Details

sample24.0ms

Algorithm

intervals

Results

6.0ms	62×	body	640	valid
4.0ms	129×	body	80	valid
4.0ms	46×	body	320	valid
1.0ms	19×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
2	15
1	12
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
2.9b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

662×	`*-un-lft-identity`
589×	`times-frac`
496×	`add-sqr-sqrt`
378×	`prod-diff`
368×	`add-cube-cbrt`
86×	`associate-/r/`
79×	`distribute-lft-out--`
76×	`distribute-lft-out`
62×	`difference-of-squares`
44×	`div-inv`
24×	`flip-+`
23×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 504

Calls

3 calls:

8.0ms	(/ 1.0 (+ x 1.0))
9.0ms	(/ 1.0 (- x 1.0))
127.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series352.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ 1.0 (+ x 1.0))
54.0ms	(/ 1.0 (- x 1.0))
250.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify2.0s

Counts

513 → 513

Iterations

Iter	Nodes
done	5000
2	4303
1	1253
0	525

prune1.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (/ 2.0 (pow x 4)) (/ 2.0 (* x x))) (/ 2.0 (pow x 6)))
0.0b	(/ 2.0 (pow x 6))
0.1b	(/ 2.0 (pow x 4))
0.2b	(/ 2.0 (* x x))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
45×	`times-frac`
39×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down`
19×	`add-exp-log`
15×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`associate-/l*` `add-log-exp`
8×	`div-exp` `div-inv` `sqr-pow`
7×	`distribute-lft-out`
5×	`fma-def`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `frac-add` `log1p-expm1-u`
3×	`clear-num` `sum-log` `frac-2neg`
2×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+`
1×	`+-commutative` `associate-+l+` `prod-exp` `cbrt-unprod`

Counts

4 → 143

Calls

4 calls:

211.0ms	(+ (+ (/ 2.0 (pow x 4)) (/ 2.0 (* x x))) (/ 2.0 (pow x 6)))
11.0ms	(/ 2.0 (pow x 6))
11.0ms	(/ 2.0 (pow x 4))
12.0ms	(/ 2.0 (* x x))

series283.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (+ (/ 2.0 (pow x 4)) (/ 2.0 (* x x))) (/ 2.0 (pow x 6)))
97.0ms	(/ 2.0 (pow x 6))
48.0ms	(/ 2.0 (pow x 4))
37.0ms	(/ 2.0 (* x x))

simplify1.9s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
2	3419
1	589
0	248

prune733.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (/ 2.0 (pow x 4)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 6)))
0.0b	(/ 2.0 (pow x 6))
0.1b	(/ 2.0 (pow x 4))
0.1b	(/ (/ 2.0 x) x)

rewrite694.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
96×	`*-un-lft-identity`
79×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down`
19×	`add-exp-log` `associate-/l*`
17×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`div-exp` `add-log-exp`
8×	`sqr-pow`
7×	`div-inv` `distribute-lft-out`
5×	`cbrt-undiv` `fma-def`
4×	`expm1-log1p-u` `pow1` `frac-add` `log1p-expm1-u`
3×	`clear-num` `sum-log` `frac-2neg`
2×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+`
1×	`+-commutative` `associate-+l+` `associate-/l/`

Counts

4 → 192

Calls

4 calls:

643.0ms	(+ (+ (/ 2.0 (pow x 4)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 6)))
11.0ms	(/ 2.0 (pow x 6))
11.0ms	(/ 2.0 (pow x 4))
16.0ms	(/ (/ 2.0 x) x)

series292.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (+ (/ 2.0 (pow x 4)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 6)))
106.0ms	(/ 2.0 (pow x 6))
51.0ms	(/ 2.0 (pow x 4))
43.0ms	(/ (/ 2.0 x) x)

simplify1.9s

Counts

204 → 204

Iterations

Iter	Nodes
done	5000
2	3739
1	787
0	337

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (pow x 6))
0.1b	(/ 2.0 (pow x 4))
0.2b	(/ (pow x 2) (sqrt 2.0))
0.3b	(/ (sqrt 2.0) (/ (pow x 2) (sqrt 2.0)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

738×	`times-frac`
377×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
354×	`sqrt-prod`
171×	`unpow-prod-down`
72×	`associate-/r*`
57×	`sqr-pow`
49×	`unpow2`
29×	`add-exp-log`
20×	`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 → 561

Calls

4 calls:

12.0ms	(/ 2.0 (pow x 6))
20.0ms	(/ 2.0 (pow x 4))
16.0ms	(/ (pow x 2) (sqrt 2.0))
20.0ms	(/ (sqrt 2.0) (/ (pow x 2) (sqrt 2.0)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ 2.0 (pow x 6))
50.0ms	(/ 2.0 (pow x 4))
100.0ms	(/ (pow x 2) (sqrt 2.0))
97.0ms	(/ (sqrt 2.0) (/ (pow x 2) (sqrt 2.0)))

simplify1.2s

Counts

573 → 573

Iterations

Iter	Nodes
done	5000
1	1670
0	664

prune2.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes94.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.1b

bsearch169.0ms

Steps

Iters	Range		Point
8	5.1212688054922095	257785.57693934403	225.84837423869962
8	-346749.28651926527	-205.8624528279525	-219.25550675598262

simplify21.0ms

Iterations

Iter	Nodes
done	75
4	75
3	74
2	69
1	58
0	41

end0.0ms

sample1.3s

Algorithm

intervals

Results

668.0ms	1925×	body	640	valid
262.0ms	4209×	body	80	valid
184.0ms	1263×	body	320	valid
46.0ms	603×	body	160	valid