Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	6
1	6
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize6.0ms

Local error

Found 1 expressions with local error:

15.0b

(/ x (+ (* x x) 1.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

20.0ms

(/ x (+ (* x x) 1.0))

series100.0ms

Counts

1 → 3

Calls

1 calls:

100.0ms

(/ x (+ (* x x) 1.0))

simplify1.3s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
2	783
1	183
0	74

prune161.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
14.9b	(sqrt (+ (* x x) 1.0))
14.9b	(sqrt (+ (* x x) 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`associate-/r*` `sqrt-div`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 71

Calls

3 calls:

18.0ms	(/ x (sqrt (+ (* x x) 1.0)))
7.0ms	(sqrt (+ (* x x) 1.0))
7.0ms	(sqrt (+ (* x x) 1.0))

series298.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(/ x (sqrt (+ (* x x) 1.0)))
50.0ms	(sqrt (+ (* x x) 1.0))
64.0ms	(sqrt (+ (* x x) 1.0))

simplify1.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1335
1	296
0	130

prune417.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ x (sqrt (sqrt (+ (* x x) 1.0))))
14.9b	(sqrt (+ (* x x) 1.0))
14.9b	(sqrt (+ (* x x) 1.0))
14.9b	(sqrt (+ (* x x) 1.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 98

Calls

4 calls:

17.0ms	(/ x (sqrt (sqrt (+ (* x x) 1.0))))
14.0ms	(sqrt (+ (* x x) 1.0))
8.0ms	(sqrt (+ (* x x) 1.0))
7.0ms	(sqrt (+ (* x x) 1.0))

series565.0ms

Counts

4 → 12

Calls

4 calls:

384.0ms	(/ x (sqrt (sqrt (+ (* x x) 1.0))))
62.0ms	(sqrt (+ (* x x) 1.0))
65.0ms	(sqrt (+ (* x x) 1.0))
50.0ms	(sqrt (+ (* x x) 1.0))

simplify1.2s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1537
1	368
0	173

prune523.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(/ 1.0 (* (* x x) x))
0.6b	(/ 1.0 (pow x 5))
19.4b	(- (/ 1.0 (pow x 5)) (/ 1.0 (* (* x x) x)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`times-frac`
25×	`*-un-lft-identity`
23×	`pow1` `add-exp-log` `add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`unpow-prod-down`
8×	`associate-/r*`
6×	`pow-plus` `div-exp` `prod-exp` `pow-prod-up` `cbrt-unprod` `associate-/l*` `add-log-exp`
5×	`sqr-pow`
4×	`cbrt-undiv` `div-inv` `difference-of-squares`
3×	`associate-r` `pow-prod-down`
2×	`pow2` `clear-num` `frac-2neg` `pow-sqr` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `pow-exp` `*-commutative` `frac-sub` `flip--` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

27.0ms	(* (* x x) x)
19.0ms	(/ 1.0 (* (* x x) x))
6.0ms	(/ 1.0 (pow x 5))
71.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (* (* x x) x)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* x x) x)
47.0ms	(/ 1.0 (* (* x x) x))
97.0ms	(/ 1.0 (pow x 5))
220.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (* (* x x) x)))

simplify1.7s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	2721
1	427
0	173

prune489.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch68.0ms

Steps

Iters	Range		Point
9	0.030359728269424062	9645967.64350026	446.32379712242954
2	-7.049573791614887e+27	-5.833600422647533e+27	-6.289590436010292e+27

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end0.0ms

sample846.0ms

Algorithm

intervals

Results

678.0ms

8000×

body

valid