Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	52×	body	1280	valid
4.0ms	41×	body	640	valid
4.0ms	124×	body	80	valid
3.0ms	14×	body	160	valid
2.0ms	25×	body	320	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: 30.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite130.0ms

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:

26.0ms	(/ (+ x 1.0) (- x 1.0))
11.0ms	(/ x (+ x 1.0))
89.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (+ x 1.0) (- x 1.0))
33.0ms	(/ x (+ x 1.0))
111.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5002	716

prune331.0ms

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))
0.1b	(/ 3.0 (pow x 3))
0.4b	(/ (- 1.0) (pow x 2))
5.0b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite873.0ms

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:

101.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
8.0ms	(/ 3.0 (pow x 3))
11.0ms	(/ (- 1.0) (pow x 2))
742.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
33.0ms	(/ 3.0 (pow x 3))
28.0ms	(/ (- 1.0) (pow x 2))
29.0ms	(- (- (/ (- 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	738	1754
1	3448	1596
2	5001	1578

prune571.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite257.0ms

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:

52.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
79.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
88.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
21.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
91.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
50.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
195.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1145	2720
1	5001	2532

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (/ 1 (pow x 2)))
0.3b	(* 6.0 (/ 1 x))
0.4b	(/ 1 (pow x 2))
6.3b	(+ (* 5.0 (/ 1 (pow x 2))) (+ (* 6.0 (/ 1 x)) (* 16.0 (/ 1 (pow x 3)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
67×	`times-frac`
50×	`*-un-lft-identity`
45×	`add-cube-cbrt`
42×	`add-exp-log`
41×	`associate-r`
23×	`unpow-prod-down`
20×	`frac-add`
16×	`associate-*r/` `un-div-inv` `add-cbrt-cube`
14×	`div-exp` `prod-exp`
12×	`unswap-sqr`
9×	`unpow2` `add-log-exp` `sqr-pow`
8×	`pow1` `associate-/r*`
7×	`rec-exp` `1-exp`
6×	`pow-to-exp` `associate-l` `pow-exp`
4×	`cbrt-unprod`
3×	`cbrt-undiv` `flip3-+` `sum-log` `flip-+` `div-inv` `associate-/l*`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `associate-+r+` `pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 181

Calls

4 calls:

25.0ms	(* 5.0 (/ 1 (pow x 2)))
15.0ms	(* 6.0 (/ 1 x))
9.0ms	(/ 1 (pow x 2))
39.0ms	(+ (* 5.0 (/ 1 (pow x 2))) (+ (* 6.0 (/ 1 x)) (* 16.0 (/ 1 (pow x 3)))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 5.0 (/ 1 (pow x 2)))
20.0ms	(* 6.0 (/ 1 x))
15.0ms	(/ 1 (pow x 2))
26.0ms	(+ (* 5.0 (/ 1 (pow x 2))) (+ (* 6.0 (/ 1 x)) (* 16.0 (/ 1 (pow x 3)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	756	1191
1	3534	991
2	5003	912

prune734.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch149.0ms

Steps

Iters	Range		Point
9	0.007285382865895221	15234496.061427226	9886.930048742035
9	-3013496178.120658	-569.2304264003914	-10044.420205958744

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	35	28

end0.0ms

sample855.0ms

Algorithm

intervals

Results

431.0ms	1753×	body	1280	valid
133.0ms	1233×	body	640	valid
125.0ms	4089×	body	80	valid
50.0ms	612×	body	320	valid
17.0ms	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