Details

sample24.0ms

Algorithm

intervals

Results

15.0ms

459×

body

valid

simplify48.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
5	45
4	42
3	35
2	23
1	13
0	7

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.0b	(+ (* x x) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
3×	`add-sqr-sqrt` `pow1` `+-commutative` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `flip-+` `insert-posit16`
2×	`associate-+l+`

Counts

3 → 41

Calls

3 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* y y))
16.0ms	(+ (* x x) (* y y))
196.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series162.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ (+ (* x x) (* y y)) (* y y))
36.0ms	(+ (* x x) (* y y))
66.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify1.3s

Counts

50 → 50

Iterations

Iter	Nodes
done	5005
2	919
1	230
0	73

prune187.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
0.2b	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
5.8b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
5.8b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-log-exp`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`sum-log` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`frac-times` `insert-posit16` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `associate-+l+` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 105

Calls

4 calls:

149.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
643.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
160.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
139.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))
56.0ms	(* (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))) (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))))
68.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
87.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify3.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5008
3	4772
2	797
1	262
0	108

prune387.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
5.8b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
5.8b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
5.8b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite959.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
52×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1` `sqrt-div`
19×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-l/` `associate-r/`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 132

Calls

4 calls:

550.0ms	(* (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
131.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
145.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
130.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))) (sqrt (sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))))
86.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
88.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
62.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify2.1s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
3	2178
2	557
1	239
0	118

prune557.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

5.8b	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.3b	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.3b	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
6.3b	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

162.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
81.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
80.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
102.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

series814.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
434.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
150.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))
158.0ms	(cbrt (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))

simplify1.7s

Counts

70 → 70

Iterations

Iter	Nodes
done	5010
3	1581
2	415
1	160
0	77

prune621.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes302.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	7

end0.0ms

sample1.0s

Algorithm

intervals

Results

782.0ms

14092×

body

valid