Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
4.0ms	49×	body	640	valid
3.0ms	123×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	3×	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: 31.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.3b	(- (/ 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))
59.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
134.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune208.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (- 1.0) (pow x 2))
0.3b	(/ 3.0 (pow x 3))
6.4b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite650.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
94×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
46×	`unpow-prod-down`
28×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
16×	`sqr-pow`
13×	`add-exp-log` `cube-prod` `associate-/l*`
11×	`unpow2`
9×	`neg-mul-1`
8×	`add-log-exp`
7×	`add-cbrt-cube` `distribute-lft-out--`
6×	`div-exp`
5×	`difference-of-squares`
4×	`cube-mult` `unpow3` `frac-sub`
3×	`pow1` `diff-log`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `pow-exp` `associate--l+` `clear-num` `flip--` `div-inv`
1×	`associate--l-` `neg-sub0` `div-sub` `distribute-frac-neg`

Counts

3 → 207

Calls

3 calls:

6.0ms	(/ (- 1.0) (pow x 2))
4.0ms	(/ 3.0 (pow x 3))
628.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series98.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(/ 3.0 (pow x 3))
32.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify90.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	685	1461
1	3384	1319
2	5001	1301

prune358.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
1.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 329

Calls

4 calls:

52.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
32.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
133.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
14.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
360.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
213.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify80.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1294	4957
1	5001	4719

prune500.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
1.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
1.3b	(- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

103×	`*-un-lft-identity`
79×	`add-sqr-sqrt`
76×	`times-frac`
43×	`add-cube-cbrt`
26×	`unpow-prod-down` `cube-prod` `associate-r`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-l` `frac-sub` `distribute-lft-out`
16×	`associate-*r/`
14×	`associate-*l/`
13×	`frac-times` `difference-of-squares`
12×	`distribute-lft-out--`
8×	`associate-/r/` `add-log-exp`
7×	`pow1`
5×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`pow-unpow`
2×	`sub-neg` `diff-log` `pow-exp` `sub-div` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `distribute-rgt-out--` `pow-pow` `flip3-+` `unpow3` `pow-prod-down` `*-commutative` `flip-+` `sqr-pow`

Counts

4 → 186

Calls

4 calls:

43.0ms	(* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
12.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
14.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
64.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
209.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
200.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1107	2069
1	5001	1848

prune480.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch87.0ms

Steps

Iters	Range		Point
11	0.08347146558812443	3.320253512051989e+22	12679.85899306799
8	-14583263.309321204	-1162.6651869185068	-11931.41196902016

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	36
1	43	36

end0.0ms

sample529.0ms

Algorithm

intervals

Results

186.0ms	1731×	body	1280	valid
105.0ms	1265×	body	640	valid
97.0ms	4084×	body	80	valid
38.0ms	618×	body	320	valid
13.0ms	302×	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