Details

sample31.0ms

Algorithm

intervals

Results

14.0ms	89×	body	1280	valid
4.0ms	43×	body	640	valid
3.0ms	176×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	15×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1633	3
7	5002	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 30.3b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.4b	(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

2×	`exp-prod`
1×	`sub-neg` `flip3--` `*-commutative` `flip--`

Counts

2 → 6

Calls

2 calls:

2.0ms	(exp (* a x))
3.0ms	(- (exp (* a x)) 1.0)

series49.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
37.0ms	(- (exp (* a x)) 1.0)

simplify191.0ms

Algorithm

egg-herbie

Counts

12 → 12

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	98	52
1	291	50
2	999	48
3	4870	48
4	5001	48

prune29.0ms

Filtered

12 candidates to 7 candidates (58.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	9	3	12
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	9	4	13

Merged error: 8.5b

Counts

13 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
12.1b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
15.4b	(* (pow a 2) (pow x 2))
17.0b	(* (pow a 3) (pow x 3))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqr-pow`
6×	`unpow2`
5×	`unswap-sqr`
4×	`pow-to-exp` `associate-r` `associate-l`
2×	`unpow3` `pow-prod-down` `prod-exp` `*-commutative` `fma-udef`

Counts

4 → 21

Calls

4 calls:

1.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
1.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
4.0ms	(* (pow a 2) (pow x 2))
5.0ms	(* (pow a 3) (pow x 3))

series317.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
98.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
35.0ms	(* (pow a 2) (pow x 2))
63.0ms	(* (pow a 3) (pow x 3))

simplify69.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	103
1	380	103
2	2014	103
3	5002	103

prune87.0ms

Filtered

33 candidates to 21 candidates (63.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	33	4	37

Merged error: 5.3b

Counts

37 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (pow (* x a) 3) (* a x))
0.2b	(pow (* x a) 3)
12.1b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
15.4b	(* (pow a 2) (pow x 2))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`sqr-pow`
6×	`unpow2`
4×	`unswap-sqr`
3×	`pow-to-exp`
2×	`unpow-prod-down` `associate-r` `associate-l` `*-commutative` `fma-udef`
1×	`unpow3` `pow-prod-down` `prod-exp`

Counts

4 → 18

Calls

4 calls:

1.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
2.0ms	(pow (* x a) 3)
1.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
4.0ms	(* (pow a 2) (pow x 2))

series243.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
44.0ms	(pow (* x a) 3)
88.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
30.0ms	(* (pow a 2) (pow x 2))

simplify75.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	99	94
1	352	93
2	1997	90
3	5001	86

prune66.0ms

Filtered

30 candidates to 19 candidates (63.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	32	2	34

Merged error: 0.0b

Counts

34 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (pow (* x a) 3) (* a x))
0.2b	(pow (* x a) 3)
0.2b	(* (* x a) (* x a))
12.1b	(fma 1/2 (* (* x a) (* x a)) (fma 1/6 (pow (* x a) 3) (* a x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-commutative`
2×	`unpow-prod-down` `swap-sqr` `associate-r` `associate-l` `fma-udef`
1×	`pow2` `pow-to-exp` `unpow3` `sqr-pow`

Counts

4 → 15

Calls

4 calls:

1.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
2.0ms	(pow (* x a) 3)
4.0ms	(* (* x a) (* x a))
1.0ms	(fma 1/2 (* (* x a) (* x a)) (fma 1/6 (pow (* x a) 3) (* a x)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
41.0ms	(pow (* x a) 3)
34.0ms	(* (* x a) (* x a))
82.0ms	(fma 1/2 (* (* x a) (* x a)) (fma 1/6 (pow (* x a) 3) (* a x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	78	85
1	267	85
2	1149	81
3	5002	75

prune55.0ms

Filtered

27 candidates to 18 candidates (66.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Merged error: 0.0b

Counts

29 → 3

regimes130.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	12

end0.0ms

sample903.0ms

Algorithm

intervals

Results

437.0ms	2769×	body	1280	valid
124.0ms	1270×	body	640	valid
102.0ms	5431×	body	80	valid
46.0ms	738×	body	320	valid
20.0ms	428×	body	160	valid