Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	63×	body	1280	valid
4.0ms	47×	body	640	valid
3.0ms	120×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify22.0ms

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: 31.7b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite136.0ms

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:

11.0ms	(/ x (+ x 1.0))
27.0ms	(/ (+ x 1.0) (- x 1.0))
93.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
132.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

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

prune208.0ms

Pruning

4 alts after pruning (4 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))
0.4b	(/ 3.0 (pow x 3))
0.6b	(/ (- 1.0) (pow x 2))
5.2b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite917.0ms

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:

107.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
8.0ms	(/ 3.0 (pow x 3))
12.0ms	(/ (- 1.0) (pow x 2))
779.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series177.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
37.0ms	(/ 3.0 (pow x 3))
31.0ms	(/ (- 1.0) (pow x 2))
34.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify98.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (79.0ms)

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

prune442.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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)))
8.2b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite133.0ms

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:

11.0ms	(/ x (+ x 1.0))
13.0ms	(/ 1 (- x 1.0))
45.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
58.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ x (+ x 1.0))
31.0ms	(/ 1 (- x 1.0))
37.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
132.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify77.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	576	950
1	2837	862
2	5001	820

prune246.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
0.3b	(/ 1 (pow x 3))
0.6b	(/ (- 1.0) (pow x 2))
5.2b	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

131×	`times-frac`
101×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
45×	`unpow-prod-down`
27×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
20×	`add-exp-log` `associate-/r*`
16×	`associate-r`
15×	`sqr-pow`
13×	`associate-/l*`
12×	`cube-prod`
11×	`unpow2`
10×	`unpow3` `add-cbrt-cube`
9×	`neg-mul-1` `div-exp`
7×	`div-inv` `distribute-lft-out`
6×	`pow1` `associate-*r/` `add-log-exp`
5×	`distribute-rgt-out`
4×	`cube-mult` `pow-to-exp` `pow-exp`
3×	`rec-exp` `1-exp` `associate-l` `frac-sub`
2×	`cbrt-undiv` `neg-sub0` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `div-sub` `frac-add` `clear-num` `flip-+` `associate--r+`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `pow-prod-down` `distribute-rgt1-in` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 241

Calls

4 calls:

168.0ms	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
10.0ms	(/ 1 (pow x 3))
11.0ms	(/ (- 1.0) (pow x 2))
76.0ms	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
33.0ms	(/ 1 (pow x 3))
28.0ms	(/ (- 1.0) (pow x 2))
39.0ms	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

simplify147.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	792	1535
1	4669	1275
2	5001	1275

prune411.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch83.0ms

Steps

Iters	Range		Point
9	41.96612619086958	53435221.69579046	8646.459775303862
9	-1873866393.190807	-0.5149414008252181	-10207.349462423768

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample550.0ms

Algorithm

intervals

Results

170.0ms	1708×	body	1280	valid
105.0ms	1246×	body	640	valid
99.0ms	4101×	body	80	valid
38.0ms	627×	body	320	valid
13.0ms	318×	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