Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	312×	body	80	nan
9.0ms	67×	body	640	valid
5.0ms	30×	body	1280	valid
4.0ms	123×	body	80	valid
3.0ms	28×	body	320	valid
1.0ms	8×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize22.0ms

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))
2.4b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite104.0ms

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:

11.0ms	(sqrt (+ x 1.0))
17.0ms	(/ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ 1.0 (sqrt x))
58.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ x 1.0))
82.0ms	(/ 1.0 (sqrt (+ x 1.0)))
43.0ms	(/ 1.0 (sqrt x))
198.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.1s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	1655
1	462
0	216

prune719.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 22.7b

localize17.0ms

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)))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite168.0ms

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:

12.0ms	(sqrt (+ x 1.0))
69.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
40.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
46.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series575.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (+ x 1.0))
363.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
77.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
78.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.9s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	3114
1	538
0	191

prune499.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 22.0b

localize22.0ms

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))

rewrite222.0ms

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:

118.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
68.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
20.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
12.0ms	(+ x (- 1.0 x))

series947.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
664.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
88.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify2.3s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
2	4777
1	749
0	261

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
31×	`sqrt-prod`
29×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
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×	`clear-num` `frac-2neg` `div-inv`
1×	`rem-sqrt-square` `sqrt-unprod` `*-commutative` `associate-/l/`

Counts

4 → 118

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
42.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
62.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series747.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1.0))
141.0ms	(/ 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))))
79.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.7s

Counts

130 → 130

Iterations

Iter	Nodes
done	5002
2	4589
1	712
0	251

prune411.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	12

end0.0ms

sample1.8s

Algorithm

intervals

Results

663.0ms	1817×	body	640	valid
287.0ms	4129×	body	80	valid
274.0ms	7998×	body	80	nan
227.0ms	1102×	body	1280	valid
68.0ms	669×	body	320	valid
22.0ms	283×	body	160	valid