Details

sample424.0ms

Algorithm

intervals

Results

388.0ms	68×	body	1280	valid
12.0ms	38×	body	640	valid
9.0ms	119×	body	80	valid
4.0ms	18×	body	320	valid
2.0ms	13×	body	160	valid

simplify168.0ms

Counts

1 → 1

Iterations

Iter	Nodes
17	209
16	209
15	207
14	188
13	140
12	109
11	96
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1) (- x 1))
0.0b	(/ x (+ x 1))
3.4b	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity`
60×	`times-frac`
57×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
20×	`distribute-lft-out`
18×	`distribute-lft-out--`
14×	`difference-of-squares`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`difference-of-sqr-1` `add-log-exp`
4×	`associate-/r/`
3×	`pow1` `insert-posit16`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 117

Calls

3 calls:

17.0ms	(/ (+ x 1) (- x 1))
9.0ms	(/ x (+ x 1))
62.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series150.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (+ x 1) (- x 1))
26.0ms	(/ x (+ x 1))
91.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify882.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	3162
2	993
1	385
0	180

prune777.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ -1 (* x x)) (/ 3 x))
0.1b	(/ (/ 3 x) (* x x))
0.6b	(/ -1 (* x x))
4.4b	(- (- (/ -1 (* x x)) (/ 3 x)) (/ (/ 3 x) (* x x)))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

41×	`times-frac`
37×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cbrt-cube` `add-exp-log`
20×	`add-cube-cbrt`
16×	`associate-/l*`
11×	`add-log-exp`
8×	`cbrt-undiv` `div-exp`
7×	`difference-of-squares`
5×	`frac-sub`
4×	`pow1` `diff-log` `insert-posit16` `div-inv` `distribute-lft-out--`
3×	`sub-neg` `flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`clear-num` `associate-/r*` `frac-2neg` `associate--l+`
1×	`associate--l-` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

38.0ms	(- (/ -1 (* x x)) (/ 3 x))
19.0ms	(/ (/ 3 x) (* x x))
12.0ms	(/ -1 (* x x))
191.0ms	(- (- (/ -1 (* x x)) (/ 3 x)) (/ (/ 3 x) (* x x)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (/ -1 (* x x)) (/ 3 x))
71.0ms	(/ (/ 3 x) (* x x))
47.0ms	(/ -1 (* x x))
39.0ms	(- (- (/ -1 (* x x)) (/ 3 x)) (/ (/ 3 x) (* x x)))

simplify19.6s

Counts

125 → 125

Iterations

Iter	Nodes
3	12969
2	1892
1	540
0	210

prune845.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (/ (/ -3 x) (* x x)) (/ -1 (* x x))) (/ -3 x))
0.1b	(/ (/ -3 x) (* x x))
0.6b	(/ -1 (* x x))
4.4b	(+ (/ (/ -3 x) (* x x)) (/ -1 (* x x)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
29×	`*-un-lft-identity`
21×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/l*`
11×	`add-log-exp`
8×	`cbrt-undiv` `div-exp`
6×	`div-inv`
5×	`frac-add` `distribute-lft-out`
4×	`pow1` `sum-log` `insert-posit16`
3×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
2×	`+-commutative` `clear-num` `associate-/r*` `frac-2neg`
1×	`associate-+l+` `distribute-rgt-out` `associate-/l/`

Counts

4 → 104

Calls

4 calls:

175.0ms	(+ (+ (/ (/ -3 x) (* x x)) (/ -1 (* x x))) (/ -3 x))
11.0ms	(/ (/ -3 x) (* x x))
6.0ms	(/ -1 (* x x))
40.0ms	(+ (/ (/ -3 x) (* x x)) (/ -1 (* x x)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (+ (/ (/ -3 x) (* x x)) (/ -1 (* x x))) (/ -3 x))
64.0ms	(/ (/ -3 x) (* x x))
37.0ms	(/ -1 (* x x))
134.0ms	(+ (/ (/ -3 x) (* x x)) (/ -1 (* x x)))

simplify7.3s

Counts

116 → 116

Iterations

Iter	Nodes
3	9745
2	1659
1	513
0	198

prune883.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
24.5b	(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
25×	`times-frac`
16×	`cbrt-prod`
10×	`difference-of-squares`
7×	`add-cube-cbrt` `distribute-lft-out--`
6×	`cbrt-div` `add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 74

Calls

4 calls:

2.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))
121.0ms	(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (+ x 1))
38.0ms	(cbrt (+ x 1))
48.0ms	(cbrt (+ x 1))
97.0ms	(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))

simplify1.3s

Counts

86 → 86

Iterations

Iter	Nodes
3	2417
2	772
1	307
0	135

prune775.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes57.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch134.0ms

Steps

Iters	Range		Point
10	1.6697130628152668	4649870806659.843	6607.223075937772
8	-250055.29886925383	-174.255226838109	-8404.501425772927

simplify10.0ms

Iterations

Iter	Nodes
2	32
1	32
0	24

end0.0ms

sample2.3s

Algorithm

intervals

Results

929.0ms	1729×	body	1280	valid
537.0ms	1227×	body	640	valid
455.0ms	4101×	body	80	valid
227.0ms	610×	body	320	valid
60.0ms	333×	body	160	valid

Iter	Nodes
17	209
16	209
15	207
14	188
13	140
12	109
11	96
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

Iter	Nodes
17	209
16	209
15	207
14	188
13	140
12	109
11	96
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7

Iter	Nodes
17	209
16	209
15	207
14	188
13	140
12	109
11	96
10	89
9	69
8	53
7	42
6	32
5	26
4	23
3	22
2	19
1	15
0	7