Details

sample46.0ms

Algorithm

intervals

Results

15.0ms	309×	body	80	nan
6.0ms	59×	body	1280	valid
4.0ms	51×	body	640	valid
4.0ms	117×	body	80	valid
1.0ms	23×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite98.0ms

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` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

86.0ms

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

series94.0ms

Counts

1 → 3

Calls

1 calls:

93.0ms

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

simplify1.1s

Counts

22 → 22

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	59	310
1	348	285
done	5001	259

prune76.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 32.6b

localize11.0ms

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)))
1.7b	(- (+ x 1.0) x)

rewrite266.0ms

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-exp-log` `add-cbrt-cube`
3×	`pow1`
2×	`flip3--` `flip3-+` `diff-log` `sum-log` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `div-sub` `div-exp` `associate--l+` `clear-num` `div-inv`

Counts

3 → 96

Calls

3 calls:

43.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
157.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(- (+ x 1.0) x)

series269.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
195.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.0ms	(- (+ x 1.0) x)

simplify3.8s

Counts

105 → 105

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	161	1866
1	1893	1734
done	5000	1658

prune259.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite116.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 55

Calls

2 calls:

45.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
66.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series306.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
225.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify3.8s

Counts

61 → 61

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	128	947
1	1863	856
done	5001	788

prune216.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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))))

rewrite486.0ms

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-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

65.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
47.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
81.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
243.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

208.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
223.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
515.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
210.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify3.4s

Counts

457 → 457

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	440	15237
1	3737	12212
done	5000	11813

prune879.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

691.0ms	4137×	body	80	valid
346.0ms	1721×	body	1280	valid
331.0ms	8101×	body	80	nan
241.0ms	1224×	body	640	valid
96.0ms	610×	body	320	valid
26.0ms	308×	body	160	valid