Details

sample56.0ms

Algorithm

intervals

Results

20.0ms	66×	body	1280	valid
11.0ms	245×	body	80	nan
6.0ms	138×	body	80	valid
3.0ms	21×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.9b	(- (sqrt (+ x 1)) (sqrt x))

rewrite39.0ms

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))
29.0ms	(- (sqrt (+ x 1)) (sqrt x))

series146.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(sqrt (+ x 1))
104.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.0s

Counts

43 → 43

Iterations

Iter	Nodes
done	5003
4	2286
3	925
2	368
1	165
0	81

prune176.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(/ (+ 0 1) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`insert-posit16`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

8.0ms	(sqrt (+ x 1))
26.0ms	(+ (sqrt (+ x 1)) (sqrt x))
49.0ms	(/ (+ 0 1) (+ (sqrt (+ x 1)) (sqrt x)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(sqrt (+ x 1))
70.0ms	(+ (sqrt (+ x 1)) (sqrt x))
86.0ms	(/ (+ 0 1) (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	5002
4	3738
3	1691
2	655
1	276
0	133

prune382.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ (+ 0 1) (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
0.3b	(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
78×	`*-un-lft-identity`
34×	`distribute-lft-out`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
21×	`pow1`
16×	`add-cube-cbrt`
15×	`flip3-+` `swap-sqr` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-pow1` `pow1/2`
9×	`associate-r` `associate-l`
8×	`frac-times` `associate-/r/`
5×	`pow-prod-up`
4×	`times-frac` `associate-l/` `associate-r/` `insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`pow2` `clear-num` `associate-/r` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `-commutative` `div-inv`

Counts

4 → 143

Calls

4 calls:

21.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
42.0ms	(/ (+ 0 1) (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
170.0ms	(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
125.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
96.0ms	(/ (+ 0 1) (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
56.0ms	(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.1s

Counts

155 → 155

Iterations

Iter	Nodes
done	5004
3	3372
2	1104
1	396
0	165

prune563.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ (+ 0 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ (/ (+ 0 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

1122×	`*-un-lft-identity`
900×	`sqrt-prod`
774×	`times-frac`
460×	`distribute-lft-out`
294×	`add-sqr-sqrt`
292×	`add-cube-cbrt`
46×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
15×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 551

Calls

4 calls:

22.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
25.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
71.0ms	(/ (+ 0 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
105.0ms	(/ (/ (+ 0 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
123.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
181.0ms	(/ (+ 0 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
112.0ms	(/ (/ (+ 0 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.0s

Counts

563 → 563

Iterations

Iter	Nodes
done	5000
2	1731
1	862
0	373

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.7s

Algorithm

intervals

Results

924.0ms	7851×	body	80	nan
693.0ms	1731×	body	1280	valid
362.0ms	1233×	body	640	valid
305.0ms	4077×	body	80	valid
109.0ms	636×	body	320	valid
38.0ms	323×	body	160	valid