Details

sample544.0ms

Algorithm

intervals

Results

119.0ms	55×	body	1280	valid
93.0ms	37×	body	640	valid
59.0ms	19×	body	320	valid
56.0ms	155×	body	80	valid
38.0ms	17×	body	160	valid
18.0ms	61×	body	80	nan

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2007
7	2007
6	1403
5	705
4	360
3	169
2	91
1	46
0	20

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.6b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.1b	(/ x (tan B))
5.6b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
14.1b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

181×	`times-frac`
106×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
45×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`sqr-pow`
13×	`add-cbrt-cube` `associate-/l*`
11×	`div-exp` `div-inv`
5×	`pow1` `cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `clear-num` `frac-2neg` `pow-exp`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot`

Counts

4 → 206

Calls

4 calls:

7.0ms	(/ (sin B) F)
5.0ms	(/ x (tan B))
89.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
22.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series574.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (sin B) F)
138.0ms	(/ x (tan B))
253.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
127.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.2s

Counts

218 → 218

Iterations

Iter	Nodes
done	2000
2	2000
1	912
0	375

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (sin B)) (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F)))
0.4b	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F))
14.1b	(sqrt (+ (+ 2 (* F F)) (* x 2)))
14.1b	(sqrt (+ (+ 2 (* F F)) (* x 2)))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

631×	`times-frac`
491×	`add-sqr-sqrt`
275×	`*-un-lft-identity`
255×	`add-cube-cbrt`
236×	`unpow-prod-down`
201×	`add-exp-log`
135×	`associate-r`
129×	`div-exp`
124×	`sqrt-prod`
65×	`unswap-sqr`
58×	`sqr-pow`
52×	`prod-exp`
34×	`associate-l`
33×	`pow-to-exp` `pow-exp`
30×	`add-cbrt-cube`
24×	`div-inv`
15×	`rec-exp` `1-exp`
13×	`associate-/r*`
12×	`cbrt-undiv`
10×	`associate-/l*`
8×	`pow1`
6×	`cbrt-unprod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip-+`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 516

Calls

4 calls:

166.0ms	(* (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (sin B)) (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F)))
78.0ms	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F))
35.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
23.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (sin B)) (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F)))
124.0ms	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F))
87.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
86.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

simplify1.6s

Counts

528 → 528

Iterations

Iter	Nodes
done	2000
1	2000
0	615

prune3.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))))
14.1b	(sqrt (+ (+ 2 (* F F)) (* x 2)))
14.1b	(sqrt (+ (+ 2 (* F F)) (* x 2)))
14.1b	(sqrt (+ (+ 2 (* F F)) (* x 2)))

rewrite203.0ms

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:

133.0ms	(* (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))))
14.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
24.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
28.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))))
64.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
63.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
70.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

simplify998.0ms

Counts

144 → 144

Iterations

Iter	Nodes
done	2002
3	2002
2	689
1	271
0	126

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))))
14.1b	(sqrt (+ (+ 2 (* F F)) (* x 2)))
14.1b	(sqrt (+ (+ 2 (* F F)) (* x 2)))
14.1b	(sqrt (+ (+ 2 (* F F)) (* x 2)))

rewrite225.0ms

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:

125.0ms	(* (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))))
29.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
29.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
38.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))) (sqrt (sqrt (+ (+ 2 (* F F)) (* x 2)))))
76.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
91.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
91.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

simplify1.2s

Counts

144 → 144

Iterations

Iter	Nodes
done	2002
3	2002
2	689
1	271
0	126

prune1.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.0b

regimes626.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch518.0ms

Steps

Iters	Range		Point
8	232.09055164250086	657359.5389414565	60130.553479946095
6	-8748.371804340544	-1395.4681145621753	-8575.24190677927

simplify11.0ms

Iterations

Iter	Nodes
done	42
1	42
0	36

end0.0ms

sample13.6s

Algorithm

intervals

Results

4.7s	1648×	body	1280	valid
3.5s	1385×	body	640	valid
2.5s	4834×	body	80	valid
959.0ms	360×	body	160	valid
897.0ms	690×	body	320	valid
726.0ms	1778×	body	80	nan