Details

sample60.0ms

Algorithm

intervals

Results

14.0ms	56×	body	1280	valid
14.0ms	277×	body	80	nan
8.0ms	41×	body	640	valid
7.0ms	134×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
3.0b	(- (sqrt (+ x 1)) (sqrt x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
55×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
42×	`prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `hypot-def` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 92

Calls

2 calls:

5.0ms	(sqrt (+ x 1))
53.0ms	(- (sqrt (+ x 1)) (sqrt x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(sqrt (+ x 1))
79.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	2000
4	2000
3	1554
2	618
1	294
0	134

prune329.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 28.6b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
2.7b	(- (+ x 1) x)

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
41×	`distribute-lft-out`
36×	`times-frac`
32×	`sqrt-prod`
26×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
8×	`add-log-exp` `difference-of-squares`
6×	`associate-/r` `associate-/l`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `fma-neg`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`flip3-+` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip-+` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `div-inv`

Counts

3 → 125

Calls

3 calls:

9.0ms	(sqrt (+ x 1))
109.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
41.0ms	(- (+ x 1) x)

series142.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(sqrt (+ x 1))
115.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
2.0ms	(- (+ x 1) x)

simplify1.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	2001
3	2001
2	1288
1	427
0	174

prune387.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
20×	`sqrt-prod`
18×	`add-sqr-sqrt` `times-frac`
17×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`associate-/r*` `add-exp-log`
4×	`pow1` `add-cbrt-cube`
3×	`associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `hypot-def` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

2 → 69

Calls

2 calls:

9.0ms	(sqrt (+ x 1))
39.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series146.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(sqrt (+ x 1))
120.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	2015
4	2015
3	1699
2	669
1	243
0	116

prune265.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`pow1` `sqrt-div`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l` `add-exp-log`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 177

Calls

4 calls:

11.0ms	(sqrt (sqrt (+ x 1)))
11.0ms	(sqrt (sqrt (+ x 1)))
66.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
58.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series222.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (sqrt (+ x 1)))
50.0ms	(sqrt (sqrt (+ x 1)))
89.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
44.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify1.2s

Counts

189 → 189

Iterations

Iter	Nodes
done	2001
3	2001
2	1049
1	458
0	217

prune613.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.7s

Algorithm

intervals

Results

942.0ms	8141×	body	80	nan
671.0ms	1668×	body	1280	valid
379.0ms	1277×	body	640	valid
321.0ms	4111×	body	80	valid
109.0ms	628×	body	320	valid
38.0ms	316×	body	160	valid