Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	48×	body	1280	valid
4.0ms	52×	body	640	valid
3.0ms	134×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	8×	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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

2 → 71

Calls

2 calls:

10.0ms	(/ (+ x 1.0) (- x 1.0))
56.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series164.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
127.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify151.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	317	591
1	1003	565
2	4508	559
3	5003	559

prune129.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

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)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite158.0ms

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:

47.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
32.0ms	(* (/ x (+ x 1.0)) (/ x (+ 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))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
41.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
53.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
196.0ms	(- (* (/ 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 (28.0ms)

Iter	Nodes	Cost
0	1145	2720
1	5001	2532

prune385.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
0.5b	(/ (- 1.0) (pow x 2))
0.9b	(/ 1 (pow x 3))
7.2b	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

rewrite200.0ms

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:

126.0ms	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
6.0ms	(/ (- 1.0) (pow x 2))
4.0ms	(/ 1 (pow x 3))
53.0ms	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

series157.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* 3.0 (+ (/ 1 x) (/ 1 (pow x 3))))
24.0ms	(/ (- 1.0) (pow x 2))
33.0ms	(/ 1 (pow x 3))
32.0ms	(- (/ (- 1.0) (pow x 2)) (* 3.0 (+ (/ 1 x) (/ 1 (pow x 3)))))

simplify141.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	792	1535
1	4675	1275
2	5002	1261

prune381.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1.0 (pow x 2))
0.9b	(/ 3.0 (pow x 3))
9.0b	(+ (+ (/ 1.0 (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
17.3b	(/ 0 (pow x 2))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
74×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
28×	`associate-/r*`
19×	`add-exp-log`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*` `add-log-exp`
8×	`unpow2`
5×	`distribute-lft-out`
4×	`pow1` `cube-mult` `unpow3` `frac-add`
3×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `div-inv`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+l+` `div0`

Counts

4 → 183

Calls

4 calls:

3.0ms	(/ 1.0 (pow x 2))
4.0ms	(/ 3.0 (pow x 3))
188.0ms	(+ (+ (/ 1.0 (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
4.0ms	(/ 0 (pow x 2))

series89.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (pow x 2))
34.0ms	(/ 3.0 (pow x 3))
28.0ms	(+ (+ (/ 1.0 (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
1.0ms	(/ 0 (pow x 2))

simplify85.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	591	993
1	3223	830
2	5003	757

prune310.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch92.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	14618.947191620917
10	-64880754058.88788	-2.651420353119469e-05	-11755.062723959316

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	30
1	37	30

end0.0ms

sample535.0ms

Algorithm

intervals

Results

189.0ms	1719×	body	1280	valid
107.0ms	1224×	body	640	valid
93.0ms	4124×	body	80	valid
39.0ms	618×	body	320	valid
14.0ms	315×	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