Details

sample411.0ms

Algorithm

intervals

Results

78.0ms	48×	body	1280	valid
77.0ms	57×	body	80	nan
38.0ms	154×	body	80	valid
38.0ms	34×	body	640	valid
27.0ms	34×	body	320	valid
7.0ms	16×	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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize93.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* (/ 1.0 (tan B)) x)
6.5b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
15.4b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite186.0ms

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

Counts

4 → 243

Calls

4 calls:

5.0ms	(/ 1.0 (tan B))
16.0ms	(* (/ 1.0 (tan B)) x)
109.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
34.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series858.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1.0 (tan B))
140.0ms	(* (/ 1.0 (tan B)) x)
483.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
180.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify3.3s

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
2	3842
1	1281
0	475

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize139.0ms

Local error

Found 4 expressions with local error:

9.0b	(pow (* (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x))) (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))) (/ (- 1.0) 2.0))
16.3b	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
16.3b	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
16.3b	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow-unpow`
30×	`times-frac`
27×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
9×	`cbrt-prod` `distribute-lft-neg-in` `pow-pow` `distribute-rgt-neg-in` `pow1/3`
7×	`add-exp-log`
6×	`cbrt-div`
4×	`add-cbrt-cube` `add-log-exp`
3×	`neg-mul-1` `flip3-+` `flip-+`
2×	`pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up`
1×	`pow2` `neg-sub0` `pow-to-exp` `pow-neg` `unpow-prod-down` `pow-plus` `div-sub` `prod-exp` `distribute-frac-neg` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

37.0ms	(pow (* (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x))) (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))) (/ (- 1.0) 2.0))
11.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
10.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
10.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

326.0ms	(pow (* (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x))) (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))) (/ (- 1.0) 2.0))
614.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
176.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
201.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1689
1	587
0	206

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.1b	(/ x (tan B))
6.5b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
15.4b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

211×	`times-frac`
125×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
45×	`unpow-prod-down`
34×	`pow-unpow`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`sqr-pow`
13×	`add-cbrt-cube` `associate-/l*`
12×	`div-inv`
11×	`div-exp`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1` `cbrt-undiv`
4×	`add-log-exp`
3×	`pow-to-exp` `clear-num` `neg-mul-1` `frac-2neg` `pow-exp`
2×	`neg-sub0` `pow-neg` `div-sub` `distribute-frac-neg` `associate-/r/` `pow-sub` `associate-/l/`
1×	`pow-pow` `tan-quot`

Counts

4 → 237

Calls

4 calls:

13.0ms	(/ (sin B) F)
10.0ms	(/ x (tan B))
115.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
47.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series934.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (sin B) F)
147.0ms	(/ x (tan B))
573.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
181.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify2.9s

Counts

249 → 249

Iterations

Iter	Nodes
done	5004
2	3756
1	1190
0	453

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize94.0ms

Local error

Found 4 expressions with local error:

9.0b	(pow (* (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x))) (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))) (/ (- 1.0) 2.0))
16.3b	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
16.3b	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
16.3b	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow-unpow`
30×	`times-frac`
27×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
9×	`cbrt-prod` `distribute-lft-neg-in` `pow-pow` `distribute-rgt-neg-in` `pow1/3`
7×	`add-exp-log`
6×	`cbrt-div`
4×	`add-cbrt-cube` `add-log-exp`
3×	`neg-mul-1` `flip3-+` `flip-+`
2×	`pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up`
1×	`pow2` `neg-sub0` `pow-to-exp` `pow-neg` `unpow-prod-down` `pow-plus` `div-sub` `prod-exp` `distribute-frac-neg` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

39.0ms	(pow (* (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x))) (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))) (/ (- 1.0) 2.0))
18.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
19.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
14.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(pow (* (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x))) (cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))) (/ (- 1.0) 2.0))
160.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
130.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))
138.0ms	(cbrt (+ (+ 2.0 (* F F)) (* 2.0 x)))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1689
1	587
0	206

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes539.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 11.5b

bsearch431.0ms

Steps

Iters	Range		Point
9	12146952.384825662	1779227265816.5227	18488014.17021184
8	-1.104215127425016e+22	-3.778620241827087e+19	-7.808301409423445e+19

simplify11.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample9.9s

Algorithm

intervals

Results

3.7s	1643×	body	1280	valid
2.3s	1354×	body	640	valid
1.7s	4816×	body	80	valid
904.0ms	1579×	body	80	nan
646.0ms	719×	body	320	valid
179.0ms	346×	body	160	valid