Details

sample139.0ms

Algorithm

intervals

Results

46.0ms	86×	body	1280	valid
29.0ms	66×	body	640	valid
24.0ms	284×	body	80	valid
8.0ms	30×	body	320	valid
3.0ms	15×	body	160	valid

simplify214.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	19
1	25	13
2	49	13
3	76	13
4	95	13
5	111	13
6	126	13
7	142	13
done	142	13

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 168

Calls

4 calls:

53.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
62.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
23.0ms	(/ (cos th) (sqrt 2.0))
22.0ms	(/ (cos th) (sqrt 2.0))

series455.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
130.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
78.0ms	(/ (cos th) (sqrt 2.0))
90.0ms	(/ (cos th) (sqrt 2.0))

simplify2.0s

Counts

180 → 180

Iterations

Useful iterations: 2 (555.0ms)

Iter	Nodes	Cost
0	181	2118
1	541	2012
2	2848	1832
done	5001	1832

prune856.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
0.2b	(/ (pow a2 2) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
121×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
77×	`sqrt-prod`
53×	`associate-r`
41×	`unpow-prod-down`
33×	`add-exp-log`
25×	`associate-l` `add-cbrt-cube`
15×	`unpow2` `sqr-pow`
12×	`associate-/r*` `unswap-sqr`
11×	`pow1` `associate-/l*`
10×	`prod-exp`
9×	`div-exp`
8×	`cbrt-unprod`
5×	`cbrt-undiv`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative`
1×	`associate-r/` `associate-l/`

Counts

4 → 240

Calls

4 calls:

70.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
21.0ms	(/ (pow a2 2) (sqrt 2.0))
76.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
21.0ms	(/ (cos th) (sqrt 2.0))

series533.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
97.0ms	(/ (pow a2 2) (sqrt 2.0))
156.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
95.0ms	(/ (cos th) (sqrt 2.0))

simplify567.0ms

Counts

252 → 252

Iterations

Useful iterations: done (557.0ms)

Iter	Nodes	Cost
0	299	3180
1	754	2865
done	5000	2556

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (pow a2 2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`times-frac`
39×	`add-cube-cbrt` `*-un-lft-identity`
33×	`add-exp-log`
28×	`sqrt-prod`
25×	`associate-l` `add-cbrt-cube`
12×	`prod-exp` `associate-/r*`
9×	`pow1` `associate-r`
8×	`cbrt-unprod`
7×	`div-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`unpow-prod-down` `associate-/l*` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative` `unpow2` `sqr-pow`
1×	`associate-*l/`

Counts

4 → 140

Calls

4 calls:

17.0ms	(* (cos th) (pow a2 2))
35.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
19.0ms	(/ (cos th) (sqrt 2.0))

series493.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (cos th) (pow a2 2))
147.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
174.0ms	(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
90.0ms	(/ (cos th) (sqrt 2.0))

simplify2.4s

Counts

152 → 152

Iterations

Useful iterations: 2 (917.0ms)

Iter	Nodes	Cost
0	204	1751
1	531	1636
2	3236	1475
done	5000	1475

prune727.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.1b	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
0.2b	(/ (pow a2 2) (sqrt 2.0))
0.3b	(/ (pow a1 2) (sqrt 2.0))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
172×	`add-sqr-sqrt`
128×	`add-cube-cbrt` `*-un-lft-identity`
110×	`sqrt-prod`
104×	`associate-r`
82×	`unpow-prod-down`
34×	`add-exp-log`
30×	`unpow2` `sqr-pow`
18×	`add-cbrt-cube` `unswap-sqr`
16×	`associate-/l*`
12×	`div-exp` `associate-/r*`
8×	`pow1` `prod-exp`
6×	`associate-l`
4×	`cbrt-undiv` `pow-to-exp` `pow-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 312

Calls

4 calls:

37.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
71.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
20.0ms	(/ (pow a2 2) (sqrt 2.0))
12.0ms	(/ (pow a1 2) (sqrt 2.0))

series521.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
149.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
104.0ms	(/ (pow a2 2) (sqrt 2.0))
85.0ms	(/ (pow a1 2) (sqrt 2.0))

simplify646.0ms

Counts

324 → 324

Iterations

Useful iterations: done (633.0ms)

Iter	Nodes	Cost
0	352	4242
1	827	3734
done	5001	3224

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes345.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	19
1	17	19
done	17	19

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.3s	2377×	body	1280	valid
1.5s	2165×	body	640	valid
1.1s	8068×	body	80	valid
415.0ms	1084×	body	320	valid
105.0ms	524×	body	160	valid