Details

sample72.0ms

Algorithm

intervals

Results

21.0ms	32×	body	1280	valid
14.0ms	72×	body	640	valid
8.0ms	198×	body	80	nan
7.0ms	121×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	14	11
done	14	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.5b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

14.0ms	(sqrt (+ x 1.0))
25.0ms	(/ 1.0 (sqrt (+ x 1.0)))
13.0ms	(/ 1.0 (sqrt x))
103.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1.0))
97.0ms	(/ 1.0 (sqrt (+ x 1.0)))
66.0ms	(/ 1.0 (sqrt x))
175.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.3s

Counts

145 → 145

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	215	1942
1	444	1778
2	1051	1698
3	2647	1673
done	5000	1657

prune551.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b	(/ 1.0 (sqrt x))
2.7b	(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
105×	`times-frac`
65×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
52×	`sqrt-prod`
35×	`distribute-lft-out`
27×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
8×	`distribute-lft-out--`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `div-exp` `difference-of-squares`
3×	`frac-2neg` `associate-*r/` `clear-num` `associate-/l/`
2×	`flip3--` `flip3-+` `sqrt-div` `frac-sub` `flip--` `flip-+`
1×	`sub-neg` `diff-log` `frac-add` `prod-exp` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

22.0ms	(/ 1.0 (sqrt (+ x 1.0)))
197.0ms	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
12.0ms	(/ 1.0 (sqrt x))
57.0ms	(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

series881.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1.0 (sqrt (+ x 1.0)))
647.0ms	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
61.0ms	(/ 1.0 (sqrt x))
57.0ms	(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

simplify2.0s

Counts

170 → 170

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	339	3045
1	822	2803
2	2559	2592
done	5001	2590

prune593.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.2b	(- (* 1.0 (+ x 1.0)) (* x 1.0))
3.4b	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
57×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
40×	`sqrt-prod`
18×	`distribute-lft-out`
14×	`associate-l`
13×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
10×	`associate-*r/`
9×	`pow1`
8×	`flip3-+` `flip-+`
6×	`frac-times` `associate-/l*` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`div-inv`
3×	`pow-prod-down` `associate-*l/` `frac-add` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `associate--l+` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `flip--`

Counts

4 → 142

Calls

4 calls:

14.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
14.0ms	(- (* 1.0 (+ x 1.0)) (* x 1.0))
393.0ms	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1.0 (sqrt (+ x 1.0)))
54.0ms	(/ 1.0 (sqrt x))
1.0ms	(- (* 1.0 (+ x 1.0)) (* x 1.0))
456.0ms	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify1.9s

Counts

154 → 154

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	284	2489
1	726	2318
2	2653	2121
done	5002	2119

prune671.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
0.8b	(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
3.4b	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite484.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
58×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
40×	`sqrt-prod`
34×	`add-exp-log` `add-cbrt-cube`
20×	`associate-*r/`
18×	`distribute-lft-out`
15×	`flip3-+` `flip-+`
14×	`associate-l` `associate-/r*`
13×	`associate-/r/`
12×	`frac-times` `prod-exp` `cbrt-unprod`
9×	`pow1`
8×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
6×	`associate-*l/` `frac-add`
5×	`div-inv`
4×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
2×	`sqrt-div`
1×	`associate-r` `*-commutative`

Counts

4 → 164

Calls

4 calls:

13.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
137.0ms	(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
316.0ms	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1.0 (sqrt (+ x 1.0)))
45.0ms	(/ 1.0 (sqrt x))
765.0ms	(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
472.0ms	(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify2.5s

Counts

176 → 176

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	359	3687
1	988	3475
2	4112	3014
done	5000	3014

prune528.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.6b

regimes54.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	21
1	16	21
done	16	21

end0.0ms

sample2.2s

Algorithm

intervals

Results

731.0ms	1173×	body	1280	valid
445.0ms	1857×	body	640	valid
400.0ms	8006×	body	80	nan
177.0ms	3994×	body	80	valid
87.0ms	659×	body	320	valid
27.0ms	317×	body	160	valid