Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	61×	body	1280	valid
3.0ms	39×	body	640	valid
3.0ms	121×	body	80	valid
1.0ms	23×	body	320	valid
1.0ms	12×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite47.0ms

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))
31.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
127.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune206.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.3b	(/ 3.0 (pow x 3))
0.5b	(/ (- 1.0) (pow x 2))
5.6b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite152.0ms

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	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
78.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (/ (- 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)))

simplify97.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	738	1754
1	3448	1596
2	5001	1578

prune419.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

342×	`*-un-lft-identity`
208×	`times-frac`
152×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
73×	`distribute-lft-out`
72×	`swap-sqr`
44×	`associate-r` `associate-l`
36×	`distribute-lft-out--`
28×	`add-exp-log` `add-cbrt-cube`
21×	`difference-of-squares`
18×	`pow1`
16×	`associate-/r/`
9×	`frac-sub`
8×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
5×	`flip3--` `flip3-+` `flip--` `flip-+`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `sub-neg` `diff-log` `frac-add` `sum-log`

Counts

4 → 259

Calls

4 calls:

27.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
28.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
17.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
52.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
44.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
201.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1145	2720
1	5002	2529

prune406.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(* (+ x 1.0) (/ (/ (+ x 1.0) (- x 1.0)) (- x 1.0)))
5.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (+ x 1.0) (/ (/ (+ x 1.0) (- x 1.0)) (- x 1.0))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

350×	`*-un-lft-identity`
313×	`times-frac`
231×	`add-sqr-sqrt`
154×	`associate-r`
118×	`add-cube-cbrt`
61×	`distribute-lft-out`
50×	`distribute-lft-out--`
46×	`difference-of-squares`
25×	`add-exp-log` `add-cbrt-cube`
24×	`swap-sqr`
22×	`associate-l`
20×	`associate-/r/`
15×	`frac-sub`
14×	`frac-times` `associate-*l/`
13×	`pow1` `flip3-+` `flip-+`
10×	`associate-*r/` `div-inv`
8×	`add-log-exp`
7×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `unswap-sqr`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `pow2` `sub-neg` `pow-plus` `diff-log` `frac-add` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 299

Calls

4 calls:

31.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
17.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
43.0ms	(* (+ x 1.0) (/ (/ (+ x 1.0) (- x 1.0)) (- x 1.0)))
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (+ x 1.0) (/ (/ (+ x 1.0) (- x 1.0)) (- x 1.0))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
47.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
53.0ms	(* (+ x 1.0) (/ (/ (+ x 1.0) (- x 1.0)) (- x 1.0)))
211.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (+ x 1.0) (/ (/ (+ x 1.0) (- x 1.0)) (- x 1.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1445	3029
1	5001	2887

prune561.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch108.0ms

Steps

Iters	Range		Point
8	4050.4462513149238	24048332.968690775	9184.42281507242
7	-225931.74046194248	-3253.153967321615	-12923.888472784707

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	47
1	62	47

end0.0ms

sample538.0ms

Algorithm

intervals

Results

176.0ms	1666×	body	1280	valid
111.0ms	1273×	body	640	valid
99.0ms	4075×	body	80	valid
44.0ms	663×	body	320	valid
14.0ms	323×	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