Details

sample34.0ms

Algorithm

intervals

Results

10.0ms	57×	body	1280	valid
7.0ms	61×	body	640	valid
4.0ms	185×	body	80	valid
2.0ms	29×	body	320	valid
1.0ms	16×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune6.0ms

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: 39.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
5.7b	(- (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-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

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

series7.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ (- (exp x) 1.0) x)
3.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

58 → 58

Iterations

Useful iterations: 4 (682.0ms)

Iter	Nodes	Cost
0	99	596
1	221	572
2	558	544
3	1434	538
4	4272	536
done	5001	536

prune86.0ms

Filtered

42 candidates to 58 candidates (-38.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	3	59

Merged error: 0.1b

Counts

59 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
2×	`associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 40

Calls

2 calls:

7.0ms	(* x (+ (* x 1/6) 1/2))
4.0ms	(* x 1/6)

series8.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(* x (+ (* x 1/6) 1/2))
2.0ms	(* x 1/6)

simplify1.4s

Counts

46 → 46

Iterations

Useful iterations: 4 (603.0ms)

Iter	Nodes	Cost
0	70	356
1	185	338
2	512	302
3	1346	300
4	3292	298
done	5000	298

prune55.0ms

Filtered

31 candidates to 46 candidates (-48.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	46	3	49

Merged error: 0.1b

Counts

49 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
5.1b	(- (/ (exp x) x) (/ 1.0 x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

8.0ms	(/ (exp x) x)
14.0ms	(- (/ (exp x) x) (/ 1.0 x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(/ (exp x) x)
5.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify877.0ms

Counts

56 → 56

Iterations

Useful iterations: 4 (357.0ms)

Iter	Nodes	Cost
0	105	581
1	218	558
2	554	525
3	1215	505
4	3590	502
done	5000	502

prune63.0ms

Filtered

44 candidates to 56 candidates (-27.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	55	4	59

Merged error: 0.1b

Counts

59 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (exp x) (/ 1 x))
5.1b	(- (* (exp x) (/ 1 x)) (/ 1.0 x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`associate-r`
11×	`*-un-lft-identity` `times-frac`
10×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `prod-exp` `add-log-exp`
3×	`associate-r/` `associate-l*` `un-div-inv` `unswap-sqr`
2×	`div-exp` `frac-sub` `cbrt-unprod` `div-inv` `sub-div`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3--` `distribute-rgt-out--` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `flip--`

Counts

2 → 53

Calls

2 calls:

9.0ms	(* (exp x) (/ 1 x))
9.0ms	(- (* (exp x) (/ 1 x)) (/ 1.0 x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* (exp x) (/ 1 x))
6.0ms	(- (* (exp x) (/ 1 x)) (/ 1.0 x))

simplify691.0ms

Counts

59 → 59

Iterations

Useful iterations: done (690.0ms)

Iter	Nodes	Cost
0	117	612
1	292	473
2	884	399
3	2511	395
done	5000	394

prune53.0ms

Filtered

40 candidates to 59 candidates (-47.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	59	4	63

Merged error: 0.1b

Counts

63 → 4

regimes37.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.1b

bsearch13.0ms

Steps

Iters	Range		Point
9	-0.0001616040529746431	-1.1951251334293225e-11	-9.525718599919936e-05

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	24	23
done	24	23

end0.0ms

sample1.0s

Algorithm

intervals

Results

399.0ms	2294×	body	1280	valid
189.0ms	1658×	body	640	valid
124.0ms	5384×	body	80	valid
66.0ms	810×	body	320	valid
26.0ms	431×	body	160	valid

Details

sample34.0ms

simplify5.0ms

prune6.0ms

localize4.0ms

rewrite13.0ms

series7.0ms

simplify1.3s

prune86.0ms

localize6.0ms

rewrite12.0ms

series8.0ms

simplify1.4s

prune55.0ms

localize6.0ms

rewrite24.0ms

series9.0ms

simplify877.0ms

prune63.0ms

localize7.0ms

rewrite19.0ms

series9.0ms

simplify691.0ms

prune53.0ms

regimes37.0ms

bsearch13.0ms

simplify2.0ms

end0.0ms

sample1.0s

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