Details

sample407.0ms

Algorithm

intervals

Results

64.0ms	63×	body	1280	valid
38.0ms	58×	body	640	valid
18.0ms	132×	body	80	valid
8.0ms	17×	body	320	valid
6.0ms	42×	body	80	nan
3.0ms	12×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	80	26
3	146	26
4	325	26
5	860	26
6	2806	26
done	5000	26

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
6.2b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
21.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 154

Calls

4 calls:

2.0ms	(/ F (sin B))
9.0ms	(* x (/ 1.0 (tan B)))
89.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
28.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ F (sin B))
115.0ms	(* x (/ 1.0 (tan B)))
291.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
158.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify922.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (379.0ms)

Iter	Nodes	Cost
0	303	2726
1	766	2555
2	2100	2401
done	5000	2401

prune658.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
21.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

33.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
82.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
9.0ms	(* x (/ 1.0 (tan B)))
26.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series825.0ms

Counts

4 → 12

Calls

4 calls:

358.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
209.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
115.0ms	(* x (/ 1.0 (tan B)))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify878.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (350.0ms)

Iter	Nodes	Cost
0	285	2554
1	722	2386
2	2033	2189
done	5000	2189

prune537.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
21.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

4.0ms	(/ (* x 1.0) (tan B))
33.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
78.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
29.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series834.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* x 1.0) (tan B))
358.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
214.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
152.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify801.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (331.0ms)

Iter	Nodes	Cost
0	270	2456
1	675	2298
2	1995	2101
done	5000	2101

prune510.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
21.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
112×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`unpow-prod-down`
29×	`associate-/l*`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp`
8×	`div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 214

Calls

4 calls:

4.0ms	(/ (* x 1.0) (tan B))
38.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
66.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series828.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (* x 1.0) (tan B))
235.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
357.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
129.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.1s

Counts

226 → 226

Iterations

Useful iterations: 2 (579.0ms)

Iter	Nodes	Cost
0	420	6265
1	990	6030
2	2812	5818
done	5000	5818

prune979.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes145.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch277.0ms

Steps

Iters	Range		Point
10	0.00016167321766412214	3568380.5266111037	1829504.7016831513
7	-9.425219211724608e+95	-1.5545673558437717e+94	-2.1024600832345152e+95

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	70
1	45	70
2	51	70
done	51	70

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1659×	body	1280	valid
933.0ms	1440×	body	640	valid
673.0ms	4757×	body	80	valid
294.0ms	659×	body	320	valid
169.0ms	1589×	body	80	nan
119.0ms	369×	body	160	valid