Details

sample37.0ms

Algorithm

intervals

Results

14.0ms	88×	body	1280	valid
5.0ms	46×	body	640	valid
4.0ms	149×	body	80	valid
2.0ms	29×	body	320	valid
1.0ms	16×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	26	3
3	48	3
4	110	3
5	318	3
6	1623	3
7	5001	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: 31.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.9b	(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

2.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series45.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
33.0ms	(- (exp (* a x)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	115	135
1	333	127
2	1116	125
3	5001	125

prune68.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	25	5	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	6	31

Merged error: 10.6b

Counts

31 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

1.9b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
7.0b	(* (* 1/2 (pow a 2)) x)
10.8b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
18.7b	(* (pow a 3) (pow x 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
28×	`add-exp-log`
18×	`associate-r`
17×	`prod-exp` `unswap-sqr`
16×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
13×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`sqr-pow`
8×	`pow1`
7×	`pow-to-exp` `pow-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
3×	`pow-prod-down` `*-commutative`
2×	`distribute-rgt-in` `cube-mult` `associate-+l+` `distribute-lft-in` `flip3-+` `unpow3` `associate-*r/` `flip-+`
1×	`+-commutative` `sum-log`

Counts

4 → 113

Calls

4 calls:

5.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms	(* (* 1/2 (pow a 2)) x)
7.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
9.0ms	(* (pow a 3) (pow x 3))

series236.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
20.0ms	(* (* 1/2 (pow a 2)) x)
93.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
65.0ms	(* (pow a 3) (pow x 3))

simplify111.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	471	797
1	2758	738
2	5001	738

prune281.0ms

Filtered

125 candidates to 75 candidates (60.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	125	6	131

Merged error: 3.3b

Counts

131 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 (pow (* a x) 3))
1.9b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
7.0b	(* (* 1/2 (pow a 2)) x)
10.8b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
14×	`add-sqr-sqrt` `associate-r`
13×	`prod-exp` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
7×	`associate-l`
6×	`add-log-exp`
5×	`cbrt-unprod`
3×	`pow-exp` `*-commutative` `unswap-sqr`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-lft-in` `flip3-+` `associate-*r/` `pow-prod-down` `flip-+` `sqr-pow`
1×	`+-commutative` `cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sum-log`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* 1/6 (pow (* a x) 3))
5.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms	(* (* 1/2 (pow a 2)) x)
6.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* 1/6 (pow (* a x) 3))
58.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
24.0ms	(* (* 1/2 (pow a 2)) x)
92.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify80.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	407	580
1	2395	538
2	5001	538

prune197.0ms

Filtered

92 candidates to 61 candidates (66.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	92	6	98

Merged error: 0.2b

Counts

98 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a x) (* 1/6 (pow (* a x) 3)))
0.3b	(pow (* a x) 3)
0.3b	(* 1/6 (pow (* a x) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log`
9×	`add-sqr-sqrt`
8×	`associate-r` `add-cbrt-cube`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `prod-exp`
5×	`add-log-exp`
4×	`pow-exp`
3×	`pow-unpow` `associate-l` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

3 → 59

Calls

3 calls:

6.0ms	(+ (* a x) (* 1/6 (pow (* a x) 3)))
4.0ms	(pow (* a x) 3)
5.0ms	(* 1/6 (pow (* a x) 3))

series230.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(+ (* a x) (* 1/6 (pow (* a x) 3)))
49.0ms	(pow (* a x) 3)
76.0ms	(* 1/6 (pow (* a x) 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	200	286
1	1072	261
2	5002	260

prune95.0ms

Filtered

68 candidates to 44 candidates (64.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	67	7	74

Merged error: 0.2b

Counts

74 → 7

regimes199.0ms

Accuracy

96.6% (0.7b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 22.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	20
1	27	20

end0.0ms

sample1.0s

Algorithm

intervals

Results

483.0ms	2678×	body	1280	valid
150.0ms	1284×	body	640	valid
135.0ms	5524×	body	80	valid
61.0ms	785×	body	320	valid
22.0ms	412×	body	160	valid