Details

sample386.0ms

Algorithm

intervals

Results

52.0ms	50×	body	1280	valid
35.0ms	55×	body	640	valid
20.0ms	148×	body	80	valid
8.0ms	18×	body	320	valid
8.0ms	60×	body	80	nan
3.0ms	11×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	80	26
3	146	26
4	317	26
5	811	26
6	3228	26
done	5000	26

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
5.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite127.0ms

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))
10.0ms	(* x (/ 1.0 (tan B)))
82.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ F (sin B))
110.0ms	(* x (/ 1.0 (tan B)))
289.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
156.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.2s

Counts

166 → 166

Iterations

Useful iterations: 2 (440.0ms)

Iter	Nodes	Cost
0	303	2726
1	766	2555
2	2656	2401
done	5000	2401

prune611.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(* x (/ 1.0 (tan B)))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
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×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 108

Calls

4 calls:

21.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
73.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
8.0ms	(* x (/ 1.0 (tan B)))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series777.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
241.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
109.0ms	(* x (/ 1.0 (tan B)))
131.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify847.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (300.0ms)

Iter	Nodes	Cost
0	265	2158
1	654	2039
2	2392	1853
done	5001	1853

prune423.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

3.0ms	(/ (* x 1.0) (tan B))
23.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
72.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
21.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series781.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* x 1.0) (tan B))
296.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
244.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify784.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (274.0ms)

Iter	Nodes	Cost
0	250	2060
1	608	1951
2	2183	1765
done	5001	1765

prune390.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num`
1×	`pow-pow` `*-commutative`

Counts

4 → 96

Calls

4 calls:

4.0ms	(/ (* x (cos B)) (sin B))
22.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
73.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
21.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series776.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (* x (cos B)) (sin B))
299.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
248.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
132.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify721.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (241.0ms)

Iter	Nodes	Cost
0	238	2075
1	584	1966
2	2143	1774
done	5001	1774

prune363.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes191.0ms

Accuracy

96.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 10.8b

bsearch255.0ms

Steps

Iters	Range		Point
7	2.439402138504368e+81	2.9303186768988254e+83	2.4906907027944938e+81
9	-2.6381962027638094e+36	-3.072127055585697e+28	-2.980655836879585e+29

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	73
1	41	73
done	41	73

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	1680×	body	1280	valid
960.0ms	1485×	body	640	valid
655.0ms	4748×	body	80	valid
299.0ms	695×	body	320	valid
172.0ms	1629×	body	80	nan
109.0ms	329×	body	160	valid