Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	51×	body	1280	valid
5.0ms	41×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	22×	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

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: 28.5b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.1b	(- (/ 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)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(/ x (+ x 1.0))
3.0ms	(/ (+ x 1.0) (- x 1.0))
7.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune163.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 0.0b

Counts

114 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (- x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
8.5b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
5.0ms	(/ 1 (- x 1.0))
13.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
9.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
2.0ms	(/ 1 (- x 1.0))
3.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify74.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	576	948
1	2837	860
2	5001	818

prune163.0ms

Filtered

98 candidates to 153 candidates (-56.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Merged error: 0.0b

Counts

157 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- x 1.0))
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)))
17.7b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

6.0ms	(* x (- x 1.0))
8.0ms	(* (+ x 1.0) (+ x 1.0))
14.0ms	(/ (- (* 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)))

series16.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* x (- x 1.0))
2.0ms	(* (+ x 1.0) (+ x 1.0))
4.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
4.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify131.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	769	1735
1	4437	1626
2	5003	1621

prune258.0ms

Filtered

110 candidates to 164 candidates (-49.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	166	2	168

Merged error: 0b

Counts

168 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3.0 x) 1.0)
13.9b	(/ (neg (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

rewrite16.0ms

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:

3.0ms	(+ (* 3.0 x) 1.0)
9.0ms	(/ (neg (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

series7.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	396	958
1	1618	921
2	5001	919

prune122.0ms

Filtered

70 candidates to 89 candidates (-27.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	89	2	91

Merged error: 0b

Counts

91 → 2

regimes32.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch38.0ms

Steps

Iters	Range		Point
10	1.6467731241392944e-08	62869179882.65231	393170.98048391176
11	-1.7554059141447428e+34	-2742411761.3317285	-6.416759838363408e+31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	15
1	44	15
2	44	15

end0.0ms

sample721.0ms

Algorithm

intervals

Results

251.0ms	1733×	body	1280	valid
144.0ms	1266×	body	640	valid
125.0ms	4091×	body	80	valid
49.0ms	580×	body	320	valid
21.0ms	330×	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

sample24.0ms

simplify17.0ms

prune2.0ms

localize10.0ms

rewrite46.0ms

series12.0ms

simplify41.0ms

prune163.0ms

localize8.0ms

rewrite38.0ms

series17.0ms

simplify74.0ms

prune163.0ms

localize10.0ms

rewrite44.0ms

series16.0ms

simplify131.0ms

prune258.0ms

localize8.0ms

rewrite16.0ms

series7.0ms

simplify43.0ms

prune122.0ms

regimes32.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample721.0ms

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