Details

sample51.0ms

Algorithm

intervals

Results

12.0ms	41×	body	1280	valid
10.0ms	63×	body	640	valid
8.0ms	249×	body	80	nan
5.0ms	122×	body	80	valid
3.0ms	24×	body	320	valid
0.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 20.0b

Counts

2 → 1

localize8.0ms

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))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite55.0ms

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:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
31.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series32.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ 1.0 (sqrt x))
13.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify504.0ms

Counts

145 → 145

Iterations

Useful iterations: done (500.0ms)

Iter	Nodes	Cost
0	264	2096
1	620	1955
2	1968	1879
done	5000	1871

prune284.0ms

Filtered

100 candidates to 145 candidates (-45.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	134	11	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Merged error: 19.5b

Counts

146 → 11

localize9.0ms

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `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×	`sub-neg` `rem-sqrt-square` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
18.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
9.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series57.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
36.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
7.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify828.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (279.0ms)

Iter	Nodes	Cost
0	288	1964
1	849	1818
2	3752	1594
done	5000	1594

prune219.0ms

Filtered

74 candidates to 105 candidates (-41.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Merged error: 19.1b

Counts

116 → 10

localize11.0ms

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))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.2b	(- (+ x 1.0) x)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

113×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
39×	`sqrt-prod`
37×	`times-frac` `distribute-lft-out`
29×	`add-exp-log` `add-cbrt-cube`
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×	`flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `flip--` `div-inv`
1×	`sub-neg` `sqrt-unprod` `div-sub` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 143

Calls

4 calls:

16.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
12.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
7.0ms	(- (+ x 1.0) x)

series58.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
41.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
7.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(- (+ x 1.0) x)

simplify913.0ms

Counts

155 → 155

Iterations

Useful iterations: 2 (338.0ms)

Iter	Nodes	Cost
0	335	3372
1	984	3183
2	4634	2724
done	5000	2724

prune281.0ms

Filtered

90 candidates to 155 candidates (-72.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	152	3	155
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	157	8	165

Merged error: 0.2b

Counts

165 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
11.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
20.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
9.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
37.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
7.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify867.0ms

Counts

130 → 130

Iterations

Useful iterations: 2 (330.0ms)

Iter	Nodes	Cost
0	331	2497
1	947	2308
2	4288	1959
done	5000	1959

prune245.0ms

Filtered

85 candidates to 130 candidates (-52.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	121	9	130
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	126	12	138

Merged error: 0.0b

Counts

138 → 12

regimes66.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	13	18
done	13	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

296.0ms	1853×	body	640	valid
291.0ms	8058×	body	80	nan
226.0ms	1111×	body	1280	valid
175.0ms	4117×	body	80	valid
73.0ms	623×	body	320	valid
23.0ms	296×	body	160	valid

Details

sample51.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite55.0ms

series32.0ms

simplify504.0ms

prune284.0ms

localize9.0ms

rewrite42.0ms

series57.0ms

simplify828.0ms

prune219.0ms

localize11.0ms

rewrite66.0ms

series58.0ms

simplify913.0ms

prune281.0ms

localize10.0ms

rewrite50.0ms

series57.0ms

simplify867.0ms

prune245.0ms

regimes66.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

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