Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	74.6%	25.4%	0
0%	74.6%	25.4%	1
37.3%	37.3%	25.4%	2
37.3%	18.7%	44%	3
46.7%	9.3%	44%	4
46.7%	4.7%	48.7%	5
49%	2.3%	48.7%	6
49%	1.2%	49.8%	7
49.6%	0.6%	49.8%	8
49.9%	0.3%	49.8%	9
49.9%	0.1%	50%	10
49.9%	0.1%	50.1%	11
49.9%	0%	50.1%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

sample38.0ms

Algorithm

intervals

Results

16.0ms	95×	body	1280	valid
8.0ms	86×	body	640	valid
3.0ms	44×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	24×	body	160	valid
0.0ms	7×	body	80	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4702	4
1	4702	4

prune6.0ms

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: 58.6b

Counts

2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

6.6b	(- (exp x) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 13

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

(- (exp x) 1.0)

simplify33.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4961	115
1	4961	115

prune41.0ms

Filtered

12 candidates to 16 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	12	4	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	4	17

Merged error: 0.1b

Counts

17 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* x (* x (+ 1/2 (* x 1/6)))))
0.0b	(* x (+ 1/2 (* x 1/6)))
0.0b	(* x (* x (+ 1/2 (* x 1/6))))
0.3b	(* x 1/6)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

4.0ms	(+ x (* x (* x (+ 1/2 (* x 1/6)))))
5.0ms	(* x (+ 1/2 (* x 1/6)))
6.0ms	(* x (* x (+ 1/2 (* x 1/6))))
3.0ms	(* x 1/6)

series18.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ x (* x (* x (+ 1/2 (* x 1/6)))))
6.0ms	(* x (+ 1/2 (* x 1/6)))
6.0ms	(* x (* x (+ 1/2 (* x 1/6))))
2.0ms	(* x 1/6)

simplify49.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4933	799
1	4933	799

prune105.0ms

Filtered

62 candidates to 91 candidates (-46.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	91	4	95

Merged error: 0.1b

Counts

95 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(pow (exp x) 2)
6.5b	(- (pow (exp x) 2) (* 1.0 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
28×	`times-frac`
24×	`difference-of-squares`
20×	`add-cube-cbrt`
9×	`unpow-prod-down` `distribute-lft-out`
8×	`add-log-exp`
7×	`associate-/l*` `unpow2` `sqr-pow`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`pow-pow` `associate-/r*`
3×	`pow-unpow` `exp-prod`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 104

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
10.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
3.0ms	(pow (exp x) 2)
5.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

series20.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ (exp x) 1.0)
10.0ms	(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
5.0ms	(pow (exp x) 2)
4.0ms	(- (pow (exp x) 2) (* 1.0 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5732	1315

prune145.0ms

Filtered

77 candidates to 116 candidates (-50.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0.1b

Counts

120 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2)
0.1b	(pow (exp x) 4)
0.1b	(pow (exp x) 6)
6.4b	(- (pow (exp x) 6) (pow 1.0 6))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`unpow-prod-down` `*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`pow-pow`
9×	`pow-unpow` `exp-prod` `difference-of-squares` `sqr-pow`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow-to-exp` `pow-exp`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `unpow2`

Counts

4 → 83

Calls

4 calls:

3.0ms	(pow (exp x) 2)
3.0ms	(pow (exp x) 4)
3.0ms	(pow (exp x) 6)
7.0ms	(- (pow (exp x) 6) (pow 1.0 6))

series21.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (exp x) 2)
5.0ms	(pow (exp x) 4)
6.0ms	(pow (exp x) 6)
8.0ms	(- (pow (exp x) 6) (pow 1.0 6))

simplify33.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5401	659

prune181.0ms

Filtered

60 candidates to 95 candidates (-58.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	95	4	99

Merged error: 0.0b

Counts

99 → 4

regimes86.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	11
1	31	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

557.0ms	3450×	body	1280	valid
248.0ms	2523×	body	640	valid
84.0ms	8001×	pre	80	true
78.0ms	1189×	body	320	valid
27.0ms	653×	body	160	valid
4.0ms	185×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze3.0ms

sample38.0ms

simplify63.0ms

prune6.0ms

localize3.0ms

rewrite5.0ms

series2.0ms

simplify33.0ms

prune41.0ms

localize8.0ms

rewrite20.0ms

series18.0ms

simplify49.0ms

prune105.0ms

localize8.0ms

rewrite25.0ms

series20.0ms

simplify51.0ms

prune145.0ms

localize19.0ms

rewrite19.0ms

series21.0ms

simplify33.0ms

prune181.0ms

regimes86.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling