Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	63×	body	1280	valid
3.0ms	128×	body	80	valid
3.0ms	32×	body	640	valid
2.0ms	26×	body	320	valid
0.0ms	7×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
13.0ms	(/ (+ x 1.0) (- x 1.0))
77.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
44.0ms	(/ (+ x 1.0) (- x 1.0))
133.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify408.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292

prune754.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
0.1b	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
2.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

1155×	`*-un-lft-identity`
804×	`times-frac`
631×	`add-sqr-sqrt`
468×	`prod-diff`
417×	`add-cube-cbrt`
217×	`distribute-lft-out`
142×	`distribute-lft-out--`
97×	`difference-of-squares`
92×	`associate-/r/`
46×	`div-inv`
38×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
28×	`flip3-+` `flip-+`
22×	`flip3--` `flip--`
18×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`pow-unpow` `cbrt-div` `frac-sub`
2×	`cube-mult` `unpow3` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 667

Calls

4 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
87.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
84.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
75.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ x 1.0) (- x 1.0))
185.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
135.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify240.0ms

Algorithm

egg-herbie

Counts

679 → 679

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	1399	19382
1	4621	14418
2	5001	14397

prune946.0ms

Filtered

679 candidates to 244 candidates (35.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (cbrt (pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3)))
0.1b	(pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3)
0.2b	(cbrt (pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3))
2.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite671.0ms

Algorithm

rewrite-expression-head

Rules

1506×	`*-un-lft-identity`
944×	`times-frac`
722×	`add-sqr-sqrt`
468×	`prod-diff`
422×	`add-cube-cbrt`
275×	`distribute-lft-out`
249×	`cbrt-prod`
241×	`distribute-lft-out--`
210×	`unpow-prod-down` `cube-prod`
124×	`difference-of-squares`
90×	`associate-/r/`
45×	`div-inv`
27×	`flip3-+` `flip-+`
22×	`flip3--` `flip--`
18×	`cube-div` `fma-neg`
9×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
6×	`add-exp-log` `add-log-exp`
5×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `pow-exp` `frac-sub` `log1p-expm1-u`
3×	`pow-unpow`
2×	`pow-to-exp` `pow1/3`
1×	`sub-neg` `pow-pow` `diff-log` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 808

Calls

4 calls:

172.0ms	(cbrt (cbrt (pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3)))
172.0ms	(pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3)
169.0ms	(cbrt (pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3))
77.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (cbrt (pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3)))
216.0ms	(pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3)
187.0ms	(cbrt (pow (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3) 3))
143.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify203.0ms

Algorithm

egg-herbie

Counts

820 → 820

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1582	21723
1	5001	16642

prune1.1s

Filtered

820 candidates to 240 candidates (29.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (+ x 1.0) (- x 1.0)) 3)
0.2b	(cbrt (/ (pow (pow (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) 3) 3) (pow (pow (* (+ x 1.0) (- x 1.0)) 3) 3)))
1.2b	(/ (pow (pow (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) 3) 3) (pow (pow (* (+ x 1.0) (- x 1.0)) 3) 3))
19.8b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

1421×	`unpow-prod-down` `cube-prod`
1320×	`times-frac`
672×	`cbrt-prod`
516×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
319×	`cube-mult` `unpow3` `sqr-pow`
76×	`cube-div`
56×	`pow-exp`
50×	`add-exp-log`
46×	`associate-*r/`
33×	`flip3-+` `flip-+`
32×	`frac-sub`
30×	`div-exp` `associate-/l*`
28×	`frac-times`
27×	`flip3--` `flip--`
23×	`pow-to-exp`
22×	`associate--l+` `associate-/r*`
19×	`prod-diff`
18×	`associate-/l/`
16×	`associate-/r/`
14×	`associate-*l/`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`prod-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow`
2×	`pow-pow` `div-inv` `associate--r+` `rem-cube-cbrt`
1×	`cbrt-undiv` `cbrt-div` `frac-2neg` `fma-neg` `pow1/3` `diff-log` `pow-prod-down` `clear-num` `cbrt-unprod`

Counts

4 → 1552

Calls

4 calls:

7.0ms	(pow (* (+ x 1.0) (- x 1.0)) 3)
63.0ms	(cbrt (/ (pow (pow (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) 3) 3) (pow (pow (* (+ x 1.0) (- x 1.0)) 3) 3)))
96.0ms	(/ (pow (pow (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) 3) 3) (pow (pow (* (+ x 1.0) (- x 1.0)) 3) 3))
12.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(pow (* (+ x 1.0) (- x 1.0)) 3)
177.0ms	(cbrt (/ (pow (pow (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) 3) 3) (pow (pow (* (+ x 1.0) (- x 1.0)) 3) 3)))
200.0ms	(/ (pow (pow (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) 3) 3) (pow (pow (* (+ x 1.0) (- x 1.0)) 3) 3))
48.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify428.0ms

Algorithm

egg-herbie

Counts

1564 → 1564

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2003	42474
1	5001	41256

prune1.4s

Filtered

1564 candidates to 285 candidates (18.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes72.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.0b

bsearch103.0ms

Steps

Iters	Range		Point
9	4717.815806685034	26105877676.696735	86764.44817167475
9	-1117730599.3323822	-0.37949367736095085	-550341021.6647582

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	37
1	67	37
2	80	37
3	82	37
4	82	37

end0.0ms

sample510.0ms

Algorithm

intervals

Results

176.0ms	1775×	body	1280	valid
102.0ms	1202×	body	640	valid
92.0ms	4142×	body	80	valid
39.0ms	600×	body	320	valid
11.0ms	281×	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