Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	54×	body	1280	valid
3.0ms	40×	body	640	valid
3.0ms	136×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	5×	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: 28.5b

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))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite49.0ms

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))
8.0ms	(/ (+ x 1.0) (- x 1.0))
32.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
131.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

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

prune190.0ms

Filtered

113 candidates to 76 candidates (67.3%)

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: 0b

Counts

114 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(/ x (+ x 1.0))
0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
2.9b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

211×	`times-frac`
209×	`*-un-lft-identity`
166×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
34×	`associate-/r*`
31×	`distribute-lft-out` `difference-of-squares`
25×	`distribute-lft-out--`
19×	`add-exp-log`
13×	`associate-/r/` `add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `frac-sub` `inv-pow`

Counts

4 → 234

Calls

4 calls:

7.0ms	(/ (- x 1.0) (+ x 1.0))
5.0ms	(/ x (+ x 1.0))
11.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
66.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- x 1.0) (+ x 1.0))
35.0ms	(/ x (+ x 1.0))
37.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
130.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	742	2083
1	3390	1767
2	5001	1758

prune242.0ms

Filtered

246 candidates to 126 candidates (51.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	246	4	250

Merged error: 0b

Counts

250 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.0b	(/ x (+ x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
6.1b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite41.0ms

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	(/ 1 (- x 1.0))
5.0ms	(/ x (+ x 1.0))
16.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
9.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (- x 1.0))
34.0ms	(/ x (+ x 1.0))
40.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
128.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify73.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	576	950
1	2837	862
2	5001	820

prune185.0ms

Filtered

153 candidates to 100 candidates (65.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	153	4	157

Merged error: 0b

Counts

157 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
0.1b	(/ (- x 1.0) (sqrt (+ x 1.0)))
7.4b	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

rewrite328.0ms

Algorithm

rewrite-expression-head

Rules

645×	`times-frac`
584×	`*-un-lft-identity`
444×	`add-sqr-sqrt`
362×	`sqrt-prod`
261×	`add-cube-cbrt`
93×	`distribute-lft-out`
78×	`difference-of-squares`
67×	`distribute-lft-out--`
52×	`associate-/r*`
21×	`associate-/r/`
20×	`sqrt-div`
15×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
11×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log` `div-sub` `frac-sub`

Counts

4 → 479

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
19.0ms	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
8.0ms	(/ (- x 1.0) (sqrt (+ x 1.0)))
257.0ms	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ x (+ x 1.0))
44.0ms	(/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0))))
96.0ms	(/ (- x 1.0) (sqrt (+ x 1.0)))
128.0ms	(- (/ x (+ x 1.0)) (/ (sqrt (+ x 1.0)) (/ (- x 1.0) (sqrt (+ x 1.0)))))

simplify97.0ms

Algorithm

egg-herbie

Counts

491 → 491

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1122	6922
1	5002	6212

prune521.0ms

Filtered

491 candidates to 201 candidates (40.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	491	4	495

Merged error: 0b

Counts

495 → 4

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch78.0ms

Steps

Iters	Range		Point
10	0.475758948552502	3048118974.682059	10939.136774846365
9	-164485.30314980465	-0.009598081335721272	-14024.47786235224

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	35	15

end0.0ms

sample534.0ms

Algorithm

intervals

Results

178.0ms	1702×	body	1280	valid
105.0ms	4110×	body	80	valid
103.0ms	1269×	body	640	valid
41.0ms	616×	body	320	valid
13.0ms	303×	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