Details

sample552.0ms

Algorithm

intervals

Results

157.0ms	161×	body	80	valid
129.0ms	53×	body	1280	valid
52.0ms	31×	body	640	valid
32.0ms	28×	body	320	valid
19.0ms	60×	body	80	nan
13.0ms	13×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.1b	(/ x (tan B))
7.4b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
19.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite179.0ms

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:

15.0ms	(/ (sin B) F)
9.0ms	(/ x (tan B))
107.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
39.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series576.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (sin B) F)
166.0ms	(/ x (tan B))
245.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
120.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.5s

Counts

218 → 218

Iterations

Iter	Nodes
done	2000
2	2000
1	912
0	375

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
0.7b	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
19.4b	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

58×	`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`
10×	`div-exp`
9×	`unpow-prod-down`
8×	`pow1`
7×	`cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
5×	`rec-exp` `1-exp`
4×	`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/` `pow-flip` `inv-pow`

Counts

4 → 123

Calls

4 calls:

11.0ms	(/ 1 (sin B))
190.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
140.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
50.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

series625.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1 (sin B))
146.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
174.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
286.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

simplify1.7s

Counts

135 → 135

Iterations

Iter	Nodes
done	2001
3	2001
2	1506
1	546
0	214

prune964.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ (/ (sin B) F) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2)))
4.0b	(/ (/ (sin B) F) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2))
19.4b	(sqrt (+ (+ 2 (* F F)) (* x 2)))
19.4b	(sqrt (+ (+ 2 (* F F)) (* x 2)))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

3989×	`times-frac`
1752×	`unpow-prod-down`
1742×	`add-sqr-sqrt`
1740×	`*-un-lft-identity` `add-cube-cbrt`
882×	`sqrt-prod`
292×	`sqr-pow`
144×	`associate-/r*`
134×	`div-inv`
73×	`add-exp-log`
57×	`div-exp`
23×	`associate-/l*`
18×	`add-cbrt-cube`
15×	`pow-to-exp` `pow-exp`
9×	`cbrt-undiv`
6×	`pow1`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 1725

Calls

4 calls:

122.0ms	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ (/ (sin B) F) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2)))
77.0ms	(/ (/ (sin B) F) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2))
37.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
21.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

series931.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ (/ (sin B) F) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2)))
162.0ms	(/ (/ (sin B) F) (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2))
85.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
459.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

simplify3.1s

Counts

1737 → 1737

Iterations

Iter	Nodes
done	2198
0	2198

prune17.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.2b	(* (/ x (sin B)) (cos B))
7.4b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
19.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
111×	`add-sqr-sqrt`
106×	`*-un-lft-identity` `add-cube-cbrt`
45×	`unpow-prod-down`
25×	`add-exp-log`
16×	`associate-/r*` `add-cbrt-cube`
15×	`sqr-pow`
13×	`associate-l`
11×	`div-exp` `div-inv`
10×	`associate-/l*`
7×	`pow1`
5×	`cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `associate-r` `pow-exp`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`pow-pow` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative`

Counts

4 → 210

Calls

4 calls:

13.0ms	(/ (sin B) F)
27.0ms	(* (/ x (sin B)) (cos B))
98.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
33.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series460.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (sin B) F)
99.0ms	(* (/ x (sin B)) (cos B))
225.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
101.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.4s

Counts

222 → 222

Iterations

Iter	Nodes
done	2000
2	2000
1	970
0	383

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes345.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.9b

bsearch590.0ms

Steps

Iters	Range		Point
8	52.608009985765236	394280.51970978006	15215.487136152646
8	-3.517512888848555e+19	-9.65375265711548e+16	-6.519456150228116e+18

simplify10.0ms

Iterations

Iter	Nodes
done	38
1	38
0	30

end0.0ms

sample13.5s

Algorithm

intervals

Results

5.3s	1681×	body	1280	valid
2.8s	1442×	body	640	valid
2.4s	4781×	body	80	valid
1.3s	700×	body	320	valid
1.1s	1697×	body	80	nan
249.0ms	304×	body	160	valid