Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	68×	body	1280	valid
6.0ms	49×	body	640	valid
3.0ms	104×	body	80	valid
2.0ms	88×	body	80	overflowed
2.0ms	21×	body	320	valid
1.0ms	14×	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: 38.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite12.0ms

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:

6.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series46.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify72.0ms

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

prune95.0ms

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

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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)

series54.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(+ (* 1/12 x) (/ 1 x))
14.0ms	(* 1/12 x)

simplify69.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (17.0ms)

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

prune48.0ms

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: 0.0b

Counts

38 → 4

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
3.7b	(- 1 (/ 1.0 (exp x)))

rewrite23.0ms

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:

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

series105.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(/ 1.0 (exp x))
49.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
40.0ms	(- 1 (/ 1.0 (exp x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	310	724
1	1324	622
2	5002	621

prune119.0ms

Filtered

106 candidates to 61 candidates (57.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	105	5	110

Merged error: 0b

Counts

110 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.0b	(- (+ (* 0.16666666666666666 (pow x 3)) (* 1.0 x)) (* 0.5 (pow x 2)))
0.1b	(/ 1 (- (+ (* 0.16666666666666666 (pow x 3)) (* 1.0 x)) (* 0.5 (pow x 2))))
0.1b	(* 0.16666666666666666 (pow x 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`associate-r`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`times-frac` `add-log-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`pow1`
4×	`cube-prod` `sqr-pow`
3×	`associate-/r` `associate-/l`
2×	`pow-to-exp` `flip3--` `diff-log` `div-exp` `pow-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `unpow2`
1×	`cbrt-undiv` `cube-mult` `sub-neg` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `unpow3` `associate--l+` `clear-num` `sum-log` `div-inv` `inv-pow`

Counts

4 → 105

Calls

4 calls:

5.0ms	(* 0.5 (pow x 2))
7.0ms	(- (+ (* 0.16666666666666666 (pow x 3)) (* 1.0 x)) (* 0.5 (pow x 2)))
9.0ms	(/ 1 (- (+ (* 0.16666666666666666 (pow x 3)) (* 1.0 x)) (* 0.5 (pow x 2))))
6.0ms	(* 0.16666666666666666 (pow x 3))

series154.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 0.5 (pow x 2))
35.0ms	(- (+ (* 0.16666666666666666 (pow x 3)) (* 1.0 x)) (* 0.5 (pow x 2)))
55.0ms	(/ 1 (- (+ (* 0.16666666666666666 (pow x 3)) (* 1.0 x)) (* 0.5 (pow x 2))))
37.0ms	(* 0.16666666666666666 (pow x 3))

simplify65.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	410	838
1	1945	740
2	5002	730

prune176.0ms

Filtered

117 candidates to 68 candidates (58.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	117	5	122

Merged error: 0b

Counts

122 → 5

regimes44.0ms

Accuracy

89.6% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 7.6b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample985.0ms

Algorithm

intervals

Results

430.0ms	2253×	body	1280	valid
194.0ms	1579×	body	640	valid
71.0ms	836×	body	320	valid
66.0ms	2904×	body	80	valid
57.0ms	2509×	body	80	overflowed
25.0ms	430×	body	160	valid