Details

sample41.0ms

Algorithm

intervals

Results

14.0ms	110×	body	1280	valid
7.0ms	78×	body	640	valid
4.0ms	383×	pre	80	true
2.0ms	43×	body	320	valid
2.0ms	135×	body	80	valid
1.0ms	17×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	4	4
1	6	4
2	7	4
done	7	4

prune2.0ms

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: 58.4b

Counts

2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

5.3b	(- (exp x) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

(- (exp x) 1.0)

simplify684.0ms

Counts

17 → 17

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	39	132
1	83	127
2	191	119
3	368	117
4	728	117
5	1712	117
done	5000	117

prune40.0ms

Filtered

12 candidates to 17 candidates (-41.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	3	18

Merged error: 0.1b

Counts

18 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)
0.0b	(* (pow x 2) (+ 1/2 (* 1/6 x)))
0.3b	(* 1/6 x)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`associate-l`
10×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
6×	`associate-r`
5×	`pow1` `add-log-exp` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-prod-down` `pow-exp` `sum-log`

Counts

3 → 62

Calls

3 calls:

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

series13.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)
7.0ms	(* (pow x 2) (+ 1/2 (* 1/6 x)))
2.0ms	(* 1/6 x)

simplify479.0ms

Counts

71 → 71

Iterations

Useful iterations: done (477.0ms)

Iter	Nodes	Cost
0	109	816
1	313	732
2	1214	673
done	5000	667

prune98.0ms

Filtered

49 candidates to 71 candidates (-44.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	70	4	74

Merged error: 0.1b

Counts

74 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)) (cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
0.6b	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
0.6b	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
0.6b	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

17.0ms	(* (cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)) (cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
7.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
6.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
7.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))

series37.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)) (cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x)))
9.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
9.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
9.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))

simplify834.0ms

Counts

99 → 99

Iterations

Useful iterations: 3 (297.0ms)

Iter	Nodes	Cost
0	147	3133
1	325	2957
2	930	2665
3	3090	2294
done	5001	2294

prune349.0ms

Filtered

75 candidates to 99 candidates (-32.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	99	4	103

Merged error: 0.1b

Counts

103 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
0.6b	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-div` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `flip-+`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
7.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
7.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))

series67.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt x)
26.0ms	(cbrt x)
9.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))
9.0ms	(cbrt (+ (* (pow x 2) (+ 1/2 (* 1/6 x))) x))

simplify725.0ms

Counts

60 → 60

Iterations

Useful iterations: 3 (163.0ms)

Iter	Nodes	Cost
0	93	1008
1	199	974
2	540	860
3	1748	794
done	5000	794

prune168.0ms

Filtered

48 candidates to 60 candidates (-25.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	60	4	64

Merged error: 0.1b

Counts

64 → 4

regimes93.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	13	11
done	13	11

end0.0ms

sample1.2s

Algorithm

intervals

Results

456.0ms	3450×	body	1280	valid
212.0ms	2483×	body	640	valid
124.0ms	11954×	pre	80	true
73.0ms	1272×	body	320	valid
64.0ms	4145×	body	80	valid
24.0ms	604×	body	160	valid

Details

sample41.0ms

simplify3.0ms

prune2.0ms

localize3.0ms

rewrite5.0ms

series2.0ms

simplify684.0ms

prune40.0ms

localize7.0ms

rewrite19.0ms

series13.0ms

simplify479.0ms

prune98.0ms

localize12.0ms

rewrite39.0ms

series37.0ms

simplify834.0ms

prune349.0ms

localize19.0ms

rewrite17.0ms

series67.0ms

simplify725.0ms

prune168.0ms

regimes93.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling