Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	76×	body	1280	valid
9.0ms	78×	body	10240	exit
8.0ms	62×	body	640	valid
2.0ms	86×	body	80	valid
2.0ms	26×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

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: 43.0b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
2.7b	(- (exp x) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

7.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series44.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	180	378
1	542	357
2	2210	354
3	5001	354

prune104.0ms

Filtered

57 candidates to 41 candidates (71.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Merged error: 0.0b

Counts

58 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (/ 1 x))
0.3b	(* 1/12 x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 29

Calls

2 calls:

5.0ms	(+ (* 1/12 x) (/ 1 x))
3.0ms	(* 1/12 x)

series56.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(+ (* 1/12 x) (/ 1 x))
16.0ms	(* 1/12 x)

simplify68.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	130	119
1	448	110
2	2305	109
3	5001	109

prune49.0ms

Filtered

35 candidates to 23 candidates (65.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	34	4	38

Merged error: 0b

Counts

38 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (/ 1 x)) x)
0.2b	(* 1/144 (* x x))
0.3b	(* 1/12 x)
28.9b	(/ (+ (/ (- (/ 1 x)) x) (* 1/144 (* x x))) (- (* 1/12 x) (/ 1 x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

171×	`times-frac`
109×	`add-sqr-sqrt`
106×	`add-cube-cbrt` `*-un-lft-identity`
52×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
33×	`associate-/l*`
15×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`div-inv`
6×	`associate-l` `associate-/r*`
4×	`neg-mul-1` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-exp` `clear-num` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`associate-+l-` `flip3--` `flip3-+` `distribute-frac-neg` `flip--` `flip-+` `distribute-neg-frac`

Counts

4 → 207

Calls

4 calls:

9.0ms	(/ (- (/ 1 x)) x)
5.0ms	(* 1/144 (* x x))
4.0ms	(* 1/12 x)
35.0ms	(/ (+ (/ (- (/ 1 x)) x) (* 1/144 (* x x))) (- (* 1/12 x) (/ 1 x)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (- (/ 1 x)) x)
25.0ms	(* 1/144 (* x x))
13.0ms	(* 1/12 x)
132.0ms	(/ (+ (/ (- (/ 1 x)) x) (* 1/144 (* x x))) (- (* 1/12 x) (/ 1 x)))

simplify81.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	793	1686
1	3062	1440
2	5001	1417

prune321.0ms

Filtered

219 candidates to 127 candidates (58.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	219	4	223

Merged error: 0b

Counts

223 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.2b	(/ 1.0 (exp x))
2.7b	(- 1 (/ 1.0 (exp x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
43×	`times-frac`
24×	`add-cube-cbrt`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`div-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--` `div-inv`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 97

Calls

3 calls:

9.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
4.0ms	(/ 1.0 (exp x))
7.0ms	(- 1 (/ 1.0 (exp x)))

series99.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
13.0ms	(/ 1.0 (exp x))
35.0ms	(- 1 (/ 1.0 (exp x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	310	724
1	1324	622
2	5001	621

prune119.0ms

Filtered

106 candidates to 61 candidates (57.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	106	4	110

Merged error: 0b

Counts

110 → 4

regimes52.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 21.3b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	25
1	27	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

395.0ms	2220×	body	1280	valid
293.0ms	2549×	body	10240	exit
196.0ms	1757×	body	640	valid
60.0ms	2825×	body	80	valid
58.0ms	777×	body	320	valid
20.0ms	427×	body	160	valid