Details

sample1.0s

Algorithm

intervals

Results

588.0ms	54×	body	1280	valid
62.0ms	38×	body	640	valid
49.0ms	157×	body	80	valid
17.0ms	54×	body	80	nan
13.0ms	14×	body	320	valid
11.0ms	16×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1702
4	362
3	152
2	83
1	42
0	20

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.3b

localize64.0ms

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

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 243

Calls

4 calls:

16.0ms	(/ (* x 1.0) (tan B))
110.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
113.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
42.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (* x 1.0) (tan B))
406.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
323.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
212.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
1	1326
0	474

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

207×	`times-frac`
125×	`add-sqr-sqrt`
123×	`*-un-lft-identity` `add-cube-cbrt`
51×	`unpow-prod-down`
34×	`associate-/r*`
30×	`pow-unpow`
29×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`sqr-pow`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`div-exp`
11×	`associate-/r/`
9×	`div-inv`
7×	`pow1` `associate-l`
6×	`neg-sub0` `cbrt-undiv` `pow-neg` `associate-/l*` `pow-sub`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-exp`
2×	`clear-num` `frac-2neg`
1×	`neg-mul-1` `pow-pow` `pow-prod-down` `associate-l/` `-commutative` `unswap-sqr`

Counts

4 → 248

Calls

4 calls:

28.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
132.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
98.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
46.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
424.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
329.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
218.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

simplify2.0s

Counts

260 → 260

Iterations

Iter	Nodes
done	5001
1	1371
0	484

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize116.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

15042×	`times-frac`
5994×	`add-sqr-sqrt`
5992×	`*-un-lft-identity` `add-cube-cbrt`
4122×	`unpow-prod-down`
2067×	`sqrt-prod`
687×	`sqr-pow`
497×	`associate-/r/`
268×	`div-inv`
229×	`neg-sub0` `pow-neg` `pow-sub`
174×	`add-exp-log`
157×	`div-exp`
116×	`associate-/l*`
72×	`associate-/r*`
30×	`add-cbrt-cube`
26×	`pow-to-exp` `pow-exp`
18×	`cbrt-undiv`
15×	`rec-exp` `1-exp`
6×	`pow1`
4×	`sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`associate-/l/`

Counts

4 → 4479

Calls

4 calls:

89.0ms	(/ F (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* x 2.0))) (- (/ 1.0 2.0)))))
422.0ms	(/ (/ F (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* x 2.0))) (- (/ 1.0 2.0))))) (/ (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* x 2.0))) (- (/ 1.0 2.0)))))
52.0ms	(sqrt (+ (+ (* F F) 2.0) (* x 2.0)))
36.0ms	(sqrt (+ (+ (* F F) 2.0) (* x 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

401.0ms	(/ F (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* x 2.0))) (- (/ 1.0 2.0)))))
571.0ms	(/ (/ F (/ 1 (pow (sqrt (+ (+ (* F F) 2.0) (* x 2.0))) (- (/ 1.0 2.0))))) (/ (sin B) (pow (sqrt (+ (+ (* F F) 2.0) (* x 2.0))) (- (/ 1.0 2.0)))))
89.0ms	(sqrt (+ (+ (* F F) 2.0) (* x 2.0)))
115.0ms	(sqrt (+ (+ (* F F) 2.0) (* x 2.0)))

simplify8.6s

Counts

4491 → 4491

Iterations

Iter	Nodes
done	5683
0	5683

prune53.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

237×	`times-frac`
136×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
51×	`unpow-prod-down`
41×	`associate-/r*` `add-exp-log`
30×	`pow-unpow`
22×	`div-exp`
20×	`add-cbrt-cube`
17×	`sqr-pow`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `div-inv`
12×	`associate-/r/`
9×	`cbrt-undiv` `associate-/l*`
6×	`neg-sub0` `pow1` `pow-neg` `pow-sub`
4×	`add-log-exp`
3×	`pow-to-exp` `rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-exp` `prod-exp`
1×	`neg-mul-1` `pow-pow` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 277

Calls

4 calls:

98.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
24.0ms	(/ 1 (/ (tan B) (* x 1.0)))
124.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
57.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

450.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
114.0ms	(/ 1 (/ (tan B) (* x 1.0)))
377.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
223.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

simplify1.9s

Counts

289 → 289

Iterations

Iter	Nodes
done	5001
1	1488
0	533

prune2.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes581.0ms

Accuracy

98% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.4b

bsearch391.0ms

Steps

Iters	Range		Point
6	0.6893947674185039	4.9803363081918155	4.890764603747723
8	-81829953.9245951	-84463.33967257517	-45183016.35048651

simplify33.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample9.9s

Algorithm

intervals

Results

3.5s	1709×	body	1280	valid
2.1s	4667×	body	80	valid
2.1s	1420×	body	640	valid
1.1s	710×	body	320	valid
455.0ms	1640×	body	80	nan
183.0ms	354×	body	160	valid