Details

sample37.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.987793%

Results

9.0ms	39×	body	640	valid
8.0ms	53×	body	1280	valid
4.0ms	138×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid

simplify18.0ms

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: 27.4b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite46.0ms

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

series16.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ x (+ x 1.0))
6.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune173.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	3	114

Merged error: 0.0b

Counts

114 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
2.2b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite108.0ms

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:

32.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
27.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
17.0ms	(* (/ x (+ x 1.0)) (/ x (+ 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))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
4.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
11.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify59.0ms

Algorithm

egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1145	2720
1	5002	2529

prune464.0ms

Filtered

142 candidates to 271 candidates (-90.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	268	3	271
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	269	5	274

Merged error: 0.0b

Counts

274 → 5

localize14.0ms

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	(pow (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
2.2b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

391×	`*-un-lft-identity`
224×	`times-frac`
155×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
90×	`distribute-lft-out`
72×	`swap-sqr`
44×	`associate-r` `associate-l`
40×	`distribute-lft-out--`
29×	`add-exp-log` `add-cbrt-cube`
21×	`difference-of-squares`
19×	`pow1`
16×	`associate-/r/`
12×	`unpow-prod-down` `cube-prod`
9×	`frac-sub`
8×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
6×	`add-log-exp`
5×	`flip3--` `flip3-+` `flip--` `flip-+`
3×	`cube-div` `pow-unpow`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `diff-log` `unpow3` `frac-add` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 282

Calls

4 calls:

31.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
20.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
44.0ms	(pow (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
7.0ms	(pow (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify65.0ms

Algorithm

egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1244	2928
1	5002	2765

prune573.0ms

Filtered

147 candidates to 294 candidates (-100.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	294	5	299

Merged error: 0.0b

Counts

299 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))))) (- (* x x) (* 1.0 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))))) (- (* x x) (* 1.0 1.0)))
0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
17.5b	(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0)))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

1056×	`*-un-lft-identity`
704×	`times-frac`
340×	`distribute-lft-out`
250×	`associate-*r/`
228×	`frac-times`
170×	`frac-sub`
136×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`flip3-+` `flip-+`
114×	`associate-*l/`
88×	`associate-/l/`
84×	`flip3--` `flip--`
80×	`distribute-lft-out--`
43×	`difference-of-squares`
31×	`associate-/r/`
21×	`associate-/l*`
16×	`associate-/r*`
15×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp` `associate--l+`
3×	`sub-neg` `div-sub`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `frac-add` `clear-num`
1×	`+-commutative` `diff-log` `sum-log`

Counts

4 → 508

Calls

4 calls:

47.0ms	(/ (/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))))) (- (* x x) (* 1.0 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
31.0ms	(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))))) (- (* x x) (* 1.0 1.0)))
29.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
17.0ms	(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0)))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))))) (- (* x x) (* 1.0 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
24.0ms	(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0))))) (- (* x x) (* 1.0 1.0)))
6.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
15.0ms	(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ x 1.0) (/ (+ x 1.0) (- x 1.0)))))

simplify188.0ms

Algorithm

egg-herbie

Counts

520 → 520

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2073	16275
1	5001	15996

prune2.5s

Filtered

295 candidates to 520 candidates (-76.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	518	2	520
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	518	7	525

Merged error: 0.0b

Counts

525 → 7

regimes58.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch32.0ms

Steps

Iters	Range		Point
8	81.18943540732513	84242.96603183816	12828.87251172184
8	-1668307.5034652743	-26.15695727702824	-14977.6836537101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	32
1	45	32

end0.0ms

sample775.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.987793%

Results

263.0ms	1713×	body	1280	valid
151.0ms	1241×	body	640	valid
131.0ms	4067×	body	80	valid
60.0ms	650×	body	320	valid
22.0ms	329×	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

sample37.0ms

simplify18.0ms

prune2.0ms

localize7.0ms

rewrite46.0ms

series16.0ms

simplify42.0ms

prune173.0ms

localize11.0ms

rewrite108.0ms

series25.0ms

simplify59.0ms

prune464.0ms

localize14.0ms

rewrite135.0ms

series25.0ms

simplify65.0ms

prune573.0ms

localize21.0ms

rewrite180.0ms

series69.0ms

simplify188.0ms

prune2.5s

regimes58.0ms

bsearch32.0ms

simplify2.0ms

end0.0ms

sample775.0ms

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