Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	53×	body	1280	valid
4.0ms	38×	body	640	valid
4.0ms	136×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	9×	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

prune3.0ms

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: 28.3b

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))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite51.0ms

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))
35.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

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

prune445.0ms

Filtered

113 candidates to 76 candidates (32.7%)

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
2.7b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite160.0ms

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:

10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
17.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
7.0ms	(pow (/ x (+ x 1.0)) 3)
108.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series29.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.0ms	(pow (/ x (+ x 1.0)) 3)
19.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify61.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1164	2932
1	5002	2690

prune2.0s

Filtered

315 candidates to 141 candidates (55.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	314	1	315
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	315	5	320

Merged error: 0.0b

Counts

320 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ x (+ x 1.0)))
0.4b	(pow (cbrt (/ x (+ x 1.0))) 4)
2.7b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
15.4b	(cbrt (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

220×	`*-un-lft-identity`
112×	`times-frac`
106×	`add-sqr-sqrt`
81×	`unpow-prod-down`
60×	`cube-prod`
53×	`distribute-lft-out--`
38×	`distribute-lft-out`
37×	`cbrt-prod`
36×	`difference-of-squares`
22×	`add-cube-cbrt`
13×	`sqr-pow`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `associate-/r/` `add-cbrt-cube`
3×	`pow-unpow` `pow1/3`
2×	`cube-div` `pow-pow` `flip3-+` `flip-+` `div-inv`
1×	`difference-cubes` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-r/` `associate-l/` `pow-exp` `frac-sub` `flip--`

Counts

4 → 162

Calls

4 calls:

5.0ms	(cbrt (/ x (+ x 1.0)))
8.0ms	(pow (cbrt (/ x (+ x 1.0))) 4)
109.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
9.0ms	(cbrt (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cbrt (/ x (+ x 1.0)))
15.0ms	(pow (cbrt (/ x (+ x 1.0))) 4)
14.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
7.0ms	(cbrt (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	755	1996
1	2641	1923
2	5002	1916

prune1.5s

Filtered

174 candidates to 96 candidates (44.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	174	5	179

Merged error: 0.0b

Counts

179 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(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))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

273×	`*-un-lft-identity`
120×	`times-frac`
91×	`add-sqr-sqrt`
70×	`distribute-lft-out--`
46×	`distribute-lft-out`
38×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
25×	`difference-of-squares`
21×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`flip3--` `flip--` `associate-/l*`
3×	`pow-unpow` `cbrt-div` `frac-sub`
2×	`cube-mult` `unpow3` `associate-/r/` `associate-/l/` `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 → 173

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
32.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
36.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify66.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	547	1756
1	2156	1696
2	5001	1685

prune689.0ms

Filtered

185 candidates to 91 candidates (50.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	184	6	190

Merged error: 0.0b

Counts

190 → 6

regimes99.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch123.0ms

Steps

Iters	Range		Point
9	41.84587058567329	170944420.23003155	11074.398044080288
8	-41296.44367278978	-27.465585783021098	-11356.529822975868

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	39
1	46	39

end0.0ms

sample645.0ms

Algorithm

intervals

Results

216.0ms	1720×	body	1280	valid
123.0ms	1266×	body	640	valid
110.0ms	4117×	body	80	valid
43.0ms	579×	body	320	valid
16.0ms	318×	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

sample25.0ms

simplify17.0ms

prune3.0ms

localize6.0ms

rewrite51.0ms

series12.0ms

simplify42.0ms

prune445.0ms

localize15.0ms

rewrite160.0ms

series29.0ms

simplify61.0ms

prune2.0s

localize24.0ms

rewrite141.0ms

series48.0ms

simplify83.0ms

prune1.5s

localize9.0ms

rewrite118.0ms

series25.0ms

simplify66.0ms

prune689.0ms

regimes99.0ms

bsearch123.0ms

simplify2.0ms

end0.0ms

sample645.0ms

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