Details

sample128.0ms

Algorithm

intervals

Results

81.0ms

684×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	29
1	51	29
2	154	29
3	455	29
4	1681	29
done	5001	29

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(* (* b b) (+ 3.0 a))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1` `add-exp-log`
16×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`associate-r`
10×	`add-cube-cbrt`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`associate-l`
4×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `frac-add` `flip-+` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

181.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
71.0ms	(* (* a a) (- 1.0 a))
65.0ms	(* (* b b) (+ 3.0 a))
23.0ms	(pow (+ (* a a) (* b b)) 2.0)

series490.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))
99.0ms	(* (* a a) (- 1.0 a))
64.0ms	(* (* b b) (+ 3.0 a))
201.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify4.7s

Counts

106 → 106

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	215	1577
1	708	1478
2	4981	1336
done	5002	1336

prune720.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
17.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

143.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
16.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
15.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

258.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
253.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
263.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
256.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify1.4s

Counts

121 → 121

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	119	2918
1	237	2763
2	980	2621
done	5001	2467

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize107.0ms

Local error

Found 4 expressions with local error:

7.8b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
7.8b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
17.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-prod`
18×	`unpow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

18.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
18.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
16.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
241.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
261.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
273.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify3.4s

Counts

78 → 78

Iterations

Useful iterations: 3 (304.0ms)

Iter	Nodes	Cost
0	97	1398
1	173	1356
2	348	1272
3	999	1260
4	4297	1260
done	5000	1260

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize154.0ms

Local error

Found 4 expressions with local error:

7.2b	(sqrt (+ (* a a) (* b b)))
7.8b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
17.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.2b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
6×	`sqrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 63

Calls

4 calls:

16.0ms	(sqrt (+ (* a a) (* b b)))
21.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
19.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series964.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ (* a a) (* b b)))
302.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
297.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
297.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify3.0s

Counts

75 → 75

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	118	1213
1	252	1161
2	669	1079
3	2823	1068
done	5001	1068

prune921.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	29
1	25	29
done	25	29

end0.0ms

sample4.4s

Algorithm

intervals

Results

3.5s

20353×

body

valid