Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	58×	body	640	valid
5.0ms	269×	body	80	nan
4.0ms	34×	body	1280	valid
4.0ms	143×	body	80	valid
1.0ms	12×	body	320	valid
0.0ms	9×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
1.8b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite66.0ms

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:

4.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
47.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1.0))
76.0ms	(/ 1.0 (sqrt (+ x 1.0)))
37.0ms	(/ 1.0 (sqrt x))
136.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify637.0ms

Counts

145 → 145

Iterations

Useful iterations: done (633.0ms)

Iter	Nodes	Cost
0	215	1942
1	454	1802
2	1385	1688
done	5001	1680

prune294.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite79.0ms

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:

5.0ms	(sqrt (+ x 1.0))
32.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
25.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series441.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ x 1.0))
262.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
80.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify781.0ms

Counts

105 → 105

Iterations

Useful iterations: done (778.0ms)

Iter	Nodes	Cost
0	189	1624
1	529	1463
2	2343	1218
done	5001	1209

prune235.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.4b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

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:

59.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
39.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
18.0ms	(- (+ x 1.0) x)

series745.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
538.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
63.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(- (+ x 1.0) x)

simplify1.4s

Counts

155 → 155

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	269	3162
1	761	2959
2	3796	2509
done	5001	2502

prune301.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

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:

19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
27.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
15.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
30.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series809.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
146.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
534.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify1.2s

Counts

128 → 128

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	250	2311
1	697	2102
2	3300	1730
done	5000	1721

prune277.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes40.0ms

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	14	18
done	14	18

end0.0ms

sample873.0ms

Algorithm

intervals

Results

180.0ms	1842×	body	640	valid
177.0ms	8101×	body	80	nan
146.0ms	1127×	body	1280	valid
110.0ms	4061×	body	80	valid
45.0ms	616×	body	320	valid
18.0ms	354×	body	160	valid