Details

sample41.0ms

Algorithm

intervals

Results

16.0ms	78×	body	1280	valid
7.0ms	69×	body	10240	exit
6.0ms	56×	body	640	valid
2.0ms	25×	body	320	valid
2.0ms	88×	body	80	valid
0.0ms	9×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	8	7
done	8	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
2.7b	(- (exp x) 1.0)

rewrite15.0ms

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:

9.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series42.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

57 → 57

Iterations

Useful iterations: 4 (507.0ms)

Iter	Nodes	Cost
0	91	640
1	181	614
2	422	579
3	927	577
4	2547	576
done	5000	576

prune128.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
0.0b	(+ (* 1/12 x) (/ 1 x))
0.3b	(* 1/12 x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

19.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
6.0ms	(+ (* 1/12 x) (/ 1 x))
3.0ms	(* 1/12 x)

series75.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
46.0ms	(+ (* 1/12 x) (/ 1 x))
14.0ms	(* 1/12 x)

simplify840.0ms

Counts

52 → 52

Iterations

Useful iterations: 3 (261.0ms)

Iter	Nodes	Cost
0	73	503
1	205	450
2	514	424
3	1539	422
done	5002	422

prune87.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (* 1/12 x) (/ 1 x)))
0.5b	(cbrt (+ (* 1/12 x) (/ 1 x)))
0.5b	(cbrt (+ (* 1/12 x) (/ 1 x)))
0.5b	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))

rewrite74.0ms

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:

6.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
6.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
6.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
53.0ms	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
114.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
112.0ms	(cbrt (+ (* 1/12 x) (/ 1 x)))
136.0ms	(* (cbrt (+ (* 1/12 x) (/ 1 x))) (cbrt (+ (* 1/12 x) (/ 1 x))))

simplify1.6s

Counts

99 → 99

Iterations

Useful iterations: 3 (877.0ms)

Iter	Nodes	Cost
0	154	2300
1	366	2119
2	1005	1947
3	3548	1684
done	5001	1684

prune250.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

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:

19.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
3.0ms	(/ 1.0 (exp x))
9.0ms	(- 1 (/ 1.0 (exp x)))

series101.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
13.0ms	(/ 1.0 (exp x))
40.0ms	(- 1 (/ 1.0 (exp x)))

simplify3.6s

Counts

106 → 106

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	162	1303
1	310	1155
2	599	1099
3	1442	1094
4	4862	1092
done	5000	1092

prune136.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

96.1% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 21.1b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	21	22
done	21	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

398.0ms	2327×	body	1280	valid
280.0ms	2534×	body	10240	exit
176.0ms	1635×	body	640	valid
57.0ms	2835×	body	80	valid
55.0ms	807×	body	320	valid
17.0ms	397×	body	160	valid