Details

sample1.5s

Algorithm

intervals

Results

738.0ms	123×	body	1280	valid
304.0ms	72×	body	2560	valid
187.0ms	25×	body	5120	valid
101.0ms	73×	body	640	valid
84.0ms	29×	body	320	valid
15.0ms	50×	body	80	valid
7.0ms	12×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3616
3	688
2	142
1	44
0	19

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.4b

localize77.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (/ 2.0 (sin k)) (/ (pow t 3.0) (/ (* l l) (tan k))))
4.3b	(/ (* l l) (tan k))
14.7b	(/ (pow t 3.0) (/ (* l l) (tan k)))
30.2b	(/ (/ (/ 2.0 (sin k)) (/ (pow t 3.0) (/ (* l l) (tan k)))) (pow (/ k t) 2.0))

rewrite6.3s

Algorithm

rewrite-expression-head

Rules

65443×	`times-frac`
22258×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16366×	`unpow-prod-down`
3973×	`div-inv`
2792×	`sqr-pow`
2013×	`associate-/r/`
1745×	`tan-quot`
819×	`associate-/l*`
521×	`add-exp-log`
422×	`div-exp`
92×	`add-cbrt-cube`
89×	`associate-/r*`
75×	`pow-exp`
60×	`cbrt-undiv`
54×	`pow-to-exp`
34×	`prod-exp`
6×	`cbrt-unprod`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 15508

Calls

4 calls:

104.0ms	(/ (/ 2.0 (sin k)) (/ (pow t 3.0) (/ (* l l) (tan k))))
23.0ms	(/ (* l l) (tan k))
36.0ms	(/ (pow t 3.0) (/ (* l l) (tan k)))
1.0s	(/ (/ (/ 2.0 (sin k)) (/ (pow t 3.0) (/ (* l l) (tan k)))) (pow (/ k t) 2.0))

series4.0s

Counts

4 → 12

Calls

4 calls:

1.1s	(/ (/ 2.0 (sin k)) (/ (pow t 3.0) (/ (* l l) (tan k))))
145.0ms	(/ (* l l) (tan k))
545.0ms	(/ (pow t 3.0) (/ (* l l) (tan k)))
2.2s	(/ (/ (/ 2.0 (sin k)) (/ (pow t 3.0) (/ (* l l) (tan k)))) (pow (/ k t) 2.0))

simplify41.8s

Counts

15520 → 15520

Iterations

Iter	Nodes
done	25473
0	25473

prune4.6m

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.8b

localize87.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.1b	(* (pow k 2.0) (pow t 1.0))
6.7b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.6b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

Calls

4 calls:

40.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
36.0ms	(* (pow k 2.0) (pow t 1.0))
37.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
160.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.7s

Counts

4 → 12

Calls

4 calls:

682.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
629.0ms	(* (pow k 2.0) (pow t 1.0))
171.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.2s	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify8.4s

Counts

612 → 612

Iterations

Iter	Nodes
done	5006
2	3582
1	1283
0	483

prune2.0s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 5.5b

localize98.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (pow k 2.0))
0.6b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
6.8b	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (pow (/ 1 (pow t 1.0)) 1.0))
14.3b	(* (pow (/ 1 (pow k 2.0)) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (pow (/ 1 (pow t 1.0)) 1.0)))

rewrite903.0ms

Algorithm

rewrite-expression-head

Rules

4668×	`add-exp-log`
2440×	`prod-exp`
2325×	`div-exp`
1966×	`pow-exp`
607×	`pow-to-exp`
456×	`rec-exp` `1-exp`
98×	`unpow-prod-down`
90×	`add-sqr-sqrt` `times-frac`
82×	`add-cbrt-cube`
60×	`*-un-lft-identity`
54×	`add-cube-cbrt`
39×	`associate-l`
31×	`cbrt-unprod`
30×	`associate-r`
28×	`cbrt-undiv`
18×	`unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`associate-/r/` `associate-/l*`
5×	`div-inv`
4×	`pow1` `associate-*l/` `add-log-exp`
3×	`associate-*r/`
2×	`frac-times` `frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 1149

Calls

4 calls:

16.0ms	(/ 1 (pow k 2.0))
36.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
166.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (pow (/ 1 (pow t 1.0)) 1.0))
401.0ms	(* (pow (/ 1 (pow k 2.0)) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (pow (/ 1 (pow t 1.0)) 1.0)))

series2.3s

Counts

4 → 12

Calls

4 calls:

721.0ms	(/ 1 (pow k 2.0))
168.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
622.0ms	(* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (pow (/ 1 (pow t 1.0)) 1.0))
763.0ms	(* (pow (/ 1 (pow k 2.0)) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) (pow (/ 1 (pow t 1.0)) 1.0)))

simplify7.5s

Counts

1161 → 1161

Iterations

Iter	Nodes
done	5000
1	2346
0	849

prune2.9s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 3.0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos k))
0.5b	(cbrt (cos k))
0.5b	(/ 1 (pow k 2.0))
14.3b	(* (pow (/ 1 (pow k 2.0)) 1.0) (* (/ (* (cbrt (cos k)) (cbrt (cos k))) (/ (sin k) l)) (* (/ (cbrt (cos k)) (/ (sin k) l)) (pow (/ 1 (pow t 1.0)) 1.0))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

14203×	`add-exp-log`
7500×	`prod-exp`
7026×	`div-exp`
4761×	`pow-exp`
1467×	`pow-to-exp`
1101×	`rec-exp` `1-exp`
104×	`add-cbrt-cube`
64×	`cbrt-unprod`
46×	`unpow-prod-down`
42×	`times-frac`
40×	`cbrt-undiv`
37×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
29×	`associate-l`
8×	`sqr-pow`
7×	`associate-/r*`
6×	`cbrt-prod`
4×	`pow1` `associate-*r/` `add-log-exp`
3×	`associate-l/` `associate-/l`
2×	`pow1/3` `div-inv`
1×	`frac-times` `pow-flip` `frac-2neg` `associate-r` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 2369

Calls

4 calls:

2.0ms	(cbrt (cos k))
2.0ms	(cbrt (cos k))
17.0ms	(/ 1 (pow k 2.0))
707.0ms	(* (pow (/ 1 (pow k 2.0)) 1.0) (* (/ (* (cbrt (cos k)) (cbrt (cos k))) (/ (sin k) l)) (* (/ (cbrt (cos k)) (/ (sin k) l)) (pow (/ 1 (pow t 1.0)) 1.0))))

series1.9s

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (cos k))
193.0ms	(cbrt (cos k))
754.0ms	(/ 1 (pow k 2.0))
764.0ms	(* (pow (/ 1 (pow k 2.0)) 1.0) (* (/ (* (cbrt (cos k)) (cbrt (cos k))) (/ (sin k) l)) (* (/ (cbrt (cos k)) (/ (sin k) l)) (pow (/ 1 (pow t 1.0)) 1.0))))

simplify54.0s

Counts

2381 → 2381

Iterations

Iter	Nodes
done	5000
1	3763
0	1476

prune1.8s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 2.0b

regimes1.8s

Accuracy

22.3% (6.1b remaining)

Error of 9.9b against oracle of 3.8b and baseline of 11.6b

bsearch4.9s

Steps

Iters	Range		Point
6	1.4661899792536296e+172	1.8886095170077467e+173	1.4881104557168329e+172
12	2.2424311005949938e-190	2.1841612986458417e-134	6.303690353095153e-135
8	-1.8272794692916533e-143	-1.3329395220112687e-147	-9.730288504549286e-144
7	-1.506080509388271e+137	-2.0317388966812166e+135	-1.483471567911308e+137

simplify55.0ms

Iterations

Iter	Nodes
done	77
3	77
2	74
1	71
0	55

end0.0ms

sample38.7s

Algorithm

intervals

Results

11.0s	2270×	body	2560	valid
10.4s	4080×	body	1280	valid
8.5s	964×	body	5120	valid
5.2s	2577×	body	640	valid
1.6s	1014×	body	320	valid
707.0ms	2047×	body	80	valid
251.0ms	428×	body	160	valid