Details

sample608.0ms

Algorithm

intervals

Results

161.0ms	52×	body	1280	valid
135.0ms	154×	body	80	valid
62.0ms	44×	body	640	valid
21.0ms	17×	body	320	valid
17.0ms	60×	body	80	nan
6.0ms	11×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin B) F)
0.3b	(* (/ 1.0 (tan B)) x)
8.1b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
18.4b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite245.0ms

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`
2×	`neg-sub0` `pow-neg` `clear-num` `frac-2neg` `div-sub` `prod-exp` `distribute-frac-neg` `associate-/r/` `cbrt-unprod` `pow-sub` `unswap-sqr` `associate-/l/`
1×	`pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `-commutative`

Counts

4 → 242

Calls

4 calls:

13.0ms	(/ (sin B) F)
29.0ms	(* (/ 1.0 (tan B)) x)
130.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
51.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series899.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (sin B) F)
109.0ms	(* (/ 1.0 (tan B)) x)
550.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
195.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify3.9s

Counts

254 → 254

Iterations

Iter	Nodes
done	5000
2	3915
1	1264
0	470

prune2.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 (tan B)) x)
0.3b	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
0.3b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
18.4b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite304.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

15.0ms	(* (/ 1.0 (tan B)) x)
152.0ms	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
80.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
51.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (/ 1.0 (tan B)) x)
551.0ms	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
493.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
206.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify2.3s

Counts

190 → 190

Iterations

Iter	Nodes
done	5000
2	2708
1	954
0	352

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 1.0 x) (tan B))
0.3b	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
0.3b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
18.4b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
68×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `add-cube-cbrt`
34×	`pow-unpow`
25×	`unpow-prod-down` `associate-l` `add-exp-log`
16×	`add-cbrt-cube`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
8×	`div-exp` `associate-/l*`
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 → 167

Calls

4 calls:

9.0ms	(/ (* 1.0 x) (tan B))
146.0ms	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
126.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
49.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (* 1.0 x) (tan B))
497.0ms	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
560.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
214.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify2.4s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	2724
1	931
0	336

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* 1.0 x) (sin B)) (cos B))
0.3b	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
0.3b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
18.4b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
71×	`add-sqr-sqrt`
59×	`*-un-lft-identity` `add-cube-cbrt`
34×	`pow-unpow`
32×	`associate-l`
29×	`add-exp-log`
25×	`unpow-prod-down`
20×	`add-cbrt-cube`
9×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in` `sqr-pow`
8×	`div-exp` `prod-exp`
7×	`associate-/l*`
6×	`associate-r` `cbrt-unprod`
5×	`unswap-sqr`
4×	`cbrt-undiv` `div-inv` `add-log-exp`
3×	`pow-to-exp` `associate-/r*` `neg-mul-1` `pow-exp`
2×	`neg-sub0` `pow-neg` `div-sub` `pow-prod-down` `associate-l/` `distribute-frac-neg` `-commutative` `pow-sub` `associate-/l/`
1×	`clear-num` `pow-pow` `frac-2neg`

Counts

4 → 172

Calls

4 calls:

30.0ms	(* (/ (* 1.0 x) (sin B)) (cos B))
127.0ms	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
118.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
46.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ (* 1.0 x) (sin B)) (cos B))
562.0ms	(* (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) F)
484.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
174.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify2.7s

Counts

184 → 184

Iterations

Iter	Nodes
done	5000
2	3048
1	963
0	346

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes591.0ms

Accuracy

98% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.3b

bsearch616.0ms

Steps

Iters	Range		Point
10	0.019618473278136022	56593606606875.23	196580.81506278712
9	-5.191765127262994e+58	-2.4005474304550297e+53	-2.5003358195053265e+53

simplify9.0ms

Iterations

Iter	Nodes
done	49
1	49
0	38

end0.0ms

sample10.3s

Algorithm

intervals

Results

4.7s	1681×	body	1280	valid
1.7s	1374×	body	640	valid
1.5s	4727×	body	80	valid
766.0ms	1635×	body	80	nan
604.0ms	358×	body	160	valid
589.0ms	721×	body	320	valid