Details

sample932.0ms

Algorithm

intervals

Results

282.0ms	48×	body	5120	valid
261.0ms	71×	body	2560	valid
180.0ms	123×	body	1280	valid
124.0ms	81×	body	640	valid
26.0ms	33×	body	320	valid
14.0ms	65×	body	80	valid
7.0ms	14×	body	160	valid

simplify451.0ms

Counts: 1 → 1

prune81.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow t 3.0) (tan k))
0.4b	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
22.1b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.2b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

392×	`add-exp-log`
265×	`prod-exp`
74×	`div-exp` `add-cbrt-cube`
61×	`pow-exp`
41×	`pow-to-exp`
40×	`cbrt-unprod`
25×	`associate-l`
21×	`add-sqr-sqrt`
17×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-undiv`
10×	`times-frac`
7×	`associate-r/` `associate-r*`
6×	`pow1`
4×	`tan-quot` `add-log-exp`
3×	`*-commutative` `unswap-sqr` `sqr-pow`
2×	`associate-*l/` `div-inv`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 185

Calls

4 calls:

24.0ms	(* (pow t 3.0) (tan k))
116.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
133.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
95.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.7s

Counts

4 → 12

Calls

4 calls:

410.0ms	(* (pow t 3.0) (tan k))
429.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
570.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
332.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify2.0s

Counts: 197 → 197

prune563.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.1b	(* (pow k 2.0) (pow t 1.0))
6.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.5b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite236.0ms

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:

24.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
25.0ms	(* (pow k 2.0) (pow t 1.0))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
104.0ms	(* (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:

496.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
498.0ms	(* (pow k 2.0) (pow t 1.0))
145.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
965.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.9s

Counts: 612 → 612

prune960.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.2b	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
6.1b	(* (pow k 2.0) (pow t 1.0))
15.5b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

rewrite774.0ms

Algorithm

rewrite-expression-head

Rules

3129×	`times-frac`
1393×	`add-sqr-sqrt`
1326×	`add-cube-cbrt` `*-un-lft-identity`
829×	`add-exp-log`
460×	`div-exp`
413×	`associate-r`
336×	`prod-exp`
269×	`pow-exp`
137×	`associate-/l*`
119×	`pow-to-exp`
95×	`div-inv`
60×	`rec-exp` `1-exp`
45×	`add-cbrt-cube`
24×	`unpow-prod-down` `unswap-sqr`
22×	`cbrt-undiv`
18×	`associate-l`
14×	`sqr-pow`
7×	`associate-/r/` `cbrt-unprod`
5×	`pow1`
4×	`associate-/r*` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `associate-/l/` `inv-pow`

Counts

4 → 1261

Calls

4 calls:

18.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
94.0ms	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
25.0ms	(* (pow k 2.0) (pow t 1.0))
404.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

series2.6s

Counts

4 → 12

Calls

4 calls:

573.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
160.0ms	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
477.0ms	(* (pow k 2.0) (pow t 1.0))
1.4s	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

simplify1.4s

Counts: 1273 → 1273

prune9.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.9b	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l))) (/ (/ (cos k) (/ 1 l)) (sin k)))
5.2b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l)))
6.1b	(* (pow k 2.0) (pow t 1.0))

rewrite862.0ms

Algorithm

rewrite-expression-head

Rules

9054×	`add-exp-log`
5169×	`div-exp`
4368×	`prod-exp`
2425×	`pow-exp`
1194×	`rec-exp` `1-exp`
955×	`pow-to-exp`
420×	`times-frac`
247×	`add-sqr-sqrt`
204×	`*-un-lft-identity`
198×	`add-cube-cbrt`
187×	`associate-r`
100×	`add-cbrt-cube`
41×	`cbrt-undiv`
33×	`cbrt-unprod`
24×	`unpow-prod-down` `unswap-sqr`
19×	`associate-l` `div-inv`
14×	`sqr-pow`
7×	`pow1`
4×	`associate-*r/` `associate-/r/` `add-log-exp`
3×	`un-div-inv` `-commutative` `associate-/l`
2×	`frac-times` `associate-*l/`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `inv-pow`

Counts

4 → 1965

Calls

4 calls:

39.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
252.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l))) (/ (/ (cos k) (/ 1 l)) (sin k)))
140.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l)))
25.0ms	(* (pow k 2.0) (pow t 1.0))

series2.6s

Counts

4 → 12

Calls

4 calls:

492.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
979.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l))) (/ (/ (cos k) (/ 1 l)) (sin k)))
615.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ 1 (/ (sin k) l)))
505.0ms	(* (pow k 2.0) (pow t 1.0))

simplify1.8s

Counts: 1977 → 1977

prune2.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.6b

regimes682.0ms

Accuracy

35.7% (3.1b remaining)

Error of 9.3b against oracle of 6.2b and baseline of 11.1b

bsearch2.0s

Steps

Iters	Range		Point
7	1.5435400076532623e+163	4.253127246088997e+164	1.5703887349117294e+163
10	1.7015222232976972e-101	3.8027673838617767e-87	1.094978693998943e-100
4	-1.8695913449399292e-123	-1.2894119083114876e-123	-1.352185247768907e-123
7	-1.051527773372545e+155	-7.7762495558585005e+152	-1.3348197567202325e+154

simplify1.2s

end0.0ms

sample31.5s

Algorithm

intervals

Results

8.6s	4083×	body	1280	valid
8.0s	2276×	body	2560	valid
7.1s	951×	body	5120	valid
4.9s	2476×	body	640	valid
1.2s	959×	body	320	valid
435.0ms	2011×	body	80	valid
200.0ms	428×	body	160	valid