Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	57×	body	1280	valid
3.0ms	40×	body	640	valid
3.0ms	131×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	14×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 29.1b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite75.0ms

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))
10.0ms	(/ (+ x 1.0) (- x 1.0))
55.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series213.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ x (+ x 1.0))
50.0ms	(/ (+ x 1.0) (- x 1.0))
128.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

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

prune206.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
3.3b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

211×	`times-frac`
209×	`*-un-lft-identity`
166×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
34×	`associate-/r*`
31×	`distribute-lft-out` `difference-of-squares`
25×	`distribute-lft-out--`
19×	`add-exp-log`
13×	`associate-/r/` `add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `frac-sub` `inv-pow`

Counts

4 → 234

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
10.0ms	(/ (- x 1.0) (+ x 1.0))
15.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
95.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ x (+ x 1.0))
38.0ms	(/ (- x 1.0) (+ x 1.0))
36.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
130.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify77.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	742	2083
1	3390	1767
2	5001	1758

prune295.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0)))))
3.3b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
3.3b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
3.3b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

137×	`add-sqr-sqrt`
84×	`times-frac`
69×	`*-un-lft-identity`
40×	`difference-of-squares`
17×	`cbrt-prod`
16×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `frac-sub` `add-cbrt-cube` `flip--` `div-inv` `distribute-lft-out`
3×	`sub-neg` `cbrt-div` `diff-log`
1×	`pow1/3`

Counts

4 → 109

Calls

4 calls:

81.0ms	(cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0)))))
93.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
96.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
97.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series648.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt (- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0)))))
126.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
127.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
125.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify50.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	398	1833
1	1265	1749
2	5001	1633

prune300.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ 1 (/ (- x 1.0) (+ x 1.0))) 3)) (+ (* (/ 1 (/ (- x 1.0) (+ x 1.0))) (+ (/ 1 (/ (- x 1.0) (+ x 1.0))) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))))
3.3b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ 1 (/ (- x 1.0) (+ x 1.0))) 3))
3.3b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
3.3b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

959×	`add-sqr-sqrt`
769×	`times-frac`
429×	`*-un-lft-identity`
308×	`difference-of-squares`
306×	`cbrt-prod`
280×	`unpow-prod-down` `cube-prod`
101×	`add-cube-cbrt`
76×	`distribute-lft-out--`
72×	`sqr-pow`
27×	`frac-add`
23×	`associate-/r/`
19×	`div-inv`
18×	`distribute-lft-out`
16×	`frac-times` `associate-*r/`
10×	`associate-*l/` `add-log-exp`
7×	`flip3-+` `flip-+`
4×	`pow1` `difference-cubes` `add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`
2×	`cube-div`
1×	`cbrt-div` `pow1/3`

Counts

4 → 472

Calls

4 calls:

430.0ms	(cbrt (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ 1 (/ (- x 1.0) (+ x 1.0))) 3)) (+ (* (/ 1 (/ (- x 1.0) (+ x 1.0))) (+ (/ 1 (/ (- x 1.0) (+ x 1.0))) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))))
351.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ 1 (/ (- x 1.0) (+ x 1.0))) 3))
95.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
95.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

704.0ms	(cbrt (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ 1 (/ (- x 1.0) (+ x 1.0))) 3)) (+ (* (/ 1 (/ (- x 1.0) (+ x 1.0))) (+ (/ 1 (/ (- x 1.0) (+ x 1.0))) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))))
296.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ 1 (/ (- x 1.0) (+ x 1.0))) 3))
126.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))
134.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify227.0ms

Algorithm

egg-herbie

Counts

484 → 484

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1865	22435
1	5001	22096

prune950.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.0b

bsearch99.0ms

Steps

Iters	Range		Point
10	4.555257425893614e-05	47183757994.54101	9309.674525263445
9	-13600.963204601821	-0.00047371797307045637	-9843.534602931319

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	21
1	40	21

end0.0ms

sample548.0ms

Algorithm

intervals

Results

186.0ms	1725×	body	1280	valid
116.0ms	1317×	body	640	valid
98.0ms	4016×	body	80	valid
41.0ms	656×	body	320	valid
12.0ms	286×	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