Details

sample358.0ms

Algorithm

intervals

Results

113.0ms	59×	body	640	valid
76.0ms	52×	body	1280	valid
34.0ms	139×	body	80	valid
15.0ms	16×	body	320	valid
13.0ms	63×	body	80	nan
5.0ms	10×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.3b

localize50.0ms

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))))
14.4b	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

rewrite278.0ms

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))
90.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
87.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
78.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (* x 1.0) (tan B))
402.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
364.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
232.0ms	(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

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

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)))
14.4b	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

10.0ms	(/ (* x 1.0) (tan B))
73.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))))
223.0ms	(* (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:

193.0ms	(/ (* x 1.0) (tan B))
477.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))))
392.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0)))
186.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))

simplify3.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	3210
1	655
0	250

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))) F)
0.3b	(/ 1 (/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))) F))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0)))
14.4b	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
45×	`times-frac`
38×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
26×	`div-exp`
20×	`add-cbrt-cube`
15×	`prod-exp`
13×	`pow-unpow`
10×	`associate-/r*`
7×	`cbrt-undiv` `unpow-prod-down` `associate-r` `div-inv`
6×	`pow-to-exp` `pow1` `pow-exp`
5×	`rec-exp` `1-exp`
4×	`associate-/l*` `add-log-exp`
3×	`associate-l` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

68.0ms	(/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))) F)
90.0ms	(/ 1 (/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))) F))
198.0ms	(* (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))

series1.4s

Counts

4 → 12

Calls

4 calls:

280.0ms	(/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))) F)
577.0ms	(/ 1 (/ (* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))) F))
406.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0)))
169.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (/ 1.0 2.0))

simplify3.6s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
2	3908
1	755
0	275

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.3b	(* (/ (/ 1 (sin B)) (pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0))) F)
0.4b	(/ (/ 1 (sin B)) (pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0)))
14.4b	(pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

388×	`times-frac`
248×	`*-un-lft-identity`
218×	`add-sqr-sqrt`
189×	`add-cube-cbrt`
115×	`unpow-prod-down`
108×	`associate-l`
70×	`add-exp-log`
38×	`div-exp`
31×	`sqr-pow`
28×	`distribute-lft-out`
23×	`add-cbrt-cube`
21×	`div-inv`
14×	`prod-exp` `associate-/l*`
13×	`pow-unpow`
11×	`associate-/r*`
10×	`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-r`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `associate-/r/` `-commutative` `associate-/l/`

Counts

4 → 347

Calls

4 calls:

12.0ms	(/ (* x 1.0) (tan B))
168.0ms	(* (/ (/ 1 (sin B)) (pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0))) F)
64.0ms	(/ (/ 1 (sin B)) (pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0)))
28.0ms	(pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (* x 1.0) (tan B))
563.0ms	(* (/ (/ 1 (sin B)) (pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0))) F)
1.1s	(/ (/ 1 (sin B)) (pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0)))
176.0ms	(pow (+ 2.0 (+ (* F F) (* x 2.0))) (/ 1.0 2.0))

simplify1.4s

Counts

359 → 359

Iterations

Iter	Nodes
done	5001
1	1370
0	504

prune3.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes651.0ms

Accuracy

97.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.5b

bsearch297.0ms

Steps

Iters	Range		Point
8	7.830610238325062	15275.506209221001	12308.793163324062
3	-2.330089513821311e+99	-1.8288702712188364e+99	-2.0169077047552913e+99

simplify42.0ms

Iterations

Iter	Nodes
done	58
1	58
0	45

end0.0ms

sample9.9s

Algorithm

intervals

Results

3.7s	1698×	body	1280	valid
2.6s	1407×	body	640	valid
1.6s	4690×	body	80	valid
638.0ms	711×	body	320	valid
386.0ms	1650×	body	80	nan
258.0ms	351×	body	160	valid