Details

analyze41.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

sample32.0ms

Algorithm

intervals

Results

15.0ms	82×	body	1280	valid
4.0ms	34×	body	640	valid
2.0ms	98×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	15×	body	160	valid
0.0ms	5×	body	80	invalid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4793	6
1	4793	6

prune11.0ms

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: 27.0b

Counts

2 → 2

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.5b	(- (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 → 23

Calls

2 calls:

2.0ms	(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)

simplify89.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4948	224
1	4948	224

prune32.0ms

Filtered

20 candidates to 29 candidates (-45.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	28	3	31

Merged error: 2.3b

Counts

31 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
4.2b	(* x (* 1/6 (pow a 3)))
6.5b	(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
9.9b	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
10.0ms	(* x (* 1/6 (pow a 3)))
22.0ms	(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
9.0ms	(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

simplify45.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5031	1233

prune113.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	85	4	89

Merged error: 0.2b

Counts

89 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(* x (+ a (+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))))
4.2b	(* x (* 1/6 (pow a 3)))
4.9b	(* x (* x (* 1/6 (pow a 3))))
9.5b	(+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* x (+ a (+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))))
10.0ms	(* x (* 1/6 (pow a 3)))
12.0ms	(* x (* x (* 1/6 (pow a 3))))
14.0ms	(+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4967	1223
1	4967	1223

prune110.0ms

Filtered

53 candidates to 87 candidates (-64.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	88	3	91

Merged error: 0.0b

Counts

91 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a (* 1/2 x)) x)
0.2b	(pow (* a x) 3)
1.5b	(* a (+ x (* (* a (* 1/2 x)) x)))
12.1b	(+ (* a (+ x (* (* a (* 1/2 x)) x))) (* 1/6 (pow (* a x) 3)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`add-cube-cbrt` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`associate-l`
3×	`pow-unpow`
2×	`distribute-rgt-in` `associate-+l+` `pow-pow` `distribute-lft-in` `flip3-+` `associate-r/` `pow-exp` `-commutative` `flip-+` `rem-cube-cbrt`
1×	`+-commutative` `cube-mult` `pow-to-exp` `unpow-prod-down` `distribute-rgt-out` `unpow3` `cube-prod` `distribute-rgt1-in` `sum-log` `unswap-sqr` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

9.0ms	(* (* a (* 1/2 x)) x)
3.0ms	(pow (* a x) 3)
5.0ms	(* a (+ x (* (* a (* 1/2 x)) x)))
6.0ms	(+ (* a (+ x (* (* a (* 1/2 x)) x))) (* 1/6 (pow (* a x) 3)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (* a (* 1/2 x)) x)
7.0ms	(pow (* a x) 3)
12.0ms	(* a (+ x (* (* a (* 1/2 x)) x)))
19.0ms	(+ (* a (+ x (* (* a (* 1/2 x)) x))) (* 1/6 (pow (* a x) 3)))

simplify57.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4987	970
1	4987	970

prune107.0ms

Filtered

61 candidates to 92 candidates (-50.8%)

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

regimes218.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	31
1	28	31

end0.0ms

analyze40.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

sample950.0ms

Algorithm

intervals

Results

476.0ms	2622×	body	1280	valid
163.0ms	1367×	body	640	valid
76.0ms	2877×	body	80	valid
64.0ms	764×	body	320	valid
20.0ms	370×	body	160	valid
4.0ms	154×	body	80	invalid

Details

analyze41.0ms

sample32.0ms

simplify50.0ms

prune11.0ms

localize4.0ms

rewrite6.0ms

series11.0ms

simplify89.0ms

prune32.0ms

localize15.0ms

rewrite25.0ms

series62.0ms

simplify45.0ms

prune113.0ms

localize13.0ms

rewrite31.0ms

series58.0ms

simplify56.0ms

prune110.0ms

localize12.0ms

rewrite26.0ms

series45.0ms

simplify57.0ms

prune107.0ms

regimes218.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze40.0ms

sample950.0ms

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