Details

sample542.0ms

Algorithm

intervals

Results

208.0ms	50×	body	1280	valid
104.0ms	54×	body	640	valid
68.0ms	146×	body	80	valid
38.0ms	28×	body	320	valid
17.0ms	44×	body	80	nan
7.0ms	8×	body	160	valid

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin B) F)
0.2b	(/ x (tan B))
5.9b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
19.2b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite144.0ms

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:

14.0ms	(/ (sin B) F)
7.0ms	(/ x (tan B))
76.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
42.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series561.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (sin B) F)
154.0ms	(/ x (tan B))
248.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
122.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.3s

Counts

218 → 218

Iterations

Iter	Nodes
done	2000
2	2000
1	912
0	375

prune3.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.2b	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
0.8b	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
19.2b	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-l`
20×	`add-cbrt-cube`
18×	`times-frac`
9×	`unpow-prod-down` `div-exp`
7×	`pow1` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `associate-r` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv` `distribute-lft-out`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/r/`

Counts

4 → 120

Calls

4 calls:

10.0ms	(/ x (tan B))
120.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
174.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
47.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

series777.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ x (tan B))
161.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
160.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
298.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

simplify1.4s

Counts

132 → 132

Iterations

Iter	Nodes
done	2004
3	2004
2	1522
1	594
0	246

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2) (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2))
0.8b	(* (/ 1 (sin B)) (* (* (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2) (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2)) F))
19.2b	(sqrt (+ (+ (* x 2) (* F F)) 2))
19.2b	(sqrt (+ (+ (* x 2) (* F F)) 2))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

167×	`add-exp-log`
129×	`prod-exp`
55×	`add-sqr-sqrt`
52×	`unpow-prod-down`
43×	`*-un-lft-identity`
38×	`sqrt-prod`
30×	`pow-to-exp` `pow-exp`
27×	`add-cbrt-cube`
25×	`add-cube-cbrt`
24×	`associate-l`
22×	`div-exp`
16×	`unswap-sqr`
15×	`swap-sqr`
13×	`cbrt-unprod`
12×	`associate-r` `sqr-pow`
11×	`pow1` `rec-exp` `1-exp`
9×	`times-frac`
8×	`distribute-lft-out`
4×	`sqrt-div` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `*-commutative` `flip-+`
1×	`pow2` `associate-*l/` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 186

Calls

4 calls:

325.0ms	(* (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2) (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2))
885.0ms	(* (/ 1 (sin B)) (* (* (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2) (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2)) F))
30.0ms	(sqrt (+ (+ (* x 2) (* F F)) 2))
54.0ms	(sqrt (+ (+ (* x 2) (* F F)) 2))

series558.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2) (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2))
143.0ms	(* (/ 1 (sin B)) (* (* (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2) (pow (sqrt (+ (+ (* x 2) (* F F)) 2)) -1/2)) F))
159.0ms	(sqrt (+ (+ (* x 2) (* F F)) 2))
166.0ms	(sqrt (+ (+ (* x 2) (* F F)) 2))

simplify1.5s

Counts

198 → 198

Iterations

Iter	Nodes
done	2018
3	2018
2	1854
1	612
0	236

prune3.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
0.3b	(/ 1 (/ (tan B) x))
0.8b	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
19.2b	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
65×	`add-exp-log`
63×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
58×	`add-cube-cbrt`
31×	`prod-exp`
23×	`add-cbrt-cube`
21×	`associate-l`
15×	`div-exp`
13×	`associate-/r*`
9×	`unpow-prod-down`
8×	`pow1`
7×	`cbrt-unprod`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `div-inv`
5×	`cbrt-undiv`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `distribute-lft-out`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 168

Calls

4 calls:

179.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
13.0ms	(/ 1 (/ (tan B) x))
167.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
41.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

series759.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
115.0ms	(/ 1 (/ (tan B) x))
180.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
312.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

simplify1.2s

Counts

180 → 180

Iterations

Iter	Nodes
done	2001
2	2001
1	839
0	327

prune2.9s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes494.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 11.0b

bsearch512.0ms

Steps

Iters	Range		Point
7	4.6567578334119426e+47	7.766438156400323e+48	4.714618311488689e+47
7	-6.678445953832143e+18	-6.391269873263887e+16	-1.4806380137470963e+18

simplify9.0ms

Iterations

Iter	Nodes
done	40
1	40
0	32

end0.0ms

sample14.1s

Algorithm

intervals

Results

5.2s	1575×	body	1280	valid
3.6s	1430×	body	640	valid
2.9s	4800×	body	80	valid
1.0s	722×	body	320	valid
618.0ms	1614×	body	80	nan
470.0ms	374×	body	160	valid