Details

analyze4.0ms

Algorithm: search

sample23.0ms

Algorithm

intervals

Results

7.0ms	48×	body	1280	valid
4.0ms	143×	body	80	valid
4.0ms	33×	body	640	valid
1.0ms	17×	body	320	valid
1.0ms	15×	body	160	valid

simplify17.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 26.3b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite49.0ms

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:

7.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(/ x (+ x 1.0))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ (+ x 1.0) (- x 1.0))
3.0ms	(/ x (+ x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

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

prune182.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 0.0b

Counts

114 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.1b	(pow (/ x (+ x 1.0)) 3)
3.6b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

354×	`*-un-lft-identity`
216×	`times-frac`
190×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
78×	`add-cube-cbrt`
66×	`distribute-lft-out`
61×	`distribute-lft-out--`
44×	`difference-of-squares`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`associate-/r/`
14×	`sqr-pow`
13×	`pow1`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`cube-div` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 303

Calls

4 calls:

18.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
7.0ms	(pow (/ x (+ x 1.0)) 3)
109.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series29.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
8.0ms	(pow (/ x (+ x 1.0)) 3)
14.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1164	2956
1	5002	2714

prune600.0ms

Filtered

141 candidates to 315 candidates (-123.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	314	1	315
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	314	6	320

Merged error: 0.0b

Counts

320 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ x (+ x 1.0)) 3)
0.1b	(cbrt (pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3))
0.1b	(pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3)
3.6b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

969×	`*-un-lft-identity`
472×	`unpow-prod-down` `cube-prod`
464×	`times-frac`
447×	`add-sqr-sqrt`
265×	`distribute-lft-out--`
180×	`difference-of-squares`
166×	`distribute-lft-out`
160×	`cbrt-prod`
63×	`sqr-pow`
27×	`add-cube-cbrt`
13×	`cube-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `pow-unpow` `add-log-exp`
5×	`difference-cubes`
4×	`associate-/r/`
3×	`cube-mult` `cbrt-div` `flip3--` `unpow3` `pow-exp` `frac-sub` `flip--` `rem-cube-cbrt`
2×	`pow-to-exp` `pow-pow` `flip3-+` `flip-+` `div-inv`
1×	`cbrt-undiv` `sub-neg` `pow1/3` `diff-log` `div-exp` `rem-cbrt-cube`

Counts

4 → 489

Calls

4 calls:

7.0ms	(pow (/ x (+ x 1.0)) 3)
139.0ms	(cbrt (pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3))
116.0ms	(pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3)
152.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series48.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (/ x (+ x 1.0)) 3)
14.0ms	(cbrt (pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3))
16.0ms	(pow (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) 3)
14.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify170.0ms

Algorithm

egg-herbie

Counts

501 → 501

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	961	6891
1	4196	6738
2	5002	6608

prune593.0ms

Filtered

112 candidates to 501 candidates (-347.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	500	1	501
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	500	7	507

Merged error: 0.0b

Counts

507 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.1b	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
0.1b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
3.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

257×	`*-un-lft-identity`
112×	`times-frac`
79×	`add-sqr-sqrt`
65×	`distribute-lft-out--`
44×	`distribute-lft-out`
38×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
20×	`difference-of-squares`
19×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`pow-unpow` `cbrt-div` `flip3--` `frac-sub` `flip--` `associate-/l*`
2×	`cube-mult` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 161

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
34.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
34.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ x 1.0))
7.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
8.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
8.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	496	1624
1	2016	1565
2	5002	1559

prune180.0ms

Filtered

84 candidates to 173 candidates (-106.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	173	7	180

Merged error: 0.0b

Counts

180 → 7

regimes105.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch45.0ms

Steps

Iters	Range		Point
9	25.58295148917769	42043720.92738165	10255.225871395764
9	-1615134472.8236558	-14.56946306826808	-10913.572853083262

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	35
1	42	35

end0.0ms

analyze4.0ms

Algorithm: search

sample693.0ms

Algorithm

intervals

Results

251.0ms	1704×	body	1280	valid
143.0ms	1199×	body	640	valid
129.0ms	4121×	body	80	valid
57.0ms	665×	body	320	valid
20.0ms	311×	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

Details

analyze4.0ms

sample23.0ms

simplify17.0ms

prune2.0ms

localize6.0ms

rewrite49.0ms

series12.0ms

simplify41.0ms

prune182.0ms

localize17.0ms

rewrite163.0ms

series29.0ms

simplify58.0ms

prune600.0ms

localize17.0ms

rewrite468.0ms

series48.0ms

simplify170.0ms

prune593.0ms

localize9.0ms

rewrite115.0ms

series26.0ms

simplify63.0ms

prune180.0ms

regimes105.0ms

bsearch45.0ms

simplify1.0ms

end0.0ms

analyze4.0ms

sample693.0ms

Profiling

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