Details

sample58.0ms

Algorithm

intervals

Results

10.0ms	126×	body	80	valid
9.0ms	59×	body	640	valid
9.0ms	260×	body	80	nan
9.0ms	44×	body	1280	valid
2.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize24.0ms

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))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite126.0ms

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))
100.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ x 1.0))
111.0ms	(/ 1.0 (sqrt (+ x 1.0)))
48.0ms	(/ 1.0 (sqrt x))
158.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify797.0ms

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	1655
1	462
0	216

prune666.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.0b

localize14.0ms

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 1.0)) (sqrt x)))
0.3b	(* (sqrt (+ x 1.0)) (sqrt x))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite183.0ms

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-l`
6×	`sqrt-div` `associate-r` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `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/` `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:

13.0ms	(sqrt (+ x 1.0))
92.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
27.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
47.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series650.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ x 1.0))
404.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
92.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
116.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	3032
1	531
0	192

prune512.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (+ x 1.0)) (sqrt x))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
110.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
66.0ms	(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
43.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

series1.1s

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1.0))
232.0ms	(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
726.0ms	(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
75.0ms	(* (sqrt (+ x 1.0)) (sqrt x))

simplify2.2s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	4904
1	753
0	269

prune664.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ x (* (sqrt x) (sqrt (+ 1.0 x)))))
0.1b	(/ 1.0 (sqrt (+ 1.0 x)))
0.1b	(* (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (+ x (* (sqrt x) (sqrt (+ 1.0 x))))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
73×	`times-frac`
71×	`*-un-lft-identity`
55×	`add-cube-cbrt`
41×	`sqrt-prod`
33×	`associate-l`
25×	`associate-r`
22×	`add-cbrt-cube` `add-exp-log`
15×	`distribute-lft-out`
11×	`associate-/r*`
10×	`pow1` `unswap-sqr`
8×	`associate-/r/`
6×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/l*`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
4×	`pow-prod-down` `div-inv` `add-log-exp`
3×	`associate-*r/`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `*-commutative`
1×	`frac-times` `sqrt-unprod` `associate-*l/`

Counts

4 → 182

Calls

4 calls:

9.0ms	(/ 1.0 (+ x (* (sqrt x) (sqrt (+ 1.0 x)))))
10.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
53.0ms	(* (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (+ x (* (sqrt x) (sqrt (+ 1.0 x))))))
47.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

series649.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ 1.0 (+ x (* (sqrt x) (sqrt (+ 1.0 x)))))
108.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
357.0ms	(* (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (+ x (* (sqrt x) (sqrt (+ 1.0 x))))))
72.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

simplify2.1s

Counts

194 → 194

Iterations

Iter	Nodes
done	5001
2	4807
1	859
0	302

prune964.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes114.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	19
2	19
1	18
0	15

end0.0ms

sample2.5s

Algorithm

intervals

Results

844.0ms	1794×	body	640	valid
514.0ms	8020×	body	80	nan
323.0ms	1152×	body	1280	valid
268.0ms	4110×	body	80	valid
89.0ms	619×	body	320	valid
31.0ms	325×	body	160	valid