Details

sample46.0ms

Algorithm

intervals

Results

8.0ms	252×	body	80	nan
8.0ms	55×	body	1280	valid
6.0ms	45×	body	640	valid
5.0ms	125×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize6.0ms

Local error

Found 1 expressions with local error:

3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite73.0ms

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:

71.0ms

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

series107.0ms

Counts

1 → 3

Calls

1 calls:

107.0ms

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

simplify2.1s

Counts

22 → 22

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	59	310
1	133	285
2	336	263
3	802	257
4	2104	250
done	5001	246

prune97.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

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)))

rewrite81.0ms

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:

31.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
47.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series289.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
220.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.8s

Counts

61 → 61

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	128	947
1	297	865
2	790	788
3	2333	774
done	5001	766

prune171.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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)))))

rewrite484.0ms

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-exp-log` `add-cbrt-cube`
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` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

69.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
72.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
264.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series965.0ms

Counts

4 → 12

Calls

4 calls:

422.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
157.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
173.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
212.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.6s

Counts

262 → 262

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	311	6170
1	641	4386
2	2004	4124
done	5001	4023

prune805.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
82×	`sqrt-prod`
46×	`times-frac`
40×	`distribute-lft-out`
34×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
15×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `sqrt-div` `associate-/r/`
4×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `div-inv`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`sqrt-undiv` `sqrt-unprod` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

50.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
65.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
60.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
112.0ms	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

279.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
506.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
187.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
240.0ms	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.6s

Counts

144 → 144

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	298	3063
1	690	2716
2	2119	2506
done	5000	2446

prune581.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes53.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.0s

Algorithm

intervals

Results

588.0ms	4131×	body	80	valid
456.0ms	8150×	body	80	nan
300.0ms	1680×	body	1280	valid
167.0ms	1282×	body	640	valid
60.0ms	603×	body	320	valid
18.0ms	304×	body	160	valid