Details

sample674.0ms

Algorithm

intervals

Results

155.0ms	51×	body	1280	valid
102.0ms	46×	body	640	valid
84.0ms	158×	body	80	valid
75.0ms	55×	body	80	nan
23.0ms	28×	body	320	valid
5.0ms	9×	body	160	valid

simplify5.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	20	850
1	42	850
2	82	810
3	144	810
4	310	810
5	812	810
6	2685	810
done	5005	810

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
5.0b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`*-un-lft-identity` `add-cube-cbrt`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube` `associate-l`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`pow-neg` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`neg-sub0` `pow-to-exp` `cbrt-undiv` `associate-/r` `pow-exp` `associate-r/` `associate-/l*` `pow-sub`
2×	`frac-times` `tan-quot` `associate-/r/` `*-commutative`
1×	`clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

9.0ms	(/ 1.0 (tan B))
28.0ms	(* x (/ 1.0 (tan B)))
193.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
55.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series850.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1.0 (tan B))
152.0ms	(* x (/ 1.0 (tan B)))
430.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
226.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.7s

Counts

167 → 167

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	306	80437
1	852	74158
2	2505	73314
done	5001	72994

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite423.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
22×	`times-frac`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`clear-num` `associate-/r` `pow-pow` `frac-2neg` `pow-prod-down` `tan-quot` `associate-r/` `associate-/r/`

Counts

4 → 108

Calls

4 calls:

27.0ms	(* x (/ 1.0 (tan B)))
229.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
77.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
83.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

165.0ms	(* x (/ 1.0 (tan B)))
346.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
416.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
167.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify3.2s

Counts

120 → 120

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	265	60561
1	687	57341
2	2272	56709
done	5002	56149

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

18.0ms	(/ (* x (cos B)) (sin B))
200.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
79.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
83.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (* x (cos B)) (sin B))
337.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
413.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
173.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.3s

Counts

108 → 108

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	238	58121
1	619	55063
2	2244	54353
done	5061	54233

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
18.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
73×	`times-frac`
59×	`*-un-lft-identity` `add-cube-cbrt`
39×	`associate-r`
30×	`pow-unpow`
25×	`unpow-prod-down` `add-exp-log`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`pow1` `sqr-pow`
7×	`div-exp` `associate-/l*`
6×	`associate-l` `prod-exp` `unswap-sqr`
5×	`div-inv`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `associate-/r*` `pow-exp`
2×	`neg-sub0` `pow-neg` `pow-prod-down` `associate-r/` `-commutative` `pow-sub` `associate-/l/`
1×	`clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `tan-quot` `associate-/r/`

Counts

4 → 174

Calls

4 calls:

196.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
30.0ms	(* x (/ 1.0 (tan B)))
149.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
49.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

512.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
183.0ms	(* x (/ 1.0 (tan B)))
450.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
200.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify3.0s

Counts

186 → 186

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	341	113923
1	932	106371
2	2753	105325
done	5000	105165

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes583.0ms

Accuracy

97.4% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.5b

bsearch359.0ms

Steps

Iters	Range		Point
5	8.722653903301618e+16	1.898020274581904e+17	9.843886119873589e+16
7	-2.4854220506534713e+34	-1.301425076383796e+32	-2.4723146878766297e+33

simplify10.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	36	1493
1	46	1493
done	46	1493

end0.0ms

sample9.9s

Algorithm

intervals

Results

3.5s	1655×	body	1280	valid
2.5s	1366×	body	640	valid
1.8s	4840×	body	80	valid
833.0ms	1638×	body	80	nan
664.0ms	709×	body	320	valid
179.0ms	344×	body	160	valid