Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	55×	body	1280	valid
4.0ms	38×	body	640	valid
4.0ms	132×	body	80	valid
2.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 29.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite45.0ms

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:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
28.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series213.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
136.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune190.0ms

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: 0.0b

Counts

114 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0))
7.1b	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
14.3b	(/ x (- (* x x) (* 1.0 1.0)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
45×	`times-frac`
33×	`add-cube-cbrt`
18×	`associate-l`
13×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`associate-/r*`
8×	`flip3--` `flip--`
7×	`associate-/l*`
6×	`pow1` `associate-/r/` `distribute-lft-out` `distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `associate-r` `frac-sub`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `associate--l+`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 146

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
15.0ms	(* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0))
18.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
5.0ms	(/ x (- (* x x) (* 1.0 1.0)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (+ x 1.0) (- x 1.0))
56.0ms	(* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0))
357.0ms	(- (* (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
70.0ms	(/ x (- (* x x) (* 1.0 1.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	698	1357
1	3323	1273
2	5001	1271

prune255.0ms

Filtered

158 candidates to 119 candidates (75.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	157	4	161

Merged error: 0.0b

Counts

161 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:

5.0ms

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

series65.0ms

Counts

1 → 3

Calls

1 calls:

65.0ms

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

simplify103.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (6.0ms)

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

prune29.0ms

Filtered

25 candidates to 16 candidates (64.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	25	4	29

Merged error: 0.0b

Counts

29 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.4b	(/ 3.0 (pow x 3))
0.5b	(/ (- 1.0) (pow x 2))
4.6b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite153.0ms

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:

51.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
6.0ms	(/ (- 1.0) (pow x 2))
80.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series161.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
35.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ (- 1.0) (pow x 2))
35.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify99.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (74.0ms)

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

prune340.0ms

Filtered

246 candidates to 133 candidates (54.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	246	4	250

Merged error: 0.0b

Counts

250 → 4

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.6b

bsearch97.0ms

Steps

Iters	Range		Point
10	6.398614580632226	3002406562115.273	10912.93121807726
11	-55383.34621353126	-7.66540900750845e-16	-12155.681664534535

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	35	18

end0.0ms

sample676.0ms

Algorithm

intervals

Results

250.0ms	1763×	body	1280	valid
137.0ms	1251×	body	640	valid
117.0ms	4018×	body	80	valid
53.0ms	644×	body	320	valid
18.0ms	324×	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