Details

analyze68.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 24.298835%

Guaranteed chance to sample good point: 98.461538%

sample34.0ms

Algorithm

intervals

Results

16.0ms	77×	body	1280	valid
4.0ms	41×	body	640	valid
2.0ms	29×	body	320	valid
2.0ms	91×	body	80	valid
1.0ms	18×	body	160	valid
0.0ms	5×	body	80	invalid

simplify57.0ms

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

prune3.0ms

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: 30.3b

Counts

2 → 1

localize4.0ms

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:

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

series11.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(exp (* a x))
7.0ms	(- (exp (* a x)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

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

prune57.0ms

Filtered

20 candidates to 30 candidates (-50.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 6.6b

Counts

31 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.2b	(* (* 1/2 (pow a 2)) x)
12.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
17.8b	(* (pow a 3) (pow x 3))

rewrite32.0ms

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
4.0ms	(* (* 1/2 (pow a 2)) x)
18.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
10.0ms	(* (pow a 3) (pow x 3))

simplify104.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	471	797
1	2758	737
2	5001	737

prune200.0ms

Filtered

75 candidates to 125 candidates (-66.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	125	7	132

Merged error: 2.6b

Counts

132 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow a 2))
0.0b	(+ a (* (* 1/2 (pow a 2)) x))
1.4b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.2b	(* (* 1/2 (pow a 2)) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
18×	`add-sqr-sqrt`
14×	`associate-r`
13×	`add-cbrt-cube`
11×	`prod-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
7×	`associate-l`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down`
3×	`*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-prod-down` `pow-exp` `flip-+` `unpow2` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sum-log`

Counts

4 → 79

Calls

4 calls:

5.0ms	(* 1/2 (pow a 2))
2.0ms	(+ a (* (* 1/2 (pow a 2)) x))
5.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
5.0ms	(* (* 1/2 (pow a 2)) x)

series26.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 1/2 (pow a 2))
6.0ms	(+ a (* (* 1/2 (pow a 2)) x))
12.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
4.0ms	(* (* 1/2 (pow a 2)) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	317	462
1	1753	406
2	5002	404

prune116.0ms

Filtered

57 candidates to 91 candidates (-59.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	91	7	98

Merged error: 0.2b

Counts

98 → 7

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Merged error: 0.2b

Counts

7 → 7

regimes387.0ms

Accuracy

97.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 22.3b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7

end0.0ms

analyze71.0ms

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 24.298835%

Guaranteed chance to sample good point: 98.461538%

sample919.0ms

Algorithm

intervals

Results

468.0ms	2627×	body	1280	valid
149.0ms	1281×	body	640	valid
74.0ms	2941×	body	80	valid
58.0ms	759×	body	320	valid
21.0ms	392×	body	160	valid
2.0ms	63×	body	80	invalid

Details

analyze68.0ms

sample34.0ms

simplify57.0ms

prune3.0ms

localize4.0ms

rewrite6.0ms

series11.0ms

simplify39.0ms

prune57.0ms

localize14.0ms

rewrite32.0ms

series45.0ms

simplify104.0ms

prune200.0ms

localize7.0ms

rewrite20.0ms

series26.0ms

simplify58.0ms

prune116.0ms

localize2.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes387.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

analyze71.0ms

sample919.0ms

Profiling