Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	55×	body	1280	valid
4.0ms	35×	body	640	valid
4.0ms	129×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	9×	body	160	valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

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: 29.9b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite44.0ms

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))
28.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series13.0ms

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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune169.0ms

Filtered

113 candidates to 76 candidates (32.7%)

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
2.6b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
72×	`times-frac`
52×	`add-sqr-sqrt`
39×	`distribute-lft-out--`
32×	`exp-prod`
28×	`distribute-lft-out`
17×	`log-pow`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `log-prod`
4×	`exp-sum` `associate-/r*`
3×	`sub-neg` `associate-/l*`
2×	`exp-diff` `diff-log` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `frac-sub` `flip--` `flip-+` `div-inv`

Counts

4 → 118

Calls

4 calls:

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

series25.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ x (+ x 1.0))
8.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ 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)))

simplify143.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	353	877
1	1123	810
2	4298	799
3	5003	799

prune160.0ms

Filtered

130 candidates to 80 candidates (38.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	130	4	134

Merged error: 0.0b

Counts

134 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
4.7b	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
9.4b	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
16.4b	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

287×	`add-sqr-sqrt`
258×	`*-un-lft-identity`
201×	`times-frac`
144×	`difference-of-squares`
108×	`unpow-prod-down` `cube-prod`
106×	`associate-l`
72×	`sqr-pow`
66×	`add-cube-cbrt`
51×	`distribute-lft-out`
45×	`distribute-lft-out--`
25×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
9×	`difference-cubes`
6×	`pow1` `flip3-+` `flip-+`
5×	`frac-sub`
4×	`frac-times` `associate-r/` `associate-/r/` `associate-/l`
3×	`flip3--` `associate-r` `sum-log` `flip--`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `associate--r+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 308

Calls

4 calls:

6.0ms	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
17.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
9.0ms	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
35.0ms	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
5.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
13.0ms	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
6.0ms	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify66.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1183	3828
1	5001	3694

prune622.0ms

Filtered

320 candidates to 168 candidates (47.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	319	5	324

Merged error: 0.0b

Counts

324 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
0.5b	(/ 3.0 (pow x 3))
0.6b	(/ (neg 1.0) (pow x 2))
6.6b	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
120×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
78×	`add-cube-cbrt`
48×	`unpow-prod-down`
29×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`sqr-pow`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*` `unpow2`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`neg-mul-1`
8×	`add-cbrt-cube`
6×	`div-exp`
5×	`frac-sub`
4×	`pow1` `cube-mult` `diff-log` `unpow3`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `frac-2neg` `div-sub` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`distribute-frac-neg`

Counts

4 → 234

Calls

4 calls:

52.0ms	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
6.0ms	(/ (neg 1.0) (pow x 2))
78.0ms	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series21.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
4.0ms	(/ 3.0 (pow x 3))
3.0ms	(/ (neg 1.0) (pow x 2))
7.0ms	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify96.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	738	1746
1	3417	1585
2	5001	1567

prune287.0ms

Filtered

246 candidates to 129 candidates (47.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	245	6	251

Merged error: 0.0b

Counts

251 → 6

regimes85.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.5b

bsearch31.0ms

Steps

Iters	Range		Point
9	1.132733130973407	94732.78899832016	15667.749443421773
9	-4857749967.132658	-1.3201891031641613	-12984.832060830957

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample761.0ms

Algorithm

intervals

Results

256.0ms	1719×	body	1280	valid
147.0ms	1230×	body	640	valid
132.0ms	4077×	body	80	valid
61.0ms	661×	body	320	valid
19.0ms	313×	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

sample27.0ms

simplify23.0ms

prune6.0ms

localize7.0ms

rewrite44.0ms

series13.0ms

simplify46.0ms

prune169.0ms

localize10.0ms

rewrite103.0ms

series25.0ms

simplify143.0ms

prune160.0ms

localize15.0ms

rewrite90.0ms

series26.0ms

simplify66.0ms

prune622.0ms

localize11.0ms

rewrite150.0ms

series21.0ms

simplify96.0ms

prune287.0ms

regimes85.0ms

bsearch31.0ms

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