Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	20	12
3	22	12
done	22	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
30.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
55.0ms	(+ (+ (* x x) (* y y)) (* z z))
34.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series269.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* x x) (* y y))
68.0ms	(+ (+ (* x x) (* y y)) (* z z))
154.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.4s

Counts

48 → 48

Iterations

Useful iterations: 3 (717.0ms)

Iter	Nodes	Cost
0	74	742
1	203	681
2	653	621
3	2437	605
done	5001	605

prune147.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
0.3b	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
31.4b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
31.4b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

60.0ms	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
116.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
30.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
37.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series650.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z))))
215.0ms	(* (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
148.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
160.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.0s

Counts

86 → 86

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	141	2243
1	319	2103
2	944	1901
3	2681	1832
done	5001	1818

prune433.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
31.4b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
31.4b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
31.4b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`sqrt-prod`
14×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`pow1` `cbrt-div`
6×	`add-exp-log` `associate-l` `add-cbrt-cube` `unswap-sqr`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3` `pow-prod-down`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-*r/`
1×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

86.0ms	(* (sqrt (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
18.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
18.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
25.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(* (sqrt (fabs (cbrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt (cbrt (+ (+ (* x x) (* y y)) (* z z)))))
121.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
154.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
125.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.0s

Counts

88 → 88

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	132	2516
1	292	2382
2	874	2202
3	2575	2120
done	5000	2105

prune435.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 16.5b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 16.5b

regimes577.0ms

Accuracy

63.6% (7.1b remaining)

Error of 25.3b against oracle of 18.2b and baseline of 37.8b

bsearch95.0ms

Steps

Iters	Range		Point
11	2.7445276404852593e+146	4.63587813976503e+166	7.747364727091018e+152
8	-1.5436475226868818e+95	-1.2028430122763079e+91	-1.1361287592615157e+95

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	23
1	18	23
done	18	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

857.0ms

8000×

body

valid