Details

sample686.0ms

Algorithm

intervals

Results

194.0ms	54×	body	1280	valid
176.0ms	157×	body	80	valid
62.0ms	38×	body	640	valid
44.0ms	16×	body	160	valid
19.0ms	54×	body	80	nan
17.0ms	14×	body	320	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
6	2685
5	812
4	310
3	144
2	82
1	42
0	20

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* (/ 1.0 (tan B)) x)
6.9b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
16.2b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

212×	`times-frac`
130×	`add-sqr-sqrt`
125×	`*-un-lft-identity` `add-cube-cbrt`
45×	`unpow-prod-down`
34×	`pow-unpow`
25×	`add-exp-log`
16×	`associate-/r*` `add-cbrt-cube`
15×	`sqr-pow`
14×	`associate-l`
12×	`div-inv`
11×	`div-exp`
10×	`associate-/l*`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`pow1`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`pow-to-exp` `neg-mul-1` `associate-r` `pow-exp` `associate-/r/`
2×	`neg-sub0` `pow-neg` `clear-num` `frac-2neg` `div-sub` `prod-exp` `tan-quot` `distribute-frac-neg` `cbrt-unprod` `pow-sub` `unswap-sqr` `associate-/l/`
1×	`pow-pow` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 243

Calls

4 calls:

9.0ms	(/ 1.0 (tan B))
25.0ms	(* (/ 1.0 (tan B)) x)
67.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
36.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series921.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 1.0 (tan B))
159.0ms	(* (/ 1.0 (tan B)) x)
486.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
217.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify3.1s

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
2	3842
1	1281
0	475

prune2.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F)
0.3b	(* (/ 1.0 (tan B)) x)
0.4b	(* (/ 1 (sin B)) (* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F))
16.2b	(pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0)))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
38×	`add-cube-cbrt`
37×	`times-frac`
35×	`associate-l`
33×	`prod-exp`
30×	`pow-unpow`
23×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`pow1` `unpow-prod-down` `div-exp` `cbrt-unprod`
8×	`associate-*l/`
7×	`associate-r`
6×	`pow-to-exp` `pow-exp`
5×	`unswap-sqr`
4×	`neg-sub0` `rec-exp` `pow-neg` `1-exp` `div-inv` `pow-sub` `add-log-exp`
3×	`cbrt-undiv` `*-commutative` `sqr-pow`
2×	`frac-times` `pow-prod-down` `associate-*r/` `distribute-lft-out`
1×	`neg-mul-1` `pow-pow` `tan-quot` `associate-/r/`

Counts

4 → 156

Calls

4 calls:

129.0ms	(* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F)
20.0ms	(* (/ 1.0 (tan B)) x)
146.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F))
48.0ms	(pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

303.0ms	(* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F)
124.0ms	(* (/ 1.0 (tan B)) x)
487.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F))
239.0ms	(pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0)))

simplify2.3s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	2636
1	917
0	323

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1.0 x) (tan B))
0.2b	(* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F)
0.4b	(* (/ 1 (sin B)) (* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F))
16.2b	(pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0)))

rewrite382.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
37×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
32×	`prod-exp` `add-cube-cbrt`
30×	`pow-unpow` `times-frac`
23×	`add-cbrt-cube`
21×	`associate-l`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`div-exp`
9×	`unpow-prod-down`
8×	`cbrt-unprod`
7×	`pow1` `associate-*l/`
6×	`pow-to-exp` `pow-exp`
4×	`neg-sub0` `cbrt-undiv` `rec-exp` `pow-neg` `1-exp` `associate-r` `div-inv` `pow-sub` `add-log-exp`
3×	`associate-/r*` `unswap-sqr` `sqr-pow`
2×	`frac-times` `associate-r/` `-commutative` `distribute-lft-out`
1×	`clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `tan-quot` `associate-/r/` `associate-/l*`

Counts

4 → 145

Calls

4 calls:

9.0ms	(/ (* 1.0 x) (tan B))
168.0ms	(* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F)
152.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F))
48.0ms	(pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (* 1.0 x) (tan B))
318.0ms	(* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F)
548.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0))) F))
203.0ms	(pow (+ (+ (* F F) (* x 2.0)) 2.0) (- (/ 1.0 2.0)))

simplify2.5s

Counts

157 → 157

Iterations

Iter	Nodes
done	5002
2	2782
1	889
0	307

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1.0 x) (tan B))
0.3b	(* (/ (pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0)) (sin B)) F)
0.3b	(/ (pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0)) (sin B))
16.2b	(pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
76×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
34×	`pow-unpow`
33×	`unpow-prod-down`
28×	`associate-l`
25×	`add-exp-log`
16×	`add-cbrt-cube`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/l*` `sqr-pow`
8×	`div-exp` `distribute-lft-out`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp`
4×	`cbrt-undiv` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `neg-mul-1` `associate-r` `pow-exp` `cbrt-unprod`
2×	`neg-sub0` `pow-neg` `clear-num` `frac-2neg` `div-sub` `distribute-frac-neg` `pow-sub` `associate-/l/`
1×	`pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `associate-/r/` `-commutative`

Counts

4 → 175

Calls

4 calls:

16.0ms	(/ (* 1.0 x) (tan B))
128.0ms	(* (/ (pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0)) (sin B)) F)
111.0ms	(/ (pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0)) (sin B))
41.0ms	(pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0))

series4.1s

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (* 1.0 x) (tan B))
1.7s	(* (/ (pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0)) (sin B)) F)
1.7s	(/ (pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0)) (sin B))
450.0ms	(pow (+ 2.0 (+ (* x 2.0) (* F F))) (/ (- 1.0) 2.0))

simplify2.7s

Counts

187 → 187

Iterations

Iter	Nodes
done	5003
2	3392
1	1085
0	392

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes443.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.4b

bsearch375.0ms

Steps

Iters	Range		Point
6	0.6893947674185039	4.9803363081918155	4.890764603747723
8	-81829953.9245951	-84463.33967257517	-2914735.2818922754

simplify12.0ms

Iterations

Iter	Nodes
done	52
1	52
0	40

end0.0ms

sample9.9s

Algorithm

intervals

Results

4.3s	1709×	body	1280	valid
2.3s	1420×	body	640	valid
1.7s	4667×	body	80	valid
613.0ms	710×	body	320	valid
437.0ms	1640×	body	80	nan
245.0ms	354×	body	160	valid