Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	64×	body	1280	valid
4.0ms	42×	body	640	valid
3.0ms	118×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Filtered

1 candidates to 0 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: 32.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
6.0ms	(/ x (+ x 1.0))
37.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (+ x 1.0) (- x 1.0))
38.0ms	(/ x (+ x 1.0))
127.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5002	716

prune185.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	3	114

Merged error: 0b

Counts

114 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.1b	(/ 3.0 (pow x 3))
0.2b	(/ (- 1.0) (pow x 2))
4.4b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
120×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
78×	`add-cube-cbrt`
48×	`unpow-prod-down`
29×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`sqr-pow`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*` `unpow2`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`neg-mul-1`
8×	`add-cbrt-cube`
6×	`div-exp`
5×	`frac-sub`
4×	`pow1` `cube-mult` `diff-log` `unpow3`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `frac-2neg` `div-sub` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`distribute-frac-neg`

Counts

4 → 234

Calls

4 calls:

60.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
95.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
35.0ms	(/ 3.0 (pow x 3))
24.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify101.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	741	1813
1	3525	1605
2	5001	1602

prune376.0ms

Filtered

246 candidates to 133 candidates (54.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	246	3	249

Merged error: 0b

Counts

249 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- x 1.0))
0.0b	(* (+ x 1.0) (+ x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
20.9b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
35×	`*-un-lft-identity`
32×	`frac-sub`
30×	`flip3-+` `flip-+`
25×	`add-sqr-sqrt`
20×	`frac-times` `flip3--` `flip--`
19×	`add-cube-cbrt`
18×	`associate-/l/`
13×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
9×	`associate-r`
7×	`associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `distribute-lft-out` `add-log-exp`
5×	`sub-neg` `difference-of-squares`
4×	`associate--l+` `associate-/r*`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

6.0ms	(* x (- x 1.0))
8.0ms	(* (+ x 1.0) (+ x 1.0))
15.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
8.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* x (- x 1.0))
16.0ms	(* (+ x 1.0) (+ x 1.0))
48.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
41.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify133.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	769	1735
1	4437	1626
2	5001	1621

prune300.0ms

Filtered

164 candidates to 110 candidates (67.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	164	3	167

Merged error: 0b

Counts

167 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (+ 3.0 (* x 1.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 22

Calls

1 calls:

9.0ms

(* x (+ 3.0 (* x 1.0)))

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

(* x (+ 3.0 (* x 1.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	144	117
1	680	103
2	3770	103
3	5002	103

prune33.0ms

Filtered

25 candidates to 16 candidates (64.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	25	3	28

Merged error: 0b

Counts

28 → 3

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch102.0ms

Steps

Iters	Range		Point
10	14.716166499582775	2.5158614700293387e+20	12597.77927646208
11	-2193661101726697.2	-1.4639597033977343e-08	-11900.943894212798

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	35	18

end0.0ms

sample620.0ms

Algorithm

intervals

Results

227.0ms	1782×	body	1280	valid
125.0ms	1206×	body	640	valid
110.0ms	4076×	body	80	valid
47.0ms	630×	body	320	valid
16.0ms	306×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6