Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	60×	body	640	valid
6.0ms	145×	body	80	valid
3.0ms	19×	body	1280	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
10	4810
9	1188
8	437
7	210
6	162
5	135
4	89
3	41
2	31
1	18
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite514.0ms

Algorithm

rewrite-expression-head

Rules

707×	`*-un-lft-identity`
691×	`times-frac`
514×	`add-sqr-sqrt`
482×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
91×	`distribute-lft-out`
64×	`div-inv`
56×	`associate-/r/`
28×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
10×	`fma-def` `add-log-exp`
5×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `flip3--` `frac-add` `log1p-expm1-u` `flip--` `associate-/l*`
2×	`sum-log` `sub-neg` `diff-log` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `div-exp` `associate-+l-`

Counts

3 → 583

Calls

3 calls:

8.0ms	(/ 1.0 (- x 1.0))
83.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
355.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series694.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ 1.0 (- x 1.0))
59.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
606.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.8s

Counts

592 → 592

Iterations

Iter	Nodes
done	5000
2	3882
1	1139
0	484

prune2.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 2.0 (pow x 7))
0.2b	(/ 2.0 (pow x 5))
0.3b	(/ 2.0 (pow x 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
60×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
36×	`unpow-prod-down`
26×	`associate-/r*`
18×	`add-exp-log`
12×	`cube-prod` `sqr-pow`
9×	`add-cbrt-cube` `div-exp` `associate-/l*`
4×	`cube-mult` `unpow3`
3×	`expm1-log1p-u` `pow-to-exp` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `pow-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

3 → 161

Calls

3 calls:

6.0ms	(/ 2.0 (pow x 7))
6.0ms	(/ 2.0 (pow x 5))
7.0ms	(/ 2.0 (pow x 3))

series234.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(/ 2.0 (pow x 7))
91.0ms	(/ 2.0 (pow x 5))
40.0ms	(/ 2.0 (pow x 3))

simplify805.0ms

Counts

170 → 170

Iterations

Iter	Nodes
done	5002
2	2157
1	461
0	234

prune763.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 2.0 (pow x 7))
0.1b	(* (/ 1 (* x x)) (/ 2.0 x))
0.2b	(/ 2.0 (pow x 5))
0.3b	(/ 1 (* x x))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log`
64×	`times-frac`
60×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`add-cbrt-cube`
25×	`div-exp`
24×	`unpow-prod-down`
23×	`prod-exp`
15×	`associate-/r*`
14×	`pow1`
13×	`associate-r`
11×	`cbrt-undiv`
9×	`cbrt-unprod` `associate-/l*`
8×	`sqr-pow`
7×	`associate-l`
6×	`rec-exp` `1-exp` `pow-flip` `unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`pow-to-exp` `pow-prod-down` `pow-exp`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `inv-pow`

Counts

4 → 188

Calls

4 calls:

11.0ms	(/ 2.0 (pow x 7))
66.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
6.0ms	(/ 2.0 (pow x 5))
9.0ms	(/ 1 (* x x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ 2.0 (pow x 7))
69.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
68.0ms	(/ 2.0 (pow x 5))
31.0ms	(/ 1 (* x x))

simplify2.7s

Counts

200 → 200

Iterations

Iter	Nodes
done	5002
2	4601
1	706
0	277

prune866.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 2.0 (pow x 7))
0.2b	(/ 2.0 (pow x 5))
0.2b	(/ (pow x 3) (sqrt 2.0))
0.4b	(/ (sqrt 2.0) (/ (pow x 3) (sqrt 2.0)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

1074×	`times-frac`
538×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
522×	`sqrt-prod`
171×	`unpow-prod-down`
147×	`cube-prod`
96×	`associate-/r*`
57×	`sqr-pow`
49×	`cube-mult` `unpow3`
29×	`add-exp-log`
24×	`associate-/l*`
16×	`div-exp`
15×	`add-cbrt-cube`
11×	`div-inv`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-to-exp` `pow1` `clear-num` `frac-2neg` `pow-exp` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/`

Counts

4 → 757

Calls

4 calls:

6.0ms	(/ 2.0 (pow x 7))
6.0ms	(/ 2.0 (pow x 5))
9.0ms	(/ (pow x 3) (sqrt 2.0))
54.0ms	(/ (sqrt 2.0) (/ (pow x 3) (sqrt 2.0)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ 2.0 (pow x 7))
56.0ms	(/ 2.0 (pow x 5))
89.0ms	(/ (pow x 3) (sqrt 2.0))
115.0ms	(/ (sqrt 2.0) (/ (pow x 3) (sqrt 2.0)))

simplify915.0ms

Counts

769 → 769

Iterations

Iter	Nodes
done	5000
1	1862
0	719

prune1.8s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes128.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.0b

bsearch148.0ms

Steps

Iters	Range		Point
10	5.09324609688744e-06	47495130.80298876	139.99564384645248
10	-1138.2876542095912	-1.6260248627107784e-07	-107.12003739327044

simplify4.0ms

Iterations

Iter	Nodes
done	46
1	46
0	39

end0.0ms

sample1.7s

Algorithm

intervals

Results

798.0ms	1922×	body	640	valid
319.0ms	4099×	body	80	valid
172.0ms	961×	body	320	valid
146.0ms	554×	body	1280	valid
43.0ms	466×	body	160	valid