Details

sample711.0ms

Algorithm

intervals

Results

126.0ms	59×	body	1280	valid
99.0ms	48×	body	640	valid
97.0ms	21×	body	320	valid
46.0ms	144×	body	80	valid
15.0ms	58×	body	80	nan
6.0ms	10×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
0.4b	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
16.4b	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

rewrite336.0ms

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:

9.0ms	(/ (* x 1.0) (tan B))
91.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
137.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
76.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (* x 1.0) (tan B))
426.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
339.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
244.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

simplify759.0ms

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
1	1326
0	474

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(* F (* (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))))
0.4b	(* (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0))))
16.4b	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log`
50×	`add-sqr-sqrt`
38×	`prod-exp`
36×	`times-frac`
35×	`*-un-lft-identity`
32×	`add-cube-cbrt`
30×	`pow-unpow`
23×	`add-cbrt-cube`
16×	`associate-l`
14×	`div-exp`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-*r/`
9×	`pow-to-exp` `unpow-prod-down` `pow-exp` `unswap-sqr`
8×	`associate-r` `cbrt-unprod`
7×	`pow1` `pow-neg`
6×	`rec-exp` `1-exp`
5×	`neg-sub0` `pow-sub` `sqr-pow`
4×	`frac-times` `cbrt-undiv` `div-inv` `add-log-exp`
3×	`associate-/r*`
2×	`associate-l/` `un-div-inv` `-commutative`
1×	`clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `tan-quot` `associate-/r/` `associate-/l*`

Counts

4 → 160

Calls

4 calls:

8.0ms	(/ (* x 1.0) (tan B))
169.0ms	(* F (* (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))))
228.0ms	(* (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0))))
49.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

series3.0s

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (* x 1.0) (tan B))
429.0ms	(* F (* (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))))
1.9s	(* (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0))))
479.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

simplify2.3s

Counts

172 → 172

Iterations

Iter	Nodes
done	5001
2	4883
1	1069
0	369

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(* F (/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
0.3b	(/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
16.4b	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

rewrite870.0ms

Algorithm

rewrite-expression-head

Rules

344×	`times-frac`
204×	`add-sqr-sqrt`
178×	`*-un-lft-identity`
175×	`add-cube-cbrt`
95×	`associate-r`
87×	`unpow-prod-down`
70×	`add-exp-log`
38×	`div-exp`
31×	`sqr-pow`
23×	`add-cbrt-cube`
19×	`div-inv`
14×	`prod-exp` `associate-/l*`
13×	`pow-unpow`
10×	`associate-/r*` `unswap-sqr`
9×	`pow-to-exp` `pow-exp`
8×	`cbrt-undiv`
7×	`pow1`
6×	`rec-exp` `1-exp`
4×	`cbrt-unprod` `add-log-exp`
3×	`associate-l`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `pow-prod-down` `tan-quot` `associate-r/` `associate-/r/` `-commutative` `associate-/l/`

Counts

4 → 319

Calls

4 calls:

8.0ms	(/ (* x 1.0) (tan B))
264.0ms	(* F (/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
538.0ms	(/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
45.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

series3.1s

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (* x 1.0) (tan B))
482.0ms	(* F (/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
2.0s	(/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
435.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

simplify904.0ms

Counts

331 → 331

Iterations

Iter	Nodes
done	5000
1	1590
0	558

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
0.3b	(* F (/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
0.3b	(/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
16.4b	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

344×	`times-frac`
207×	`add-sqr-sqrt`
179×	`*-un-lft-identity`
176×	`add-cube-cbrt`
98×	`associate-r`
87×	`unpow-prod-down`
74×	`add-exp-log`
38×	`div-exp`
31×	`sqr-pow`
27×	`add-cbrt-cube`
19×	`div-inv`
17×	`prod-exp`
13×	`pow-unpow` `associate-/l*`
11×	`unswap-sqr`
10×	`associate-l`
9×	`pow-to-exp` `pow1` `pow-exp`
8×	`cbrt-undiv`
7×	`associate-/r*` `cbrt-unprod`
6×	`rec-exp` `1-exp`
4×	`add-log-exp`
2×	`pow-prod-down` `*-commutative`
1×	`clear-num` `pow-pow` `frac-2neg` `associate-l/` `associate-r/` `associate-/l/`

Counts

4 → 324

Calls

4 calls:

37.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
205.0ms	(* F (/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
87.0ms	(/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
48.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

series3.1s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
508.0ms	(* F (/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
2.0s	(/ (/ 1 (sin B)) (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
436.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

simplify1.1s

Counts

336 → 336

Iterations

Iter	Nodes
done	5000
1	1632
0	568

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes435.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.8b

bsearch659.0ms

Steps

Iters	Range		Point
10	27750.67288899747	6.552973658657202e+20	355522549.6141795
10	-3813544086202141.0	-769416.9694931002	-280062729.4583086

simplify14.0ms

Iterations

Iter	Nodes
done	42
1	42
0	33

end0.0ms

sample10.6s

Algorithm

intervals

Results

3.6s	1700×	body	1280	valid
2.6s	1414×	body	640	valid
1.5s	4731×	body	80	valid
1.1s	680×	body	320	valid
926.0ms	1608×	body	80	nan
225.0ms	328×	body	160	valid