Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	52×	body	1280	valid
4.0ms	42×	body	640	valid
3.0ms	134×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	8×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 44

Calls

3 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
39.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series415.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(cbrt (+ x 1.0))
179.0ms	(cbrt x)
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.5s

Counts

53 → 53

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	131	649
1	290	597
2	672	573
3	1717	521
4	4878	501
done	5000	501

prune149.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt (- x))
2.8b	(- (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
2×	`cbrt-div` `pow1/3`
1×	`neg-mul-1` `sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `distribute-lft-out`

Counts

3 → 44

Calls

3 calls:

4.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (- x))
41.0ms	(- (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x))))

series431.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(cbrt (+ x 1.0))
199.0ms	(cbrt (- x))
144.0ms	(- (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x))))

simplify1.3s

Counts

53 → 53

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	139	711
1	308	663
2	809	612
3	2552	561
done	5001	541

prune153.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.2b	(* (cbrt (+ x 1.0)) (+ (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x)))))
0.6b	(cbrt (- x))
3.3b	(pow (- x) 2/3)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

19×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`unpow-prod-down`
8×	`cbrt-div`
7×	`pow1` `add-exp-log` `flip3-+` `associate-l` `flip-+`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`add-cbrt-cube`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow` `associate-r`
2×	`neg-mul-1` `pow1/3` `associate-r/` `associate-l/` `distribute-lft-out` `unswap-sqr`
1×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `distribute-lft-in` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 89

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
96.0ms	(* (cbrt (+ x 1.0)) (+ (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x)))))
2.0ms	(cbrt (- x))
4.0ms	(pow (- x) 2/3)

series792.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ x 1.0))
272.0ms	(* (cbrt (+ x 1.0)) (+ (cbrt (+ x 1.0)) (* (cbrt -1) (cbrt (- x)))))
196.0ms	(cbrt (- x))
235.0ms	(pow (- x) 2/3)

simplify952.0ms

Counts

101 → 101

Iterations

Useful iterations: done (949.0ms)

Iter	Nodes	Cost
0	275	1688
1	753	1560
2	2326	1439
done	5000	1358

prune427.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- x)) (cbrt (- x)))
0.6b	(cbrt (- x))
0.6b	(cbrt (- x))
0.6b	(cbrt (- x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

78×	`cbrt-prod`
37×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
29×	`add-cube-cbrt`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
15×	`swap-sqr`
13×	`associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3`
7×	`neg-mul-1`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

20.0ms	(* (cbrt (- x)) (cbrt (- x)))
2.0ms	(cbrt (- x))
2.0ms	(cbrt (- x))
2.0ms	(cbrt (- x))

series829.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (cbrt (- x)) (cbrt (- x)))
196.0ms	(cbrt (- x))
198.0ms	(cbrt (- x))
206.0ms	(cbrt (- x))

simplify1.4s

Counts

129 → 129

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	91	1056
1	151	957
2	401	885
3	852	840
4	2398	795
done	5000	780

prune441.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.2b

regimes66.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	19	33
1	26	31
done	26	31

end0.0ms

sample572.0ms

Algorithm

intervals

Results

186.0ms	1671×	body	1280	valid
106.0ms	1233×	body	640	valid
96.0ms	4157×	body	80	valid
37.0ms	602×	body	320	valid
14.0ms	337×	body	160	valid