Details

sample42.0ms

Algorithm

intervals

Results

15.0ms	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

prune8.0ms

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

localize4.0ms

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)

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(- (exp x) 1.0)

simplify701.0ms

Counts

17 → 17

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	39	132
1	83	127
2	193	119
3	363	117
4	724	117
5	1787	117
done	5001	117

prune42.0ms

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

9.0ms	(+ (* (* x x) (+ (* x 1/6) 1/2)) x)
9.0ms	(* (* x x) (+ (* x 1/6) 1/2))
4.0ms	(* x 1/6)

series14.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify1.8s

Counts

63 → 63

Iterations

Useful iterations: 3 (593.0ms)

Iter	Nodes	Cost
0	99	712
1	295	672
2	1085	600
3	4665	579
done	5000	579

prune71.0ms

Filtered

43 candidates to 63 candidates (-46.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	62	4	66

Merged error: 0.1b

Counts

66 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x)) (cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x)))
9.0ms	(cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
13.0ms	(cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
9.0ms	(cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x))

simplify962.0ms

Counts

99 → 99

Iterations

Useful iterations: done (958.0ms)

Iter	Nodes	Cost
0	147	3133
1	327	2968
2	1024	2669
3	3300	2345
done	5001	2294

prune286.0ms

Filtered

78 candidates to 99 candidates (-26.9%)

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

rewrite23.0ms

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:

2.0ms	(cbrt x)
1.0ms	(cbrt x)
9.0ms	(cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
9.0ms	(cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x))

series71.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt x)
28.0ms	(cbrt x)
9.0ms	(cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
9.0ms	(cbrt (+ (* (* x x) (+ (* x 1/6) 1/2)) x))

simplify806.0ms

Counts

60 → 60

Iterations

Useful iterations: 3 (216.0ms)

Iter	Nodes	Cost
0	93	1008
1	201	974
2	617	860
3	2005	794
done	5000	794

prune141.0ms

Filtered

50 candidates to 60 candidates (-20.0%)

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

regimes91.0ms

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	8	11
1	12	11
done	12	11

end0.0ms

sample1.2s

Algorithm

intervals

Results

475.0ms	3450×	body	1280	valid
215.0ms	2483×	body	640	valid
132.0ms	11954×	pre	80	true
72.0ms	1272×	body	320	valid
65.0ms	4145×	body	80	valid
22.0ms	604×	body	160	valid

Details

sample42.0ms

simplify3.0ms

prune8.0ms

localize4.0ms

rewrite5.0ms

series3.0ms

simplify701.0ms

prune42.0ms

localize7.0ms

rewrite23.0ms

series14.0ms

simplify1.8s

prune71.0ms

localize11.0ms

rewrite54.0ms

series42.0ms

simplify962.0ms

prune286.0ms

localize19.0ms

rewrite23.0ms

series71.0ms

simplify806.0ms

prune141.0ms

regimes91.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling