Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	82×	body	1280	valid
4.0ms	37×	body	640	valid
4.0ms	184×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	15×	body	160	valid

simplify60.0ms

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: 27.8b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.6b	(- (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)

series51.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(exp (* a x))
35.0ms	(- (exp (* a x)) 1.0)

simplify184.0ms

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

prune30.0ms

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: 8.3b

Counts

13 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
11.3b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
17.8b	(* (pow a 2) (pow x 2))
18.8b	(* (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))

series328.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
106.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
37.0ms	(* (pow a 2) (pow x 2))
66.0ms	(* (pow a 3) (pow x 3))

simplify73.0ms

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

prune99.0ms

Filtered

33 candidates to 21 candidates (63.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	32	5	37

Merged error: 4.4b

Counts

37 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/6 (pow (* x a) 3) (* a x))
0.3b	(pow (* x a) 3)
11.3b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
17.8b	(* (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))

series439.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
47.0ms	(pow (* x a) 3)
94.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
33.0ms	(* (pow a 2) (pow x 2))

simplify77.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (74.0ms)

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

prune75.0ms

Filtered

30 candidates to 19 candidates (63.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	32	3	35

Merged error: 0.0b

Counts

35 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/6 (pow (* x a) 3) (* a x))
0.3b	(* (* x a) (* x a))
0.3b	(pow (* x a) 3)
11.3b	(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))
4.0ms	(* (* x a) (* x a))
2.0ms	(pow (* x a) 3)
1.0ms	(fma 1/2 (* (* x a) (* x a)) (fma 1/6 (pow (* x a) 3) (* a x)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(fma 1/6 (pow (* x a) 3) (* a x))
30.0ms	(* (* x a) (* x a))
46.0ms	(pow (* x a) 3)
87.0ms	(fma 1/2 (* (* x a) (* x a)) (fma 1/6 (pow (* x a) 3) (* a x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (39.0ms)

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

prune59.0ms

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	1	0	1
Picked	0	1	1
Done	0	1	1
Total	27	3	30

Merged error: 0.0b

Counts

30 → 3

regimes118.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	12

end0.0ms

sample933.0ms

Algorithm

intervals

Results

429.0ms	2664×	body	1280	valid
130.0ms	1278×	body	640	valid
112.0ms	5498×	body	80	valid
57.0ms	791×	body	320	valid
18.0ms	394×	body	160	valid