92 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 b c) (+.f64 (.f64 (.f64 x 4) i) (.f64 (*.f64 j 27) k)))
0.2b	(.f64 (.f64 j 27) k)
2.4b	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
3.8b	(.f64 (.f64 x 18) (*.f64 y z))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
5×	`associate-l_binary64`
3×	`sub-neg_binary64` `*-commutative_binary64`
2×	`flip3--_binary64` `diff-log_binary64` `associate-*r/_binary64` `flip--_binary64`
1×	`associate--r+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(-.f64 (.f64 b c) (+.f64 (.f64 (.f64 x 4) i) (.f64 (*.f64 j 27) k)))
7.0ms	(.f64 (.f64 j 27) k)
10.0ms	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
7.0ms	(.f64 (.f64 x 18) (*.f64 y z))

series65.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(-.f64 (.f64 b c) (+.f64 (.f64 (.f64 x 4) i) (.f64 (*.f64 j 27) k)))
4.0ms	(.f64 (.f64 j 27) k)
27.0ms	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
7.0ms	(.f64 (.f64 x 18) (*.f64 y z))

simplify66.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4922	984
1	4922	984

prune112.0ms

Filtered

50 candidates to 87 candidates (-74.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 2.4b

Counts

97 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 b c) (+.f64 (.f64 x (.f64 i -4)) (.f64 (*.f64 j k) -27)))
0.3b	(.f64 (.f64 j k) -27)
2.4b	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
3.8b	(.f64 (.f64 x 18) (*.f64 y z))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
5×	`associate-l_binary64`
3×	`sum-log_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 75

Calls

4 calls:

9.0ms	(+.f64 (.f64 b c) (+.f64 (.f64 x (.f64 i -4)) (.f64 (*.f64 j k) -27)))
8.0ms	(.f64 (.f64 j k) -27)
18.0ms	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
10.0ms	(.f64 (.f64 x 18) (*.f64 y z))

series67.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+.f64 (.f64 b c) (+.f64 (.f64 x (.f64 i -4)) (.f64 (*.f64 j k) -27)))
4.0ms	(.f64 (.f64 j k) -27)
29.0ms	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
7.0ms	(.f64 (.f64 x 18) (*.f64 y z))

simplify39.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4997	973
1	4997	973

prune101.0ms

Filtered

52 candidates to 87 candidates (-67.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	87	10	97

Merged error: 2.4b

Counts

97 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 b c) (+.f64 (.f64 (.f64 x 4) i) (.f64 j (*.f64 27 k))))
0.2b	(.f64 j (.f64 27 k))
2.4b	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
3.8b	(.f64 (.f64 x 18) (*.f64 y z))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
5×	`associate-r_binary64`
3×	`sub-neg_binary64` `*-commutative_binary64`
2×	`flip3--_binary64` `diff-log_binary64` `associate-*r/_binary64` `flip--_binary64`
1×	`associate--r+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(-.f64 (.f64 b c) (+.f64 (.f64 (.f64 x 4) i) (.f64 j (*.f64 27 k))))
5.0ms	(.f64 j (.f64 27 k))
10.0ms	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
7.0ms	(.f64 (.f64 x 18) (*.f64 y z))

series68.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(-.f64 (.f64 b c) (+.f64 (.f64 (.f64 x 4) i) (.f64 j (*.f64 27 k))))
4.0ms	(.f64 j (.f64 27 k))
27.0ms	(.f64 t (-.f64 (.f64 (.f64 x 18) (.f64 y z)) (*.f64 a 4)))
7.0ms	(.f64 (.f64 x 18) (*.f64 y z))

simplify64.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4955	983
1	4955	983

prune55.0ms

Filtered

52 candidates to 87 candidates (-67.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	87	10	97

Merged error: 2.4b

Counts

97 → 10

regimes2.0s

Accuracy

4.4% (3.8b remaining)

Error of 6.1b against oracle of 2.3b and baseline of 6.3b

bsearch98.0ms

Steps

Iters	Range		Point
7	1.15319379399089e+190	3.699429439761681e+191	8.041172976488391e+190
7	-4.0343268257014016e-196	-5.407724112541692e-198	-2.8289816114260935e-196

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	221	95
1	221	95

end0.0ms

sample2.3s

Algorithm

intervals

Results

723.0ms	8144×	body	80	invalid
695.0ms	8000×	body	80	valid

Details

analyze2.2s

sample82.0ms

simplify324.0ms

prune12.0ms

localize20.0ms

rewrite33.0ms

series42.0ms

simplify46.0ms

prune130.0ms

localize21.0ms

rewrite34.0ms

series65.0ms

simplify66.0ms

prune112.0ms

localize21.0ms

rewrite47.0ms

series67.0ms

simplify39.0ms

prune101.0ms

localize24.0ms

rewrite32.0ms

series68.0ms

simplify64.0ms

prune55.0ms

regimes2.0s

bsearch98.0ms

simplify4.0ms

end0.0ms

sample2.3s

Profiling