Details

sample945.0ms

Algorithm

intervals

Results

274.0ms	80×	body	2560	valid
271.0ms	140×	body	1280	valid
225.0ms	36×	body	5120	valid
63.0ms	62×	body	640	valid
40.0ms	12×	body	160	valid
20.0ms	27×	body	320	valid
14.0ms	62×	body	80	valid

simplify459.0ms

Counts: 1 → 1

prune84.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
22.5b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.3b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`associate-r` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

8.0ms	(pow (/ k t) 2.0)
19.0ms	(* (pow t 3.0) (tan k))
121.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
83.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.3s

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow (/ k t) 2.0)
279.0ms	(* (pow t 3.0) (tan k))
519.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
416.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify559.0ms

Counts: 191 → 191

prune565.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.6b

localize28.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.8b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.4b	(* (pow k 2.0) (pow t 1.0))
16.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite215.0ms

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:

18.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
18.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
20.0ms	(* (pow k 2.0) (pow t 1.0))
80.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.1s

Counts

4 → 12

Calls

4 calls:

478.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
129.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
491.0ms	(* (pow k 2.0) (pow t 1.0))
973.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.6s

Counts: 612 → 612

prune883.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
2.6b	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
7.4b	(* (pow k 2.0) (pow t 1.0))
16.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

1169×	`add-exp-log`
660×	`prod-exp`
466×	`div-exp`
367×	`pow-exp`
157×	`pow-to-exp`
90×	`times-frac`
88×	`add-sqr-sqrt`
80×	`rec-exp` `1-exp`
61×	`add-cbrt-cube`
55×	`add-cube-cbrt` `*-un-lft-identity`
52×	`associate-r`
31×	`associate-l`
21×	`cbrt-unprod`
20×	`cbrt-undiv`
19×	`unpow-prod-down`
15×	`unswap-sqr`
9×	`sqr-pow`
7×	`pow1` `div-inv`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`-commutative` `associate-/l`
2×	`frac-times` `associate-*l/`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `associate-/r/` `inv-pow`

Counts

4 → 440

Calls

4 calls:

26.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
51.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
23.0ms	(* (pow k 2.0) (pow t 1.0))
116.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series2.1s

Counts

4 → 12

Calls

4 calls:

572.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
142.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
470.0ms	(* (pow k 2.0) (pow t 1.0))
915.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify908.0ms

Counts: 452 → 452

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.9b

localize37.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.2b	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l)) (/ (fabs (sin k)) l))
5.9b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l))
7.4b	(* (pow k 2.0) (pow t 1.0))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

1420×	`add-exp-log`
774×	`prod-exp`
599×	`div-exp`
465×	`pow-exp`
195×	`pow-to-exp`
100×	`rec-exp` `1-exp`
52×	`add-cbrt-cube`
39×	`add-sqr-sqrt`
37×	`times-frac`
27×	`add-cube-cbrt` `*-un-lft-identity`
19×	`unpow-prod-down`
18×	`associate-l`
17×	`cbrt-undiv` `cbrt-unprod`
14×	`associate-/r*`
9×	`unswap-sqr` `sqr-pow`
8×	`associate-r`
5×	`pow1` `div-inv`
4×	`associate-/l*` `add-log-exp`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `*-commutative`
1×	`pow-flip` `associate-/r/` `associate-/l/` `inv-pow`

Counts

4 → 462

Calls

4 calls:

37.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
76.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l)) (/ (fabs (sin k)) l))
69.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l))
18.0ms	(* (pow k 2.0) (pow t 1.0))

series2.9s

Counts

4 → 12

Calls

4 calls:

533.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
925.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l)) (/ (fabs (sin k)) l))
547.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l))
898.0ms	(* (pow k 2.0) (pow t 1.0))

simplify873.0ms

Counts: 474 → 474

prune936.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

regimes478.0ms

Accuracy

23.6% (3.2b remaining)

Error of 10.0b against oracle of 6.8b and baseline of 11.0b

bsearch2.1s

Steps

Iters	Range		Point
10	-8.943426898549763e-144	-7.0430808488067e-155	-3.459437993813782e-153
7	-2.9102728335570422e+159	-5.486919896945144e+157	-5.603375851643622e+157

simplify793.0ms

end0.0ms

sample32.8s

Algorithm

intervals

Results

8.8s	2289×	body	2560	valid
8.4s	961×	body	5120	valid
8.0s	4039×	body	1280	valid
4.6s	2528×	body	640	valid
1.2s	987×	body	320	valid
582.0ms	2045×	body	80	valid
307.0ms	435×	body	160	valid