Details

analyze41.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

sample34.0ms

Algorithm

intervals

Results

17.0ms	97×	body	1280	valid
6.0ms	48×	body	640	valid
2.0ms	78×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	9×	body	160	valid
0.0ms	4×	body	80	invalid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4934	6
1	4934	6

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: 32.1b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

2.9b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `difference-of-sqr-1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

1 → 15

Calls

1 calls:

4.0ms

(-.f64 (exp.f64 (*.f64 a x)) 1)

series8.0ms

Counts

1 → 3

Calls

1 calls:

8.0ms

(-.f64 (exp.f64 (*.f64 a x)) 1)

simplify50.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5023	180

prune20.0ms

Filtered

12 candidates to 18 candidates (-50.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	14	4	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	15	4	19

Merged error: 3.9b

Counts

19 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
4.7b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
5.0b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.8b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

6.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
9.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
12.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
26.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
10.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify33.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5186	1359

prune60.0ms

Filtered

54 candidates to 86 candidates (-59.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Merged error: 2.2b

Counts

90 → 6

localize8.0ms

Local error

Found 2 expressions with local error:

3.4b	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
14.8b	(.f64 (.f64 a a) (*.f64 x x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1_binary64`
14×	`pow-prod-down_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `pow-plus_binary64`
2×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `pow-sqr_binary64` `pow2_binary64`
1×	`flip3-+_binary64` `associate-r_binary64` `associate-l_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 40

Calls

2 calls:

6.0ms	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
9.0ms	(.f64 (.f64 a a) (*.f64 x x))

series21.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(+.f64 (.f64 a x) (.f64 1/2 (.f64 (.f64 a a) (*.f64 x x))))
8.0ms	(.f64 (.f64 a a) (*.f64 x x))

simplify60.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4962	350
1	4962	350

prune27.0ms

Filtered

27 candidates to 46 candidates (-70.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	49	3	52

Merged error: 0.1b

Counts

52 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b	(pow.f64 (*.f64 a x) 2)
3.4b	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2×	`pow-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `unpow2_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

2 → 29

Calls

2 calls:

4.0ms	(pow.f64 (*.f64 a x) 2)
5.0ms	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))

series18.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(pow.f64 (*.f64 a x) 2)
13.0ms	(+.f64 (.f64 a x) (.f64 1/2 (pow.f64 (*.f64 a x) 2)))

simplify47.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5002	302

prune16.0ms

Filtered

22 candidates to 35 candidates (-59.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Merged error: 0.1b

Counts

38 → 3

regimes136.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.9b

bsearch10.0ms

Steps

Iters	Range		Point
9	-0.0063545529067028875	-3.4571071941180306e-11	-4.5898218916979556e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	32
1	25	32

end0.0ms

sample916.0ms

Algorithm

intervals

Results

457.0ms	2672×	body	1280	valid
150.0ms	1320×	body	640	valid
67.0ms	2836×	body	80	valid
61.0ms	763×	body	320	valid
26.0ms	409×	body	160	valid
5.0ms	129×	body	80	invalid

Details

analyze41.0ms

sample34.0ms

simplify38.0ms

prune2.0ms

localize8.0ms

rewrite5.0ms

series8.0ms

simplify50.0ms

prune20.0ms

localize12.0ms

rewrite34.0ms

series73.0ms

simplify33.0ms

prune60.0ms

localize8.0ms

rewrite16.0ms

series21.0ms

simplify60.0ms

prune27.0ms

localize6.0ms

rewrite9.0ms

series18.0ms

simplify47.0ms

prune16.0ms

regimes136.0ms

bsearch10.0ms

simplify2.0ms

end0.0ms

sample916.0ms

Profiling