Details

sample12.0ms

Algorithm

intervals

Results

6.0ms

350×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	16	7
3	20	7
4	21	7
done	21	7

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize4.0ms

Local error

Found 1 expressions with local error:

0.1b	(/ (- (* x x) 3.0) 6.0)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 34

Calls

1 calls:

8.0ms

(/ (- (* x x) 3.0) 6.0)

series68.0ms

Counts

1 → 3

Calls

1 calls:

67.0ms

(/ (- (* x x) 3.0) 6.0)

simplify2.1s

Counts

37 → 37

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	78	451
1	174	438
2	415	406
3	1126	406
4	4243	405
done	5001	405

prune73.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(* 0.16666666666666666 (pow x 2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-r`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-l` `prod-exp` `add-cbrt-cube`
2×	`unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

9.0ms

(* 0.16666666666666666 (pow x 2))

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

(* 0.16666666666666666 (pow x 2))

simplify2.6s

Counts

30 → 30

Iterations

Useful iterations: 4 (841.0ms)

Iter	Nodes	Cost
0	51	232
1	108	209
2	276	176
3	691	176
4	3215	173
done	5001	173

prune52.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (sqrt 0.16666666666666666) x)
0.2b	(* (sqrt 0.16666666666666666) x)
0.3b	(* (* (sqrt 0.16666666666666666) x) (* (sqrt 0.16666666666666666) x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
19×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
17×	`add-sqr-sqrt`
13×	`associate-l`
10×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-prod`
7×	`associate-r`
4×	`pow-sqr` `pow-prod-up` `unswap-sqr`
3×	`*-commutative` `add-log-exp`
2×	`pow-plus`
1×	`pow2` `swap-sqr`

Counts

3 → 78

Calls

3 calls:

4.0ms	(* (sqrt 0.16666666666666666) x)
4.0ms	(* (sqrt 0.16666666666666666) x)
18.0ms	(* (* (sqrt 0.16666666666666666) x) (* (sqrt 0.16666666666666666) x))

series152.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (sqrt 0.16666666666666666) x)
39.0ms	(* (sqrt 0.16666666666666666) x)
70.0ms	(* (* (sqrt 0.16666666666666666) x) (* (sqrt 0.16666666666666666) x))

simplify6.2s

Counts

87 → 87

Iterations

Useful iterations: 3 (564.0ms)

Iter	Nodes	Cost
0	58	685
1	128	512
2	443	430
3	1926	425
4	4965	425
done	5000	425

prune119.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sqrt 3.0)) 6.0)
0.0b	(- x (sqrt 3.0))
0.0b	(+ (sqrt 3.0) x)
0.7b	(* (+ (sqrt 3.0) x) (/ (- x (sqrt 3.0)) 6.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
37×	`times-frac`
26×	`add-cube-cbrt`
22×	`associate-r`
16×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-prod` `distribute-lft-out--` `add-log-exp`
6×	`pow1` `associate-/l*`
4×	`associate-l`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 115

Calls

4 calls:

10.0ms	(/ (- x (sqrt 3.0)) 6.0)
3.0ms	(- x (sqrt 3.0))
4.0ms	(+ (sqrt 3.0) x)
34.0ms	(* (+ (sqrt 3.0) x) (/ (- x (sqrt 3.0)) 6.0))

series314.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (- x (sqrt 3.0)) 6.0)
42.0ms	(- x (sqrt 3.0))
39.0ms	(+ (sqrt 3.0) x)
163.0ms	(* (+ (sqrt 3.0) x) (/ (- x (sqrt 3.0)) 6.0))

simplify849.0ms

Counts

127 → 127

Iterations

Useful iterations: 2 (208.0ms)

Iter	Nodes	Cost
0	146	1516
1	356	1345
2	1261	1243
done	5001	1243

prune208.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample287.0ms

Algorithm

intervals

Results

174.0ms

10627×

body

valid