Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	54×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	125×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	17×	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: 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))
5.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite80.0ms

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))
58.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
124.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune215.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.2b	(/ 3.0 (pow x 3))
0.3b	(/ (- 1.0) (pow x 2))
8.2b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite739.0ms

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:

84.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
4.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
633.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
39.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (- (/ (- 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 (76.0ms)

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

prune424.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(* x (/ 1 (+ x 1.0)))
10.8b	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

6.0ms	(/ 1 (+ x 1.0))
11.0ms	(/ (+ x 1.0) (- x 1.0))
18.0ms	(* x (/ 1 (+ x 1.0)))
17.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
36.0ms	(* x (/ 1 (+ x 1.0)))
127.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	507	875
1	2099	793
2	5001	754

prune234.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- x 1.0))
0.0b	(* (+ x 1.0) (+ x 1.0))
0.1b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
20.0b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite67.0ms

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:

10.0ms	(* x (- x 1.0))
20.0ms	(* (+ x 1.0) (+ x 1.0))
21.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
9.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* x (- x 1.0))
16.0ms	(* (+ x 1.0) (+ x 1.0))
52.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
39.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify137.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (120.0ms)

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

prune342.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch94.0ms

Steps

Iters	Range		Point
9	6.164824567421913	3268324.1998729478	12731.405538457477
9	-3875183.9477288676	-0.008763241487176904	-12879.754469549705

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	36
1	43	36

end0.0ms

sample563.0ms

Algorithm

intervals

Results

206.0ms	1754×	body	1280	valid
112.0ms	1255×	body	640	valid
98.0ms	4094×	body	80	valid
38.0ms	589×	body	320	valid
14.0ms	308×	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