Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
5.0ms	269×	body	80	nan
3.0ms	143×	body	80	valid
3.0ms	39×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 26.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `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×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

5.0ms	(sqrt (+ x 1.0))
32.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series106.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify3.2s

Counts

95 → 95

Iterations

Useful iterations: 3 (530.0ms)

Iter	Nodes	Cost
0	137	1993
1	309	1467
2	918	1124
3	4514	950
done	5000	950

prune144.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.2b	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
32×	`distribute-lft-out`
31×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
6×	`fma-def` `associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 93

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
11.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
27.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series262.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (+ x 1.0))
81.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
144.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify700.0ms

Counts

102 → 102

Iterations

Useful iterations: done (697.0ms)

Iter	Nodes	Cost
0	169	1453
1	413	1200
2	1507	1090
done	5000	1084

prune220.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

7.0ms	(* (cbrt x) (cbrt x))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(cbrt x)

series769.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (cbrt x) (cbrt x))
181.0ms	(cbrt x)
192.0ms	(cbrt x)
185.0ms	(cbrt x)

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: 3 (306.0ms)

Iter	Nodes	Cost
0	65	554
1	122	495
2	449	423
3	1993	405
done	5001	405

prune293.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt x))
0.6b	(cbrt (sqrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 58

Calls

4 calls:

1.0ms	(cbrt (sqrt x))
1.0ms	(cbrt (sqrt x))
0.0ms	(cbrt x)
1.0ms	(cbrt x)

series716.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (sqrt x))
176.0ms	(cbrt (sqrt x))
198.0ms	(cbrt x)
187.0ms	(cbrt x)

simplify853.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (127.0ms)

Iter	Nodes	Cost
0	59	406
1	113	380
2	283	342
3	1210	326
done	5001	326

prune255.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	15	23
1	17	23
2	21	21
done	21	21

end0.0ms

sample665.0ms

Algorithm

intervals

Results

146.0ms	1713×	body	1280	valid
139.0ms	8101×	body	80	nan
90.0ms	1251×	body	640	valid
76.0ms	4067×	body	80	valid
31.0ms	615×	body	320	valid
12.0ms	354×	body	160	valid