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

sample76.0ms

Algorithm

intervals

Results

60.0ms	181×	body	1280	valid
6.0ms	37×	body	640	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	6×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	8
1	21	8

prune7.0ms

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: 28.3b

Counts

2 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.0b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `associate-+l+` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 33

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify56.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4965	424
1	4965	424

prune63.0ms

Filtered

28 candidates to 39 candidates (-39.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.0b

Counts

41 → 3

localize9.0ms

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))

rewrite21.0ms

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:

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

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4994	849
1	4994	849

prune130.0ms

Filtered

56 candidates to 86 candidates (-53.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Merged error: 0.0b

Counts

89 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
29.9b	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))
29.9b	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))

rewrite23.0ms

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))
5.0ms	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))
6.0ms	(sqrt (+ (* 1/12 (pow x 4)) (+ (* x x) (* 1/360 (pow x 6)))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/12 (pow x 4))
4.0ms	(* 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)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4931	1116
1	4931	1116

prune223.0ms

Filtered

64 candidates to 92 candidates (-43.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	92	5	97

Merged error: 0.0b

Counts

97 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) -2)
0.0b	(pow (- (exp x) 2.0) 3)
0.1b	(pow (exp x) -3)
3.1b	(+ (pow (- (exp x) 2.0) 3) (pow (exp x) -3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
11×	`unpow-prod-down`
9×	`pow-unpow` `pow-pow`
7×	`pow1`
6×	`exp-prod` `add-log-exp`
5×	`add-exp-log` `cube-prod` `add-cbrt-cube`
3×	`pow-to-exp` `pow-exp` `sqr-pow`
2×	`cube-div` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `cube-mult` `flip3--` `flip3-+` `unpow3` `sum-log` `flip--` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 81

Calls

4 calls:

3.0ms	(pow (exp x) -2)
5.0ms	(pow (- (exp x) 2.0) 3)
3.0ms	(pow (exp x) -3)
13.0ms	(+ (pow (- (exp x) 2.0) 3) (pow (exp x) -3))

series39.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (exp x) -2)
5.0ms	(pow (- (exp x) 2.0) 3)
7.0ms	(pow (exp x) -3)
22.0ms	(+ (pow (- (exp x) 2.0) 3) (pow (exp x) -3))

simplify31.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5011	762

prune140.0ms

Filtered

60 candidates to 93 candidates (-55.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	92	6	98

Merged error: 0b

Counts

98 → 6

regimes44.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	33
1	18	33

end0.0ms

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

sample2.2s

Algorithm

intervals

Results

1.8s	5630×	body	1280	valid
223.0ms	1238×	body	640	valid
70.0ms	643×	body	320	valid
23.0ms	321×	body	160	valid
6.0ms	168×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample76.0ms

simplify3.0ms

prune7.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify56.0ms

prune63.0ms

localize9.0ms

rewrite21.0ms

series25.0ms

simplify49.0ms

prune130.0ms

localize12.0ms

rewrite23.0ms

series22.0ms

simplify61.0ms

prune223.0ms

localize19.0ms

rewrite27.0ms

series39.0ms

simplify31.0ms

prune140.0ms

regimes44.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze4.0ms

sample2.2s

Profiling