Details

sample32.0ms

Algorithm

intervals

Results

16.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
done	7	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
28.5b	(sqrt (+ (* x x) (* y y)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 26

Calls

2 calls:

16.0ms	(+ (* x x) (* y y))
16.0ms	(sqrt (+ (* x x) (* y y)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(+ (* x x) (* y y))
46.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.4s

Counts

32 → 32

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	48	379
1	124	347
2	343	295
3	968	295
4	2668	295
done	5000	295

prune82.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* x x) (* y y))))
28.5b	(sqrt (+ (* x x) (* y y)))
28.5b	(sqrt (+ (* x x) (* y y)))
28.5b	(sqrt (+ (* x x) (* y y)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

6.0ms	(cbrt (sqrt (+ (* x x) (* y y))))
8.0ms	(sqrt (+ (* x x) (* y y)))
8.0ms	(sqrt (+ (* x x) (* y y)))
8.0ms	(sqrt (+ (* x x) (* y y)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (sqrt (+ (* x x) (* y y))))
39.0ms	(sqrt (+ (* x x) (* y y)))
41.0ms	(sqrt (+ (* x x) (* y y)))
43.0ms	(sqrt (+ (* x x) (* y y)))

simplify1.7s

Counts

73 → 73

Iterations

Useful iterations: 3 (279.0ms)

Iter	Nodes	Cost
0	70	952
1	149	853
2	323	761
3	693	750
4	1885	750
done	5001	750

prune258.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize23.0ms

Local error

Found 4 expressions with local error:

28.5b	(sqrt (+ (* x x) (* y y)))
28.5b	(sqrt (+ (* x x) (* y y)))
28.5b	(sqrt (+ (* x x) (* y y)))
28.5b	(sqrt (+ (* x x) (* y y)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

14.0ms	(sqrt (+ (* x x) (* y y)))
23.0ms	(sqrt (+ (* x x) (* y y)))
14.0ms	(sqrt (+ (* x x) (* y y)))
11.0ms	(sqrt (+ (* x x) (* y y)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* x x) (* y y)))
56.0ms	(sqrt (+ (* x x) (* y y)))
49.0ms	(sqrt (+ (* x x) (* y y)))
54.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.8s

Counts

72 → 72

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	205	680
3	444	656
4	1114	656
5	3182	656
done	5001	656

prune295.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
5.7b	(exp (log (sqrt (+ (* x x) (* y y)))))
28.5b	(sqrt (+ (* x x) (* y y)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `log-prod` `exp-prod` `exp-sum` `sqrt-prod`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `rem-exp-log`

Counts

3 → 48

Calls

3 calls:

12.0ms	(+ (* x x) (* y y))
22.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
12.0ms	(sqrt (+ (* x x) (* y y)))

series113.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* x x) (* y y))
42.0ms	(exp (log (sqrt (+ (* x x) (* y y)))))
41.0ms	(sqrt (+ (* x x) (* y y)))

simplify2.2s

Counts

57 → 57

Iterations

Useful iterations: 4 (991.0ms)

Iter	Nodes	Cost
0	87	739
1	169	626
2	398	534
3	1056	534
4	2807	528
done	5001	528

prune162.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

regimes378.0ms

Accuracy

58.9% (9.9b remaining)

Error of 17.7b against oracle of 7.8b and baseline of 31.9b

bsearch57.0ms

Steps

Iters	Range		Point
10	1.2073698495971617e+61	3.217811591970086e+74	2.7153468834491098e+73
5	-1.7457635943519997e+137	-5.665103565004941e+136	-1.2876568362185878e+137

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	19
1	14	19
done	14	19

end0.0ms

sample603.0ms

Algorithm

intervals

Results

361.0ms

8000×

body

valid