Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

sample73.0ms

Algorithm

intervals

Results

57.0ms	185×	body	1280	valid
6.0ms	34×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	5×	body	80	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5718	8

prune8.0ms

Filtered

1 candidates to 1 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: 28.1b

Counts

2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp (neg x)) 2.0)
5.5b	(+ (exp x) (- (exp (neg x)) 2.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `associate-+r+` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

2 → 29

Calls

2 calls:

5.0ms	(- (exp (neg x)) 2.0)
7.0ms	(+ (exp x) (- (exp (neg x)) 2.0))

series9.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(- (exp (neg x)) 2.0)
7.0ms	(+ (exp x) (- (exp (neg x)) 2.0))

simplify33.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5187	335

prune58.0ms

Filtered

25 candidates to 35 candidates (-40.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	35	2	37

Merged error: 0.0b

Counts

37 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

5.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
7.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series24.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
5.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
4.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5022	849

prune127.0ms

Filtered

56 candidates to 86 candidates (-53.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Merged error: 0.0b

Counts

88 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
0.0b	(+ (* x x) (* 1/360 (pow x 6)))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

7.0ms	(+ (+ (* x x) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
4.0ms	(+ (* x x) (* 1/360 (pow x 6)))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (+ (* x x) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
11.0ms	(+ (* x x) (* 1/360 (pow x 6)))
4.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify36.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4849	821
1	4849	821

prune119.0ms

Filtered

54 candidates to 86 candidates (-59.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Merged error: 0.0b

Counts

89 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
30.4b	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))
30.4b	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`pow1` `associate-l` `prod-exp` `sqrt-prod` `unswap-sqr`
4×	`sqrt-div` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
7.0ms	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))
7.0ms	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 1/12 (pow x 4))
3.0ms	(* 1/12 (pow x 4))
7.0ms	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))
7.0ms	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))

simplify36.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5202	1124

prune211.0ms

Filtered

64 candidates to 92 candidates (-43.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Merged error: 0.0b

Counts

95 → 3

regimes31.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.8s	5637×	body	1280	valid
230.0ms	1265×	body	640	valid
71.0ms	630×	body	320	valid
22.0ms	293×	body	160	valid
7.0ms	175×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample73.0ms

simplify42.0ms

prune8.0ms

localize7.0ms

rewrite13.0ms

series9.0ms

simplify33.0ms

prune58.0ms

localize10.0ms

rewrite24.0ms

series24.0ms

simplify54.0ms

prune127.0ms

localize10.0ms

rewrite23.0ms

series25.0ms

simplify36.0ms

prune119.0ms

localize14.0ms

rewrite25.0ms

series21.0ms

simplify36.0ms

prune211.0ms

regimes31.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling