Details

sample36.0ms

Algorithm

intervals

Results

12.0ms	75×	body	1280	valid
8.0ms	75×	body	10240	exit
6.0ms	54×	body	640	valid
2.0ms	89×	body	80	valid
1.0ms	18×	body	320	valid
1.0ms	20×	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: 41.7b

localize4.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
4.9b	(- (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-/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:

8.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series41.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

57 → 57

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	91	640
1	189	614
2	533	579
3	2196	577
done	5001	576

prune110.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (/ 1 x))
0.4b	(* 1/12 x)

rewrite11.0ms

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:

8.0ms	(+ (* 1/12 x) (/ 1 x))
3.0ms	(* 1/12 x)

series50.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (* 1/12 x) (/ 1 x))
13.0ms	(* 1/12 x)

simplify1.7s

Counts

35 → 35

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	51	269
1	135	247
2	405	225
3	1788	225
done	5000	225

prune56.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
4.9b	(- 1 (/ 1.0 (exp x)))

rewrite31.0ms

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:

3.0ms	(/ 1.0 (exp x))
17.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
8.0ms	(- 1 (/ 1.0 (exp x)))

series95.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1.0 (exp x))
46.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
37.0ms	(- 1 (/ 1.0 (exp x)))

simplify5.1s

Counts

106 → 106

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	162	1303
1	328	1175
2	1152	1099
3	4791	1094
done	5000	1094

prune136.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (* 1/12 x) (/ 1 x)))
0.2b	(* (sqrt (+ (* 1/12 x) (/ 1 x))) (sqrt (+ (* 1/12 x) (/ 1 x))))
0.4b	(* 1/12 x)
0.4b	(* 1/12 x)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`pow1`
21×	`sqrt-prod`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`sqrt-div`
12×	`associate-r` `associate-l`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
7×	`flip3-+` `flip-+`
6×	`unswap-sqr`
5×	`pow-prod-down` `pow-prod-up`
4×	`frac-times` `add-log-exp`
3×	`prod-exp` `pow-sqr` `*-commutative` `cbrt-unprod`
2×	`associate-r/` `associate-l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 108

Calls

4 calls:

10.0ms	(sqrt (+ (* 1/12 x) (/ 1 x)))
45.0ms	(* (sqrt (+ (* 1/12 x) (/ 1 x))) (sqrt (+ (* 1/12 x) (/ 1 x))))
3.0ms	(* 1/12 x)
3.0ms	(* 1/12 x)

series101.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ (* 1/12 x) (/ 1 x)))
39.0ms	(* (sqrt (+ (* 1/12 x) (/ 1 x))) (sqrt (+ (* 1/12 x) (/ 1 x))))
13.0ms	(* 1/12 x)
16.0ms	(* 1/12 x)

simplify574.0ms

Counts

120 → 120

Iterations

Useful iterations: done (572.0ms)

Iter	Nodes	Cost
0	122	1865
1	257	1261
2	991	1135
done	5000	1131

prune178.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

96.2% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 21.7b

bsearch1.0ms

simplify2.0ms

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

387.0ms	2294×	body	1280	valid
267.0ms	2571×	body	10240	exit
172.0ms	1611×	body	640	valid
55.0ms	2923×	body	80	valid
53.0ms	789×	body	320	valid
17.0ms	383×	body	160	valid