Details

sample63.0ms

Algorithm

intervals

Results

11.0ms	54×	body	1280	valid
11.0ms	143×	body	80	valid
11.0ms	253×	body	80	nan
6.0ms	34×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
2.5b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 35

Calls

2 calls:

9.0ms	(sqrt (+ 1.0 x))
44.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series179.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(sqrt (+ 1.0 x))
122.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify1.7s

Counts

41 → 41

Iterations

Iter	Nodes
done	5000
3	2897
2	676
1	193
0	86

prune160.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 71

Calls

3 calls:

6.0ms	(sqrt (+ 1.0 x))
51.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
51.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series320.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(sqrt (+ 1.0 x))
114.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
166.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify686.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1549
1	371
0	156

prune306.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

35.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
31.0ms	(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
36.0ms	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
111.0ms	(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

209.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
181.0ms	(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
351.0ms	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
560.0ms	(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify632.0ms

Counts

457 → 457

Iterations

Iter	Nodes
done	5000
1	1157
0	474

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)))
0.3b	(cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3))
0.4b	(pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)

rewrite492.0ms

Algorithm

rewrite-expression-head

Rules

1804×	`*-un-lft-identity`
1674×	`times-frac`
1600×	`sqrt-prod`
840×	`cbrt-prod`
684×	`add-sqr-sqrt` `add-cube-cbrt`
640×	`distribute-lft-out`
324×	`unpow-prod-down` `cube-prod`
64×	`sqrt-div`
60×	`associate-/r/`
36×	`cube-mult` `associate-/r` `unpow3` `associate-/l` `sqr-pow`
32×	`flip3-+` `flip-+`
30×	`div-inv`
12×	`add-exp-log`
10×	`add-cbrt-cube`
6×	`cube-div` `pow1`
4×	`cbrt-undiv` `cbrt-div` `div-exp` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `rem-cbrt-cube` `sqrt-pow2` `rem-cube-cbrt` `associate-/l/`

Counts

4 → 1096

Calls

4 calls:

52.0ms	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
234.0ms	(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)))
41.0ms	(cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3))
31.0ms	(pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)

series1.4s

Counts

4 → 12

Calls

4 calls:

439.0ms	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
188.0ms	(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)))
197.0ms	(cbrt (pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3))
537.0ms	(pow (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))) 3)

simplify1.5s

Counts

1108 → 1108

Iterations

Iter	Nodes
done	5000
1	2263
0	872

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.8s

Algorithm

intervals

Results

547.0ms	1314×	body	640	valid
475.0ms	7946×	body	80	nan
269.0ms	1750×	body	1280	valid
129.0ms	4066×	body	80	valid
73.0ms	560×	body	320	valid
19.0ms	310×	body	160	valid