Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	61×	body	640	valid
5.0ms	237×	body	80	nan
5.0ms	39×	body	1280	valid
3.0ms	133×	body	80	valid
1.0ms	11×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 19.7b

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))
2.5b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite90.0ms

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:

6.0ms	(sqrt (+ x 1.0))
14.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
59.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt (+ x 1.0))
68.0ms	(/ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ 1.0 (sqrt x))
126.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts

145 → 145

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	215	1942
1	444	1778
2	1051	1698
3	2647	1673
done	5000	1657

prune299.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.2b

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)))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite130.0ms

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:

6.0ms	(sqrt (+ x 1.0))
56.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
41.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series409.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1.0))
254.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
51.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify810.0ms

Counts

105 → 105

Iterations

Useful iterations: 2 (284.0ms)

Iter	Nodes	Cost
0	189	1624
1	502	1459
2	2028	1218
done	5000	1218

prune254.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.3b

localize10.0ms

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)))
1.5b	(- (+ x 1.0) x)

rewrite236.0ms

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:

99.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
69.0ms	(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
37.0ms	(- (+ x 1.0) x)

series685.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
481.0ms	(/ (* 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)

simplify1.2s

Counts

155 → 155

Iterations

Useful iterations: 2 (467.0ms)

Iter	Nodes	Cost
0	269	3162
1	726	2927
2	3026	2509
done	5000	2509

prune306.0ms

Pruning

10 alts after pruning (10 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)))

rewrite143.0ms

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:

29.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
41.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
28.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series951.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
136.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
699.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
55.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify975.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (408.0ms)

Iter	Nodes	Cost
0	250	2311
1	654	2082
2	2541	1730
done	5000	1730

prune262.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	14	18
done	14	18

end0.0ms

sample862.0ms

Algorithm

intervals

Results

167.0ms	1758×	body	640	valid
157.0ms	7989×	body	80	nan
135.0ms	1129×	body	1280	valid
110.0ms	4137×	body	80	valid
47.0ms	650×	body	320	valid
15.0ms	326×	body	160	valid