Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
4.0ms	44×	body	640	valid
4.0ms	131×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	8×	body	160	valid

simplify20.0ms

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: 29.1b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite46.0ms

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))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
127.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune183.0ms

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

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
8.1b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
5.0ms	(/ 1 (- x 1.0))
12.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
9.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series229.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ x (+ x 1.0))
29.0ms	(/ 1 (- x 1.0))
37.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
130.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	576	948
1	2837	860
2	5001	818

prune192.0ms

Filtered

153 candidates to 99 candidates (64.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	152	4	156

Merged error: 0.0b

Counts

156 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

5.0ms	(+ (* x (+ 3.0 (* x 1.0))) 1.0)
5.0ms	(* x (+ 3.0 (* x 1.0)))

series86.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (* x (+ 3.0 (* x 1.0))) 1.0)
65.0ms	(* x (+ 3.0 (* x 1.0)))

simplify35.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	209	215
1	933	199
2	5002	199

prune54.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Merged error: 0.0b

Counts

45 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
0.2b	(/ 3.0 (pow x 3))
0.2b	(/ (neg 1.0) (pow x 2))
7.6b	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite154.0ms

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:

52.0ms	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (neg 1.0) (pow x 2))
81.0ms	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
35.0ms	(/ 3.0 (pow x 3))
30.0ms	(/ (neg 1.0) (pow x 2))
33.0ms	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify96.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	738	1746
1	3417	1585
2	5001	1567

prune351.0ms

Filtered

246 candidates to 129 candidates (52.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	245	5	250

Merged error: 0b

Counts

250 → 5

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.8b

bsearch88.0ms

Steps

Iters	Range		Point
10	2.2826621327002547e-07	125321.6248081686	15438.843691545057
9	-650632332.7510262	-11.514549394350572	-14198.77538024074

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	35	15

end0.0ms

sample621.0ms

Algorithm

intervals

Results

213.0ms	1718×	body	1280	valid
135.0ms	1258×	body	640	valid
114.0ms	4042×	body	80	valid
48.0ms	642×	body	320	valid
17.0ms	340×	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

Details

sample23.0ms

simplify20.0ms

prune2.0ms

localize6.0ms

rewrite46.0ms

series201.0ms

simplify46.0ms

prune183.0ms

localize7.0ms

rewrite36.0ms

series229.0ms

simplify75.0ms

prune192.0ms

localize5.0ms

rewrite11.0ms

series86.0ms

simplify35.0ms

prune54.0ms

localize11.0ms

rewrite154.0ms

series169.0ms

simplify96.0ms

prune351.0ms

regimes33.0ms

bsearch88.0ms

simplify1.0ms

end0.0ms

sample621.0ms

Profiling

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