Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	50×	body	640	valid
7.0ms	334×	body	80	nan
5.0ms	46×	body	1280	valid
3.0ms	130×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	14×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6
done	14	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize7.0ms

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))
3.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite94.0ms

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:

7.0ms	(sqrt (+ x 1.0))
12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
63.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (+ x 1.0))
75.0ms	(/ 1.0 (sqrt (+ x 1.0)))
35.0ms	(/ 1.0 (sqrt x))
132.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify48.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	443	1097
1	1434	1038
2	5001	992
done	5001	992

prune306.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.1b

localize8.0ms

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)))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite138.0ms

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:

7.0ms	(sqrt (+ x 1.0))
57.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
44.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series413.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
260.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
64.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify64.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	511	883
1	2553	762
2	5001	749
done	5001	749

prune265.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 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)))
2.4b	(+ x (- 1.0 x))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
41×	`distribute-lft-out`
35×	`sqrt-prod`
31×	`times-frac`
29×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
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-` `associate-+r+` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `sub-neg` `sqrt-unprod` `diff-log` `div-sub` `*-commutative`

Counts

4 → 136

Calls

4 calls:

84.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
28.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
15.0ms	(+ x (- 1.0 x))

series695.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
491.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify96.0ms

Counts

148 → 148

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	710	1587
1	3837	1359
2	5001	1323
done	5001	1323

prune348.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
31×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
21×	`distribute-lft-out`
19×	`add-cube-cbrt` `times-frac`
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×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

30.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
43.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
25.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series760.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
137.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
496.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify88.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	671	1264
1	3514	1071
2	5001	1043
done	5001	1043

prune493.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11
done	13	11

end0.0ms

sample893.0ms

Algorithm

intervals

Results

176.0ms	1894×	body	640	valid
171.0ms	8104×	body	80	nan
136.0ms	1147×	body	1280	valid
107.0ms	4054×	body	80	valid
41.0ms	600×	body	320	valid
17.0ms	305×	body	160	valid