Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	62×	body	640	valid
4.0ms	129×	body	80	valid
4.0ms	46×	body	320	valid
1.0ms	19×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
2	15
1	12
0	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize19.0ms

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)))

rewrite601.0ms

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:

17.0ms	(/ 1.0 (+ x 1.0))
17.0ms	(/ 1.0 (- x 1.0))
505.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series334.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ 1.0 (+ x 1.0))
49.0ms	(/ 1.0 (- x 1.0))
243.0ms	(- (/ 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

prune2.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

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))

rewrite372.0ms

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:

328.0ms	(+ (+ (/ 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))

series234.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (+ (/ 2.0 (pow x 4)) (/ 2.0 (* x x))) (/ 2.0 (pow x 6)))
85.0ms	(/ 2.0 (pow x 6))
43.0ms	(/ 2.0 (pow x 4))
39.0ms	(/ 2.0 (* x x))

simplify1.9s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
2	3419
1	589
0	248

prune786.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
103×	`*-un-lft-identity`
92×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`unpow-prod-down`
25×	`fma-def`
19×	`add-exp-log` `associate-/l*`
17×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`sqr-pow`
9×	`div-exp` `add-log-exp`
8×	`div-inv`
5×	`cbrt-undiv` `distribute-lft-out`
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-+r+` `associate-/l/`

Counts

4 → 212

Calls

4 calls:

332.0ms	(+ (/ 2.0 (pow x 6)) (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4))))
6.0ms	(/ 2.0 (pow x 6))
10.0ms	(/ 2.0 (pow x 4))
17.0ms	(/ (/ 2.0 x) x)

series288.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (/ 2.0 (pow x 6)) (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4))))
84.0ms	(/ 2.0 (pow x 6))
69.0ms	(/ 2.0 (pow x 4))
47.0ms	(/ (/ 2.0 x) x)

simplify2.1s

Counts

224 → 224

Iterations

Iter	Nodes
done	5002
2	3965
1	814
0	337

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize27.0ms

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)))

rewrite91.0ms

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:

6.0ms	(/ 2.0 (pow x 6))
6.0ms	(/ 2.0 (pow x 4))
8.0ms	(/ (pow x 2) (sqrt 2.0))
27.0ms	(/ (sqrt 2.0) (/ (pow x 2) (sqrt 2.0)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ 2.0 (pow x 6))
44.0ms	(/ 2.0 (pow x 4))
111.0ms	(/ (pow x 2) (sqrt 2.0))
90.0ms	(/ (sqrt 2.0) (/ (pow x 2) (sqrt 2.0)))

simplify1.0s

Counts

573 → 573

Iterations

Iter	Nodes
done	5000
1	1670
0	664

prune2.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes77.0ms

Accuracy

99.8% (0.1b remaining)

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

bsearch116.0ms

Steps

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

simplify18.0ms

Iterations

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

end0.0ms

sample1.7s

Algorithm

intervals

Results

766.0ms	4209×	body	80	valid
416.0ms	1925×	body	640	valid
258.0ms	1263×	body	320	valid
58.0ms	603×	body	160	valid