Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	41×	body	1280	valid
4.0ms	39×	body	640	valid
4.0ms	145×	body	80	valid
1.0ms	18×	body	320	valid
1.0ms	13×	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

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: 25.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`

Counts

2 → 71

Calls

2 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
33.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series222.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (+ x 1.0) (- x 1.0))
169.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify145.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	317	591
1	1003	565
2	4494	559
3	5003	559

prune240.0ms

Filtered

77 candidates to 50 candidates (35.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	4	78

Merged error: 0.2b

Counts

78 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
5.7b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `frac-sub`
5×	`associate-/r*` `add-log-exp`
4×	`frac-times` `flip3-+` `div-exp` `associate-l` `associate-*l/` `prod-exp` `associate-/r/` `flip-+`
3×	`flip3--` `flip--` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-*r/` `un-div-inv` `cbrt-unprod` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `*-commutative` `distribute-lft-out` `inv-pow`

Counts

3 → 108

Calls

3 calls:

5.0ms	(/ 1 (- x 1.0))
12.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
9.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series262.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ 1 (- x 1.0))
48.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
175.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	499	779
1	2438	701
2	5001	647

prune377.0ms

Filtered

117 candidates to 68 candidates (41.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	117	4	121

Merged error: 0.2b

Counts

121 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.1b	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
5.0b	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
30.0ms	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
31.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
28.0ms	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series672.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (+ x 1.0) (- x 1.0))
173.0ms	(exp (log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
170.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
281.0ms	(log (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	475	1328
1	1529	1251
2	5001	1219

prune741.0ms

Filtered

142 candidates to 89 candidates (37.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	141	5	146

Merged error: 0.0b

Counts

146 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (* 1.0 (- 1.0 x)) (pow x 2)) (+ x 1.0))
4.8b	(- (* x (- (* 1.0 1.0) (* x 1.0))) (* (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)) (+ x 1.0)))
4.9b	(/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))
20.3b	(+ (pow x 3) (- (* x (- (* 1.0 1.0) (* x 1.0))) (* (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)) (+ x 1.0))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
45×	`times-frac`
44×	`add-sqr-sqrt`
32×	`distribute-lft-out`
24×	`unpow-prod-down` `cube-prod`
22×	`add-cube-cbrt`
16×	`associate-*r/`
12×	`flip3-+` `flip-+`
11×	`add-log-exp`
10×	`frac-sub` `distribute-lft-out--` `difference-of-squares`
9×	`associate-/l*`
8×	`add-exp-log` `frac-times` `associate--l+` `add-cbrt-cube`
7×	`flip3--` `flip--`
6×	`pow1` `distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `sum-cubes`
5×	`associate-/r*`
4×	`associate-r` `associate-*l/`
3×	`associate-l`
2×	`diff-log` `sum-log` `associate-/r/` `associate-/l/` `associate--r+`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 152

Calls

4 calls:

12.0ms	(* (+ (* 1.0 (- 1.0 x)) (pow x 2)) (+ x 1.0))
7.0ms	(- (* x (- (* 1.0 1.0) (* x 1.0))) (* (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)) (+ x 1.0)))
15.0ms	(/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))
9.0ms	(+ (pow x 3) (- (* x (- (* 1.0 1.0) (* x 1.0))) (* (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)) (+ x 1.0))))

series617.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (+ (* 1.0 (- 1.0 x)) (pow x 2)) (+ x 1.0))
155.0ms	(- (* x (- (* 1.0 1.0) (* x 1.0))) (* (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)) (+ x 1.0)))
60.0ms	(/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0))
214.0ms	(+ (pow x 3) (- (* x (- (* 1.0 1.0) (* x 1.0))) (* (/ (+ (pow x 3) (pow 1.0 3)) (- x 1.0)) (+ x 1.0))))

simplify132.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	871	1983
1	4713	1875
2	5003	1874

prune1.6s

Filtered

164 candidates to 104 candidates (36.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	163	6	169

Merged error: 0.0b

Counts

169 → 6

regimes99.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.3b

bsearch129.0ms

Steps

Iters	Range		Point
9	76.94053799743773	23146340971.272755	13973.283901258525
9	-57514.079310754976	-0.04031575958609914	-0.9933408418278237

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	38
1	52	38

end0.0ms

sample640.0ms

Algorithm

intervals

Results

216.0ms	1724×	body	1280	valid
118.0ms	1220×	body	640	valid
109.0ms	4113×	body	80	valid
48.0ms	628×	body	320	valid
16.0ms	315×	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

sample23.0ms

simplify18.0ms

prune3.0ms

localize6.0ms

rewrite43.0ms

series222.0ms

simplify145.0ms

prune240.0ms

localize7.0ms

rewrite31.0ms

series262.0ms

simplify66.0ms

prune377.0ms

localize9.0ms

rewrite104.0ms

series672.0ms

simplify53.0ms

prune741.0ms

localize22.0ms

rewrite54.0ms

series617.0ms

simplify132.0ms

prune1.6s

regimes99.0ms

bsearch129.0ms

simplify2.0ms

end0.0ms

sample640.0ms

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