Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	46×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	132×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid

simplify21.0ms

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 (0.0%)

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: 29.4b

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))
4.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite52.0ms

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))
5.0ms	(/ x (+ x 1.0))
36.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
40.0ms	(/ x (+ x 1.0))
134.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5002	716

prune218.0ms

Filtered

113 candidates to 76 candidates (67.3%)

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

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*r/`
32×	`frac-sub`
30×	`*-un-lft-identity` `flip3-+` `flip-+`
20×	`frac-times`
19×	`flip3--` `flip--`
18×	`add-sqr-sqrt` `associate-/l/`
16×	`add-cube-cbrt`
12×	`times-frac`
10×	`pow1` `associate-*l/`
7×	`add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `distribute-lft-out`
5×	`add-log-exp`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `associate--l+` `associate-/r*` `difference-of-squares`
3×	`sub-neg` `associate-/l*`
2×	`associate-/r/` `associate--r+`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 126

Calls

3 calls:

8.0ms	(* (+ x 1.0) (+ x 1.0))
18.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
8.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series110.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(* (+ x 1.0) (+ x 1.0))
56.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
39.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify124.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	719	1640
1	4033	1538
2	5002	1533

prune496.0ms

Filtered

135 candidates to 93 candidates (68.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	135	3	138

Merged error: 0.0b

Counts

138 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3.0 x) 1.0)
12.5b	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`difference-of-squares`
10×	`associate-/l*`
5×	`neg-mul-1`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+` `associate-/l/` `distribute-neg-frac`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `flip3--` `frac-2neg` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 83

Calls

2 calls:

4.0ms	(+ (* 3.0 x) 1.0)
10.0ms	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(+ (* 3.0 x) 1.0)
53.0ms	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	396	962
1	1629	925
2	5001	919

prune178.0ms

Filtered

89 candidates to 70 candidates (78.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	89	3	92

Merged error: 0b

Counts

92 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 3.0 x) 1.0)
0.1b	(/ -1 (/ (- (* x x) (* 1.0 1.0)) (+ (* 3.0 x) 1.0)))
12.5b	(/ (- (* x x) (* 1.0 1.0)) (+ (* 3.0 x) 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
63×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`associate-/r*`
16×	`difference-of-squares`
11×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`flip3-+` `flip-+` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `flip3--` `div-sub` `sum-log` `flip--`

Counts

3 → 137

Calls

3 calls:

4.0ms	(+ (* 3.0 x) 1.0)
10.0ms	(/ -1 (/ (- (* x x) (* 1.0 1.0)) (+ (* 3.0 x) 1.0)))
9.0ms	(/ (- (* x x) (* 1.0 1.0)) (+ (* 3.0 x) 1.0))

series140.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (* 3.0 x) 1.0)
51.0ms	(/ -1 (/ (- (* x x) (* 1.0 1.0)) (+ (* 3.0 x) 1.0)))
52.0ms	(/ (- (* x x) (* 1.0 1.0)) (+ (* 3.0 x) 1.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	645	1737
1	3315	1654
2	5001	1573

prune265.0ms

Filtered

146 candidates to 107 candidates (73.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	146	3	149

Merged error: 0b

Counts

149 → 3

regimes23.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch81.0ms

Steps

Iters	Range		Point
9	0.3235305135594418	1774840.6331059302	96405.29383849494
9	-107831645193065.94	-647201329.329077	-7336262872.664932

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample539.0ms

Algorithm

intervals

Results

185.0ms	1670×	body	1280	valid
105.0ms	1219×	body	640	valid
95.0ms	4170×	body	80	valid
43.0ms	618×	body	320	valid
14.0ms	323×	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

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