Details

sample77.0ms

Algorithm

intervals

Results

19.0ms	55×	body	1280	valid
16.0ms	246×	body	80	nan
11.0ms	40×	body	640	valid
9.0ms	128×	body	80	valid
7.0ms	20×	body	320	valid
2.0ms	13×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
4.0b	(- (sqrt (+ x 1)) (sqrt x))

rewrite54.0ms

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` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

9.0ms	(sqrt (+ x 1))
44.0ms	(- (sqrt (+ x 1)) (sqrt x))

series137.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(sqrt (+ x 1))
89.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.2s

Counts

43 → 43

Iterations

Iter	Nodes
5	4088
4	1554
3	730
2	352
1	161
0	81

prune340.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite79.0ms

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`
7×	`add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `insert-posit16` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 78

Calls

3 calls:

4.0ms	(sqrt (+ x 1))
36.0ms	(+ (sqrt (+ x 1)) (sqrt x))
37.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(sqrt (+ x 1))
74.0ms	(+ (sqrt (+ x 1)) (sqrt x))
83.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify872.0ms

Counts

87 → 87

Iterations

Iter	Nodes
4	2176
3	1028
2	524
1	238
0	120

prune623.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity`
290×	`sqrt-prod`
168×	`times-frac`
136×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
43×	`swap-sqr`
31×	`pow1`
27×	`sqrt-pow1` `associate-r` `associate-l`
16×	`unswap-sqr`
14×	`add-exp-log` `associate-/r/`
12×	`associate-/r*`
11×	`pow-flip` `inv-pow`
10×	`add-cbrt-cube`
9×	`pow1/2` `pow-prod-up` `div-inv`
7×	`flip3-+` `flip-+`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-down` `pow-sqr`
4×	`div-exp` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 282

Calls

4 calls:

50.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
33.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
41.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
177.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
95.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
123.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
98.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

simplify1.0s

Counts

294 → 294

Iterations

Iter	Nodes
3	2193
2	1008
1	442
0	229

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))
0.3b	(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
32×	`sqrt-prod` `distribute-lft-out`
19×	`pow1`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`pow-unpow`
10×	`swap-sqr`
9×	`times-frac` `add-exp-log`
8×	`flip3-+` `flip-+` `add-log-exp`
6×	`pow-pow` `add-cbrt-cube` `associate-r` `associate-l`
4×	`frac-times` `insert-posit16`
2×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`distribute-rgt-in` `pow-to-exp` `unpow-prod-down` `distribute-lft-in` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

24.0ms	(+ (sqrt (+ x 1)) (sqrt x))
26.0ms	(+ (sqrt (+ x 1)) (sqrt x))
51.0ms	(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))
116.0ms	(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (sqrt (+ x 1)) (sqrt x))
65.0ms	(+ (sqrt (+ x 1)) (sqrt x))
243.0ms	(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (/ -1 2))
76.0ms	(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.4s

Counts

123 → 123

Iterations

Iter	Nodes
3	5140
2	1332
1	443
0	145

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	16
1	16
0	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

808.0ms	1658×	body	1280	valid
554.0ms	8213×	body	80	nan
279.0ms	1218×	body	640	valid
223.0ms	4164×	body	80	valid
97.0ms	339×	body	160	valid
95.0ms	621×	body	320	valid