Details

sample54.0ms

Algorithm

intervals

Results

13.0ms	41×	body	640	valid
11.0ms	60×	body	1280	valid
9.0ms	238×	body	80	nan
4.0ms	123×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

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

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite54.0ms

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:

53.0ms

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

series90.0ms

Counts

1 → 3

Calls

1 calls:

90.0ms

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

simplify2.3s

Counts

22 → 22

Iterations

Iter	Nodes
done	5001
4	3070
3	1015
2	347
1	140
0	61

prune102.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.2b	(- (+ x 1.0) x)

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

113×	`*-un-lft-identity`
40×	`distribute-lft-out`
36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`sqrt-prod`
17×	`add-cube-cbrt`
16×	`distribute-lft-out--`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`associate-/r` `associate-/l`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1`
2×	`sum-log` `flip3-+` `flip3--` `diff-log` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sub-neg` `frac-2neg` `div-sub` `div-exp` `associate--l+` `div-inv`

Counts

3 → 96

Calls

3 calls:

33.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
97.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
29.0ms	(- (+ x 1.0) x)

series297.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
187.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(- (+ x 1.0) x)

simplify1.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1568
1	443
0	165

prune446.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

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)))

rewrite122.0ms

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:

50.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
70.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series284.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
193.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.3s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	3100
2	932
1	319
0	132

prune299.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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)))))

rewrite544.0ms

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:

69.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
41.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
67.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
339.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

569.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
185.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
178.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
206.0ms	(* (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	5000
2	1879
1	689
0	310

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.8s

Algorithm

intervals

Results

440.0ms	618×	body	320	valid
341.0ms	1784×	body	1280	valid
316.0ms	8087×	body	80	nan
202.0ms	4033×	body	80	valid
154.0ms	1272×	body	640	valid
51.0ms	293×	body	160	valid