Details

sample79.0ms

Algorithm

intervals

Results

33.0ms	68×	body	1280	valid
15.0ms	38×	body	640	valid
12.0ms	119×	body	80	valid
5.0ms	18×	body	320	valid
3.0ms	13×	body	160	valid

simplify309.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize22.0ms

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)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

1284×	`*-un-lft-identity`
984×	`times-frac`
841×	`add-sqr-sqrt`
612×	`prod-diff`
521×	`add-cube-cbrt`
251×	`distribute-lft-out`
158×	`difference-of-squares`
110×	`associate-/r/`
90×	`distribute-lft-out--`
77×	`difference-of-sqr-1`
55×	`div-inv`
37×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
11×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 753

Calls

3 calls:

31.0ms	(/ (+ x 1) (- x 1))
18.0ms	(/ x (+ x 1))
89.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (+ x 1) (- x 1))
34.0ms	(/ x (+ x 1))
115.0ms	(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.4s

Counts

762 → 762

Iterations

Iter	Nodes
2	3099
1	1351
0	584

prune8.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 x) x)
0.2b	(fma 3 (/ 1 x) (/ (/ 1 x) x))
0.3b	(/ -3 (* x (* x x)))
4.4b	(- (/ -3 (* x (* x x))) (fma 3 (/ 1 x) (/ (/ 1 x) x)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
65×	`add-sqr-sqrt` `*-un-lft-identity`
63×	`add-cube-cbrt`
22×	`add-exp-log`
21×	`prod-diff`
18×	`add-cbrt-cube`
16×	`associate-/l*`
10×	`div-inv`
9×	`div-exp`
7×	`pow1` `fma-neg`
6×	`cbrt-undiv` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `fma-udef` `pow-div`
1×	`rec-exp` `sub-neg` `flip3--` `diff-log` `1-exp` `pow-flip` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow` `difference-of-squares` `associate-/l/`

Counts

4 → 160

Calls

4 calls:

7.0ms	(/ (/ 1 x) x)
0.0ms	(fma 3 (/ 1 x) (/ (/ 1 x) x))
18.0ms	(/ -3 (* x (* x x)))
65.0ms	(- (/ -3 (* x (* x x))) (fma 3 (/ 1 x) (/ (/ 1 x) x)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (/ 1 x) x)
76.0ms	(fma 3 (/ 1 x) (/ (/ 1 x) x))
59.0ms	(/ -3 (* x (* x x)))
40.0ms	(- (/ -3 (* x (* x x))) (fma 3 (/ 1 x) (/ (/ 1 x) x)))

simplify4.4s

Counts

172 → 172

Iterations

Iter	Nodes
3	5941
2	1428
1	566
0	267

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ -1 (* x x)) x)
0.6b	(/ -1 (* x x))
0.6b	(/ -1 (* x x))
4.5b	(fma (/ (/ -1 (* x x)) x) 3 (+ (/ -1 (* x x)) (/ -3 x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

39×	`times-frac`
24×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/l*`
9×	`cbrt-undiv` `div-exp`
7×	`div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`fma-udef` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

23.0ms	(/ (/ -1 (* x x)) x)
12.0ms	(/ -1 (* x x))
12.0ms	(/ -1 (* x x))
1.0ms	(fma (/ (/ -1 (* x x)) x) 3 (+ (/ -1 (* x x)) (/ -3 x)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (/ -1 (* x x)) x)
50.0ms	(/ -1 (* x x))
49.0ms	(/ -1 (* x x))
53.0ms	(fma (/ (/ -1 (* x x)) x) 3 (+ (/ -1 (* x x)) (/ -3 x)))

simplify1.4s

Counts

122 → 122

Iterations

Iter	Nodes
3	3085
2	795
1	297
0	142

prune799.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
0.0b	(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
0.0b	(* (/ x (+ x 1)) (/ x (+ x 1)))
3.3b	(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

636×	`*-un-lft-identity`
384×	`times-frac`
246×	`add-sqr-sqrt`
161×	`distribute-lft-out`
118×	`add-cube-cbrt`
96×	`swap-sqr`
66×	`difference-of-squares`
52×	`associate-r` `associate-l` `distribute-lft-out--`
32×	`difference-of-sqr-1`
30×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-l/` `associate-r/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `frac-add`

Counts

4 → 383

Calls

4 calls:

50.0ms	(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
125.0ms	(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
30.0ms	(* (/ x (+ x 1)) (/ x (+ x 1)))
16.0ms	(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))
324.0ms	(/ (- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1)))) (+ (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
49.0ms	(* (/ x (+ x 1)) (/ x (+ x 1)))
150.0ms	(- (* (/ x (+ x 1)) (/ x (+ x 1))) (* (/ (+ x 1) (- x 1)) (/ (+ x 1) (- x 1))))

simplify2.3s

Counts

395 → 395

Iterations

Iter	Nodes
2	5326
1	1463
0	439

prune3.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes69.0ms

Accuracy

100% (0.0b remaining)

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

bsearch160.0ms

Steps

Iters	Range		Point
10	1.6697130628152668	4649870806659.843	7931.624520828369
8	-250055.29886925383	-174.255226838109	-10766.895377459747

simplify12.0ms

Iterations

Iter	Nodes
2	35
1	35
0	27

end0.0ms

sample2.5s

Algorithm

intervals

Results

896.0ms	1729×	body	1280	valid
727.0ms	4101×	body	80	valid
510.0ms	1227×	body	640	valid
183.0ms	610×	body	320	valid
56.0ms	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