Details

sample54.0ms

Algorithm

intervals

Results

9.0ms	55×	body	640	valid
9.0ms	253×	body	80	nan
7.0ms	34×	body	1280	valid
6.0ms	142×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	12×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize15.0ms

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))))

rewrite142.0ms

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))
115.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1.0))
106.0ms	(/ 1.0 (sqrt (+ x 1.0)))
73.0ms	(/ 1.0 (sqrt x))
191.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	1655
1	462
0	216

prune861.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.7b

localize37.0ms

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))

rewrite159.0ms

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))
49.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
37.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
65.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series654.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ x 1.0))
371.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
113.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
115.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	3114
1	538
0	191

prune745.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.9b

localize43.0ms

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))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

126.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
58.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
29.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
13.0ms	(+ x (- 1.0 x))

series1.0s

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
698.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
93.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify2.9s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	4777
1	749
0	261

prune662.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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))))

rewrite164.0ms

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:

26.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
36.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
28.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
70.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series999.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
211.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
84.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
609.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify2.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	4686
1	720
0	254

prune444.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes88.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	10

end0.0ms

sample1.9s

Algorithm

intervals

Results

695.0ms	7946×	body	80	nan
279.0ms	1914×	body	640	valid
261.0ms	4059×	body	80	valid
245.0ms	1154×	body	1280	valid
62.0ms	560×	body	320	valid
23.0ms	313×	body	160	valid