Details

sample57.0ms

Algorithm

intervals

Results

12.0ms	60×	body	1280	valid
11.0ms	238×	body	80	nan
7.0ms	41×	body	640	valid
5.0ms	123×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	8×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize16.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

48.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series97.0ms

Counts

1 → 3

Calls

1 calls:

97.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts

22 → 22

Iterations

Iter	Nodes
done	5000
3	2044
2	479
1	140
0	61

prune87.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
20×	`sqrt-prod` `distribute-lft-out`
18×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 55

Calls

2 calls:

49.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
67.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series254.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
179.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.3s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
2	1291
1	319
0	132

prune296.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite509.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

72.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
64.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
70.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
273.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

590.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
158.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
228.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
258.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.1s

Counts

262 → 262

Iterations

Iter	Nodes
done	5001
2	3223
1	702
0	310

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite332.0ms

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:

36.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
39.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
56.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
140.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

227.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
225.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
476.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
223.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.6s

Counts

457 → 457

Iterations

Iter	Nodes
done	5002
2	4125
1	1072
0	442

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

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

sample2.0s

Algorithm

intervals

Results

735.0ms	8087×	body	80	nan
379.0ms	1784×	body	1280	valid
226.0ms	1272×	body	640	valid
195.0ms	4033×	body	80	valid
64.0ms	293×	body	160	valid
62.0ms	618×	body	320	valid