Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	60×	body	1280	valid
8.0ms	37×	body	640	valid
5.0ms	131×	body	80	valid
2.0ms	20×	body	320	valid
0.0ms	8×	body	160	valid

simplify23.0ms

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 (100.0%)

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: 29.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

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))
27.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series15.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
10.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune182.0ms

Filtered

113 candidates to 76 candidates (32.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0.1b

Counts

114 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
80×	`times-frac`
64×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`exp-prod`
30×	`distribute-lft-out`
18×	`add-cube-cbrt`
17×	`log-pow` `difference-of-squares`
9×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum` `associate-/l*`
3×	`sub-neg`
2×	`flip3--` `exp-diff` `diff-log` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

4 → 130

Calls

4 calls:

31.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
7.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	404	1009
1	1249	941
2	5001	931

prune212.0ms

Filtered

142 candidates to 86 candidates (39.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	141	9	150

Merged error: 0.0b

Counts

150 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

943×	`*-un-lft-identity`
364×	`times-frac`
253×	`distribute-lft-out--`
186×	`sqrt-prod`
166×	`distribute-lft-out`
117×	`add-sqr-sqrt`
79×	`swap-sqr`
29×	`difference-of-squares`
24×	`sqrt-div`
23×	`add-cube-cbrt`
19×	`pow1` `associate-r` `associate-l`
11×	`flip3--` `flip--`
10×	`frac-sub`
9×	`frac-times`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*` `pow-prod-up`
4×	`associate-/l*` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 258

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
67.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
28.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify82.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	457	2590
1	1894	2448
2	5002	2412

prune322.0ms

Filtered

270 candidates to 109 candidates (59.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	271	8	279

Merged error: 0.0b

Counts

279 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))))
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.3b	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

161×	`*-un-lft-identity`
151×	`add-sqr-sqrt`
102×	`times-frac`
44×	`difference-of-squares`
38×	`sqrt-prod`
36×	`distribute-lft-out--`
34×	`unpow-prod-down` `cube-prod`
29×	`add-cube-cbrt`
26×	`distribute-lft-out`
24×	`cbrt-prod` `sqrt-div`
21×	`associate-r`
19×	`associate-l`
12×	`flip3--` `flip--`
10×	`frac-sub`
9×	`pow1` `add-exp-log` `frac-times` `add-cbrt-cube`
8×	`add-log-exp`
6×	`cube-div`
5×	`cbrt-div` `sqr-pow`
4×	`associate-/r/` `unswap-sqr`
3×	`pow-unpow` `associate-r/` `pow-prod-down` `associate-l/`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-exp` `div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `pow-pow` `sqrt-unprod` `unpow3` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 199

Calls

4 calls:

92.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))))
9.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
54.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))))
3.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
9.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))
8.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify114.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	999	2907
1	3896	2515
2	5002	2454

prune428.0ms

Filtered

211 candidates to 116 candidates (45.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	211	8	219

Merged error: 0.0b

Counts

219 → 8

regimes111.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 28.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	48
1	35	48

end0.0ms

sample761.0ms

Algorithm

intervals

Results

254.0ms	1654×	body	1280	valid
148.0ms	1198×	body	640	valid
135.0ms	4173×	body	80	valid
67.0ms	663×	body	320	valid
20.0ms	312×	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

sample31.0ms

simplify23.0ms

prune2.0ms

localize6.0ms

rewrite43.0ms

series15.0ms

simplify44.0ms

prune182.0ms

localize10.0ms

rewrite105.0ms

series24.0ms

simplify47.0ms

prune212.0ms

localize9.0ms

rewrite163.0ms

series24.0ms

simplify82.0ms

prune322.0ms

localize14.0ms

rewrite200.0ms

series45.0ms

simplify114.0ms

prune428.0ms

regimes111.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample761.0ms

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