Details

sample91.0ms

Algorithm

intervals

Results

26.0ms	34×	body	1280	valid
15.0ms	253×	body	80	nan
15.0ms	55×	body	640	valid
9.0ms	142×	body	80	valid
3.0ms	13×	body	320	valid
2.0ms	12×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	242
1	11	242
2	14	242
done	14	242

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite121.0ms

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-cbrt-cube` `add-exp-log` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
10.0ms	(/ 1.0 (sqrt (+ x 1.0)))
5.0ms	(/ 1.0 (sqrt x))
95.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (+ x 1.0))
102.0ms	(/ 1.0 (sqrt (+ x 1.0)))
48.0ms	(/ 1.0 (sqrt x))
211.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.5s

Counts

145 → 145

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	216	48307
1	462	41329
2	1655	40241
done	5001	40121

prune705.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity`
18×	`add-cbrt-cube` `add-exp-log`
9×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `associate-*r/` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out` `distribute-lft-out--`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
48.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
20.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
57.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series492.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ x 1.0))
310.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
87.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.3s

Counts

105 → 105

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	191	35563
1	538	28828
2	3114	27700
done	5001	27380

prune588.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
1.7b	(- (+ x 1.0) x)

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

113×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
39×	`sqrt-prod`
37×	`times-frac` `distribute-lft-out`
29×	`add-cbrt-cube` `add-exp-log`
22×	`add-cube-cbrt`
16×	`distribute-lft-out--`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `difference-of-squares`
7×	`associate-/r` `associate-r` `associate-/l`
6×	`associate-l`
5×	`associate-*r/`
4×	`sqrt-div` `associate-/r/` `unswap-sqr`
3×	`flip3-+` `pow-prod-down` `flip-+` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-inv` `flip--`
1×	`sum-log` `sub-neg` `sqrt-unprod` `div-sub` `associate--l+` `*-commutative`

Counts

4 → 143

Calls

4 calls:

133.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
95.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
32.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
43.0ms	(- (+ x 1.0) x)

series992.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
688.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
76.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
2.0ms	(- (+ x 1.0) x)

simplify1.8s

Counts

155 → 155

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	271	60223
1	797	51085
done	5000	49997

prune704.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
31×	`sqrt-prod`
29×	`add-cbrt-cube` `add-exp-log`
27×	`add-sqr-sqrt`
21×	`distribute-lft-out`
19×	`times-frac` `add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-/r` `associate-r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l*` `unswap-sqr`
3×	`pow-prod-down`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-inv`
1×	`+-commutative` `sum-log` `sqrt-unprod` `*-commutative` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

25.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
49.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
38.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series1.1s

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
191.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
91.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
741.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify3.1s

Counts

128 → 128

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	254	49408
1	720	40702
2	4686	38990
done	5000	38910

prune504.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	322
1	14	322
done	14	322

end0.0ms

sample2.2s

Algorithm

intervals

Results

696.0ms	1154×	body	1280	valid
437.0ms	1914×	body	640	valid
370.0ms	7946×	body	80	nan
321.0ms	4059×	body	80	valid
74.0ms	560×	body	320	valid
29.0ms	313×	body	160	valid