Details

sample30.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
6.0ms	127×	body	80	valid
5.0ms	49×	body	640	valid
4.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify22.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite79.0ms

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))
11.0ms	(/ (+ x 1.0) (- x 1.0))
59.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (36.0ms)

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

prune200.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.2b	(/ (- 1.0) (pow x 2))
0.3b	(/ 3.0 (pow x 3))
5.0b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite757.0ms

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:

86.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
6.0ms	(/ (- 1.0) (pow x 2))
4.0ms	(/ 3.0 (pow x 3))
651.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
25.0ms	(/ (- 1.0) (pow x 2))
40.0ms	(/ 3.0 (pow x 3))
32.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify92.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	741	1813
1	3530	1605
2	5001	1602

prune406.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.9b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

483×	`*-un-lft-identity`
268×	`times-frac`
131×	`add-sqr-sqrt`
127×	`distribute-lft-out`
79×	`add-cube-cbrt`
52×	`distribute-lft-out--`
48×	`swap-sqr`
34×	`difference-of-squares`
26×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`frac-sub`
16×	`associate-/r*`
13×	`frac-times` `associate-r/` `associate-l/` `associate-/r/`
11×	`pow1` `associate-/l/`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `div-inv` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `frac-add` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 274

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
117.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
50.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ x (+ x 1.0))
353.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
58.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
206.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1013	4422
1	5001	4195

prune398.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.1b	(* (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))
2.9b	(- (* (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))) (* (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

rewrite298.0ms

Algorithm

rewrite-expression-head

Rules

529×	`frac-times`
432×	`*-un-lft-identity`
343×	`associate-r/` `associate-l/`
256×	`times-frac`
225×	`frac-sub`
204×	`add-sqr-sqrt`
158×	`add-exp-log` `add-cbrt-cube`
129×	`pow1`
100×	`add-cube-cbrt`
97×	`swap-sqr`
76×	`distribute-lft-out`
73×	`prod-exp` `cbrt-unprod`
64×	`distribute-lft-out--`
53×	`associate-r` `associate-l`
48×	`cbrt-undiv` `div-exp`
41×	`difference-of-squares`
38×	`pow-prod-up`
25×	`pow-prod-down`
24×	`pow-sqr`
20×	`pow-plus`
16×	`associate-/r/`
15×	`pow2`
9×	`flip3--` `flip--` `unswap-sqr`
8×	`div-inv`
6×	`add-log-exp`
3×	`*-commutative`
1×	`sub-neg` `diff-log`

Counts

4 → 614

Calls

4 calls:

52.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
50.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
62.0ms	(* (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))
80.0ms	(- (* (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))) (* (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
58.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
55.0ms	(* (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))
316.0ms	(- (* (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))) (* (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))))

simplify143.0ms

Algorithm

egg-herbie

Counts

626 → 626

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2317	11379
1	5001	10530

prune594.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.7b

bsearch123.0ms

Steps

Iters	Range		Point
10	4.8244160186105205e-08	257763.20554958374	10087.641379500208
9	-3246994039.700852	-772.3369502403921	-17078.695698845215

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	78
1	46	78

end0.0ms

sample754.0ms

Algorithm

intervals

Results

250.0ms	1750×	body	1280	valid
183.0ms	4087×	body	80	valid
146.0ms	1263×	body	640	valid
55.0ms	619×	body	320	valid
19.0ms	281×	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