Details

sample981.0ms

Algorithm

intervals

Results

483.0ms	131×	body	1280	valid
220.0ms	87×	body	2560	valid
146.0ms	32×	body	5120	valid
64.0ms	92×	body	640	valid
18.0ms	39×	body	320	valid
11.0ms	69×	body	80	valid
5.0ms	17×	body	160	valid

simplify25.0ms

Counts: 1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.2b	(* (pow t 3.0) (tan k))
20.8b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.1b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite200.0ms

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:

6.0ms	(pow (/ k t) 2.0)
15.0ms	(* (pow t 3.0) (tan k))
102.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
63.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.0s

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ k t) 2.0)
262.0ms	(* (pow t 3.0) (tan k))
425.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
276.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify124.0ms

Counts: 191 → 191

prune478.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.9b	(* (pow k 2.0) (pow t 1.0))
16.9b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite196.0ms

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)))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
19.0ms	(* (pow k 2.0) (pow t 1.0))
78.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

361.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
95.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
355.0ms	(* (pow k 2.0) (pow t 1.0))
719.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify149.0ms

Counts: 612 → 612

prune637.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 16.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.6b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.9b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite436.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

4.0ms	(pow (sin k) 2)
49.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
145.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sin k) 2)
357.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
96.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
728.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify264.0ms

Counts: 1472 → 1472

prune575.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
0.8b	(pow (cbrt (sin k)) 4)
0.9b	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
16.9b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

29087×	`times-frac`
11908×	`add-sqr-sqrt`
11455×	`add-cube-cbrt` `*-un-lft-identity`
10275×	`add-exp-log`
7945×	`unpow-prod-down`
6428×	`div-exp`
5073×	`prod-exp`
4257×	`pow-exp`
3951×	`cbrt-prod`
3557×	`associate-r`
2490×	`pow-to-exp`
1378×	`sqr-pow`
668×	`unpow2`
589×	`rec-exp` `1-exp`
326×	`associate-/l*`
319×	`div-inv`
117×	`associate-/r*`
108×	`unswap-sqr`
47×	`add-cbrt-cube`
26×	`cbrt-undiv`
24×	`associate-/r/`
11×	`associate-l`
5×	`pow1` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`pow1/3` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 9901

Calls

4 calls:

44.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
4.0ms	(pow (cbrt (sin k)) 4)
190.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.5s	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
138.0ms	(pow (cbrt (sin k)) 4)
100.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
700.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify2.3s

Counts: 9913 → 9913

prune1.2m

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 7.3b

regimes548.0ms

Accuracy

-3% (5.0b remaining)

Error of 12.2b against oracle of 7.2b and baseline of 12.1b

bsearch281.0ms

Steps

Iters	Range		Point
9	-5.023636380651188e+204	-4.2054725789248056e+198	-3.4993637140538663e+202

simplify1.0ms

end0.0ms

sample21.8s

Algorithm

intervals

Results

6.2s	4047×	body	1280	valid
5.5s	2189×	body	2560	valid
5.3s	941×	body	5120	valid
2.4s	2526×	body	640	valid
824.0ms	1979×	body	80	valid
660.0ms	984×	body	320	valid
179.0ms	458×	body	160	valid