Details

sample368.0ms

Algorithm

intervals

Results

126.0ms	51×	body	1280	valid
48.0ms	39×	body	640	valid
44.0ms	21×	body	320	valid
44.0ms	154×	body	80	valid
14.0ms	57×	body	80	nan
6.0ms	11×	body	160	valid

simplify993.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	2153
5	683
4	275
3	137
2	81
1	45
0	20

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.2b	(/ x (tan B))
6.5b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
17.8b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

203×	`times-frac`
143×	`*-un-lft-identity`
113×	`add-sqr-sqrt` `add-cube-cbrt`
60×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`distribute-lft-out` `sqr-pow`
14×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`div-inv`
11×	`div-exp`
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 → 221

Calls

4 calls:

16.0ms	(/ (sin B) F)
10.0ms	(/ x (tan B))
138.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
39.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series748.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (sin B) F)
152.0ms	(/ x (tan B))
220.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
338.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify1.5s

Counts

233 → 233

Iterations

Iter	Nodes
2	2521
1	920
0	396

prune3.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.6b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.3b	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
0.4b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
17.8b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

994×	`times-frac`
538×	`*-un-lft-identity`
444×	`add-sqr-sqrt` `add-cube-cbrt`
188×	`unpow-prod-down`
56×	`add-exp-log`
47×	`distribute-lft-out` `sqr-pow`
46×	`div-inv`
40×	`div-exp`
39×	`associate-/l*`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
6×	`pow-to-exp` `pow-exp`
5×	`pow1`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot` `associate-/l/`

Counts

4 → 536

Calls

4 calls:

5.0ms	(/ x (tan B))
118.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
103.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
46.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series836.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ x (tan B))
213.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
170.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
290.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify3.5s

Counts

548 → 548

Iterations

Iter	Nodes
1	2372
0	828

prune8.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.2b	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
0.3b	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
17.8b	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `associate-l`
18×	`times-frac`
9×	`div-exp`
7×	`pow1` `unpow-prod-down` `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`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/r/`

Counts

4 → 118

Calls

4 calls:

5.0ms	(/ x (tan B))
112.0ms	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
66.0ms	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
37.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

series779.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ x (tan B))
156.0ms	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
145.0ms	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
337.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

simplify3.4s

Counts

130 → 130

Iterations

Iter	Nodes
3	3992
2	1471
1	559
0	246

prune1.9s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (tan B) x))
0.3b	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
0.4b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
17.8b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

1060×	`times-frac`
572×	`*-un-lft-identity`
478×	`add-sqr-sqrt` `add-cube-cbrt`
188×	`unpow-prod-down`
65×	`add-exp-log`
50×	`div-inv`
47×	`distribute-lft-out` `sqr-pow`
46×	`div-exp`
39×	`associate-/l*`
29×	`associate-/r*`
23×	`add-cbrt-cube`
12×	`cbrt-undiv`
6×	`pow-to-exp` `pow1` `rec-exp` `1-exp` `pow-exp`
4×	`insert-posit16` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`pow-pow` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 584

Calls

4 calls:

6.0ms	(/ 1 (/ (tan B) x))
131.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
99.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
47.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series770.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (/ (tan B) x))
232.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
168.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
269.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify5.0s

Counts

596 → 596

Iterations

Iter	Nodes
1	2601
0	905

prune9.3s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 9.6b

regimes445.0ms

Accuracy

0% (0.6b remaining)

Error of 10.8b against oracle of 10.2b and baseline of 10.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	23
1	23
0	18

end0.0ms

sample13.9s

Algorithm

intervals

Results

5.1s	1662×	body	1280	valid
3.6s	1442×	body	640	valid
2.5s	4724×	body	80	valid
1.4s	719×	body	320	valid
652.0ms	1638×	body	80	nan
301.0ms	333×	body	160	valid