Details

sample985.0ms

Algorithm

intervals

Results

318.0ms	40×	body	5120	valid
213.0ms	75×	body	2560	valid
198.0ms	134×	body	1280	valid
140.0ms	77×	body	640	valid
19.0ms	28×	body	320	valid
11.0ms	54×	body	80	valid
6.0ms	15×	body	160	valid

simplify937.0ms

Counts

1 → 1

Iterations

Useful iterations: done (937.0ms)

Iter	Nodes	Cost
0	19	25
1	44	25
2	148	25
3	841	23
done	5001	21

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.1b	(* (/ (pow t 3.0) (* l l)) (sin k))
14.8b	(/ (pow t 3.0) (* l l))
30.3b	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

340×	`times-frac`
272×	`add-exp-log`
153×	`unpow-prod-down`
144×	`add-sqr-sqrt`
137×	`add-cube-cbrt` `*-un-lft-identity`
128×	`div-exp`
103×	`prod-exp`
59×	`add-cbrt-cube`
58×	`associate-*l/`
54×	`associate-/r/`
38×	`tan-quot`
34×	`pow-exp`
32×	`div-inv`
24×	`pow-to-exp`
21×	`cbrt-unprod`
19×	`cbrt-undiv` `frac-times` `associate-*r/`
18×	`associate-/r*`
17×	`associate-/l*`
15×	`sqr-pow`
12×	`associate-l`
11×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 362

Calls

4 calls:

118.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
41.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
15.0ms	(/ (pow t 3.0) (* l l))
176.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

450.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
315.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
298.0ms	(/ (pow t 3.0) (* l l))
910.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify964.0ms

Counts

374 → 374

Iterations

Useful iterations: done (942.0ms)

Iter	Nodes	Cost
0	670	10352
1	1785	9880
done	5000	9414

prune2.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.1b	(* (pow k 2.0) (pow t 1.0))
16.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite263.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 608

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))
17.0ms	(* (pow k 2.0) (pow t 1.0))
107.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.3s

Counts

4 → 12

Calls

4 calls:

506.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
135.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
443.0ms	(* (pow k 2.0) (pow t 1.0))
1.2s	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify895.0ms

Counts

620 → 620

Iterations

Useful iterations: done (857.0ms)

Iter	Nodes	Cost
0	491	15125
1	1481	13001
done	5001	12725

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.0b

localize54.0ms

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))))
6.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0b	(* (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)))

rewrite769.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 1468

Calls

4 calls:

4.0ms	(pow (sin k) 2)
96.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
34.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
203.0ms	(* (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)))

series1.6s

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (sin k) 2)
500.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
125.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
974.0ms	(* (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)))

simplify1.0s

Counts

1480 → 1480

Iterations

Useful iterations: done (946.0ms)

Iter	Nodes	Cost
0	605	50477
1	2051	33540
done	5001	31701

prune1.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
2.8b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
6.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.5b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

24975×	`add-exp-log`
19170×	`prod-exp`
16882×	`pow-exp`
11120×	`div-exp`
7942×	`pow-to-exp`
2980×	`rec-exp` `1-exp`
54×	`unpow-prod-down`
40×	`times-frac` `associate-l`
36×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
31×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r` `cbrt-unprod`
10×	`sqr-pow`
8×	`associate-/r*`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `unpow2` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 5737

Calls

4 calls:

4.0ms	(pow (sin k) 2)
277.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
35.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
103.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.1s

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (sin k) 2)
991.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
131.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1000.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.8s

Counts

5749 → 5749

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	1433	225456
done	5000	202426

prune3.0s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.0b

regimes566.0ms

Accuracy

14.2% (6.4b remaining)

Error of 16.9b against oracle of 10.5b and baseline of 18.0b

bsearch1.2s

Steps

Iters	Range		Point
10	-7.015537041391403e+155	-4.765656100776285e+142	-9.576489350063892e+153

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	72
1	52	72
done	52	72

end0.0ms

sample31.3s

Algorithm

intervals

Results

10.1s	4123×	body	1280	valid
7.9s	2203×	body	2560	valid
7.5s	939×	body	5120	valid
3.0s	2474×	body	640	valid
901.0ms	1990×	body	80	valid
731.0ms	981×	body	320	valid
202.0ms	449×	body	160	valid