Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	48×	body	1280	valid
3.0ms	43×	body	640	valid
3.0ms	127×	body	80	valid
2.0ms	28×	body	320	valid
0.0ms	10×	body	160	valid

simplify21.0ms

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: 30.3b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite51.0ms

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

series213.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ x (+ x 1.0))
44.0ms	(/ (+ x 1.0) (- x 1.0))
134.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune214.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
22.6b	(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-div`
32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
20×	`frac-times` `flip3-+` `flip-+`
17×	`frac-sub`
14×	`add-cube-cbrt` `associate-*l/`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3` `distribute-lft-out`
7×	`associate-r/` `associate-r` `associate-l*`
6×	`add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
15.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
13.0ms	(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ x 1.0))
94.0ms	(cbrt (+ x 1.0))
113.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
135.0ms	(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	670	1503
1	2386	1416
2	5002	1368

prune301.0ms

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))
0.1b	(/ 3.0 (pow x 3))
0.3b	(/ (- 1.0) (pow x 2))
6.6b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite169.0ms

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:

57.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
89.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
37.0ms	(/ 3.0 (pow x 3))
31.0ms	(/ (- 1.0) (pow x 2))
33.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify93.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	741	1813
1	3525	1605
2	5001	1602

prune432.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
5.8b	(/ x (+ (pow x 3) (pow 1.0 3)))
10.3b	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
13.9b	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

135×	`*-un-lft-identity`
75×	`times-frac`
58×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
41×	`distribute-lft-out`
33×	`associate-l`
28×	`unpow-prod-down` `cube-prod`
14×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `sum-cubes` `flip-+` `associate-/l*`
6×	`pow1` `associate-/r/` `add-log-exp`
5×	`frac-sub` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times` `associate-*r/`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `associate-*l/` `prod-exp` `associate--l+` `clear-num` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 175

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
18.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
28.0ms	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
24.0ms	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ x 1.0) (- x 1.0))
95.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
197.0ms	(- (* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))) (/ (+ x 1.0) (- x 1.0)))
77.0ms	(* (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

simplify112.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	891	1901
1	4528	1763
2	5002	1763

prune467.0ms

Pruning

6 alts after pruning (4 fresh and 2 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 31.9b

bsearch90.0ms

Steps

Iters	Range		Point
8	6793.132116615613	39135938.24223837	10797.660758833053
10	-46094758682.62103	-8.718619127186496	-19531.357482678304

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	22
1	42	22

end0.0ms

sample522.0ms

Algorithm

intervals

Results

182.0ms	1734×	body	1280	valid
99.0ms	1220×	body	640	valid
92.0ms	4115×	body	80	valid
37.0ms	618×	body	320	valid
16.0ms	313×	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