Details

sample933.0ms

Algorithm

intervals

Results

272.0ms	73×	body	2560	valid
234.0ms	35×	body	5120	valid
209.0ms	126×	body	1280	valid
79.0ms	33×	body	320	valid
76.0ms	73×	body	640	valid
15.0ms	62×	body	80	valid
8.0ms	13×	body	160	valid

simplify966.0ms

Counts

1 → 1

Iterations

Useful iterations: done (965.0ms)

Iter	Nodes	Cost
0	19	25
1	44	25
2	149	25
3	856	23
done	5001	21

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin k) (tan k))
0.7b	(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
16.6b	(/ (pow t 3.0) (* l l))
29.5b	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

405×	`add-exp-log`
213×	`div-exp`
162×	`times-frac`
139×	`prod-exp`
70×	`add-cbrt-cube`
62×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `add-cube-cbrt`
56×	`pow-exp`
45×	`associate-/l*`
38×	`pow-to-exp`
37×	`unpow-prod-down`
29×	`cbrt-undiv`
20×	`associate-l` `cbrt-unprod`
11×	`div-inv`
9×	`sqr-pow`
6×	`pow1`
5×	`associate-*r/`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `associate-/r/`
2×	`clear-num` `associate-/r` `frac-2neg` `-commutative`
1×	`pow-prod-down` `unswap-sqr` `associate-/l/`

Counts

4 → 270

Calls

4 calls:

15.0ms	(* (sin k) (tan k))
70.0ms	(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
19.0ms	(/ (pow t 3.0) (* l l))
65.0ms	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

series1.7s

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (sin k) (tan k))
395.0ms	(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
320.0ms	(/ (pow t 3.0) (* l l))
851.0ms	(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

simplify728.0ms

Counts

282 → 282

Iterations

Useful iterations: done (715.0ms)

Iter	Nodes	Cost
0	477	6316
1	1478	5901
done	5000	5316

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.4b	(* (pow t 1.0) (pow k 2.0))
16.2b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite249.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 608

Calls

4 calls:

23.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
15.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.0ms	(* (pow t 1.0) (pow k 2.0))
97.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.3s

Counts

4 → 12

Calls

4 calls:

480.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
153.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
506.0ms	(* (pow t 1.0) (pow k 2.0))
1.1s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify578.0ms

Counts

620 → 620

Iterations

Useful iterations: done (555.0ms)

Iter	Nodes	Cost
0	445	15125
1	1343	13001
done	5000	12725

prune1.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 12.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.5b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.2b	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.0s

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×	`*-un-lft-identity` `add-cube-cbrt`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-r/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 1468

Calls

4 calls:

6.0ms	(pow (sin k) 2)
83.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
25.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
226.0ms	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (sin k) 2)
506.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
119.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.1s	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.0s

Counts

1480 → 1480

Iterations

Useful iterations: done (930.0ms)

Iter	Nodes	Cost
0	582	50469
1	1996	33533
done	5000	31707

prune1.2s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))
8.2b	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

23997×	`add-exp-log`
18432×	`prod-exp`
16320×	`pow-exp`
10720×	`div-exp`
7632×	`pow-to-exp`
2906×	`rec-exp` `1-exp`
59×	`unpow-prod-down`
49×	`add-sqr-sqrt` `times-frac`
40×	`associate-l`
37×	`add-cbrt-cube`
34×	`*-un-lft-identity`
31×	`add-cube-cbrt`
14×	`cbrt-unprod`
13×	`associate-r`
11×	`sqr-pow`
9×	`associate-/r*` `unswap-sqr`
8×	`cbrt-undiv`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-*r/` `unpow2`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 5524

Calls

4 calls:

15.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
27.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
82.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))
195.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))

series2.1s

Counts

4 → 12

Calls

4 calls:

509.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
134.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
507.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))
977.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))

simplify2.5s

Counts

5536 → 5536

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	1410	218022
done	5000	196349

prune3.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.0b

regimes870.0ms

Accuracy

30.9% (5.8b remaining)

Error of 16.1b against oracle of 10.3b and baseline of 18.7b

bsearch2.3s

Steps

Iters	Range		Point
10	1.0340362933942865e+150	1.8480168599026896e+163	1.2532174228697586e+154
10	-1.3048497031372084e+178	-2.3820198978012742e+162	-2.4279636162567888e+162

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	47	114
1	59	81
done	59	81

end0.0ms

sample31.4s

Algorithm

intervals

Results

8.3s	4144×	body	1280	valid
7.9s	2198×	body	2560	valid
7.9s	950×	body	5120	valid
4.2s	2565×	body	640	valid
1.1s	948×	body	320	valid
725.0ms	1978×	body	80	valid
329.0ms	471×	body	160	valid