Details

sample1.3s

Algorithm

intervals

Results

587.0ms	76×	body	640	valid
288.0ms	36×	body	5120	valid
188.0ms	67×	body	2560	valid
188.0ms	133×	body	1280	valid
25.0ms	72×	body	80	valid
22.0ms	35×	body	320	valid
7.0ms	16×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	19	25
1	71	25
2	2482	25
done	5001	23

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (tan k) (/ (pow t 3.0) l))
5.8b	(* (/ (sin k) l) (- (pow (/ k t) 2.0) 0))
6.0b	(/ (pow t 3.0) l)
26.5b	(/ (/ 2.0 (* (tan k) (/ (pow t 3.0) l))) (* (/ (sin k) l) (- (pow (/ k t) 2.0) 0)))

rewrite414.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-sqr-sqrt`
131×	`*-un-lft-identity`
129×	`add-cube-cbrt`
126×	`times-frac`
111×	`add-exp-log`
102×	`unpow-prod-down` `prod-diff`
70×	`add-cbrt-cube`
55×	`div-exp`
53×	`distribute-rgt-in` `distribute-lft-in`
33×	`associate-r`
31×	`cbrt-undiv`
30×	`prod-exp`
18×	`cbrt-unprod`
17×	`associate-/l*`
16×	`associate-l`
15×	`sqr-pow`
12×	`div-inv`
11×	`associate-/r/`
8×	`pow1`
7×	`frac-times` `associate-*r/`
6×	`tan-quot` `unswap-sqr`
5×	`pow-to-exp` `associate-*l/` `pow-exp`
4×	`expm1-log1p-u` `flip3--` `associate-/r*` `flip--` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`sub-neg` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`
1×	`associate-/l/` `distribute-lft-out--`

Counts

4 → 317

Calls

4 calls:

42.0ms	(* (tan k) (/ (pow t 3.0) l))
227.0ms	(* (/ (sin k) l) (- (pow (/ k t) 2.0) 0))
24.0ms	(/ (pow t 3.0) l)
100.0ms	(/ (/ 2.0 (* (tan k) (/ (pow t 3.0) l))) (* (/ (sin k) l) (- (pow (/ k t) 2.0) 0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

329.0ms	(* (tan k) (/ (pow t 3.0) l))
140.0ms	(* (/ (sin k) l) (- (pow (/ k t) 2.0) 0))
220.0ms	(/ (pow t 3.0) l)
911.0ms	(/ (/ 2.0 (* (tan k) (/ (pow t 3.0) l))) (* (/ (sin k) l) (- (pow (/ k t) 2.0) 0)))

simplify11.0s

Counts

329 → 329

Iterations

Useful iterations: done (11.0s)

Iter	Nodes	Cost
0	628	8803
done	5001	6685

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (sin k) 2) (pow k 2))
0.4b	(pow (sin k) 2)
4.9b	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (* (pow (sin k) 2) (pow k 2))))
18.6b	(/ (* (cos k) (pow l 2)) (* (pow (sin k) 2) (pow k 2)))

rewrite566.0ms

Algorithm

rewrite-expression-head

Rules

5949×	`add-exp-log`
4713×	`prod-exp`
3172×	`pow-exp`
2180×	`div-exp`
1942×	`pow-to-exp`
410×	`rec-exp` `1-exp`
36×	`add-cbrt-cube`
35×	`add-sqr-sqrt`
25×	`unpow-prod-down`
19×	`associate-l` `unswap-sqr`
14×	`add-cube-cbrt` `*-un-lft-identity` `cbrt-unprod`
13×	`associate-r` `sqr-pow`
11×	`unpow2`
8×	`cbrt-undiv`
5×	`pow1` `times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/l*`

Counts

4 → 1520

Calls

4 calls:

44.0ms	(* (pow (sin k) 2) (pow k 2))
8.0ms	(pow (sin k) 2)
159.0ms	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (* (pow (sin k) 2) (pow k 2))))
25.0ms	(/ (* (cos k) (pow l 2)) (* (pow (sin k) 2) (pow k 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (pow (sin k) 2) (pow k 2))
23.0ms	(pow (sin k) 2)
1.2s	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (* (pow (sin k) 2) (pow k 2))))
167.0ms	(/ (* (cos k) (pow l 2)) (* (pow (sin k) 2) (pow k 2)))

simplify1.0s

Counts

1532 → 1532

Iterations

Useful iterations: done (903.0ms)

Iter	Nodes	Cost
0	549	47394
done	5001	41437

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
1.9b	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2)))
4.7b	(* (* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2))) (/ (pow l 2) (pow k 2)))
17.0b	(/ (pow l 2) (pow k 2))

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

6178×	`add-exp-log`
3970×	`prod-exp`
3324×	`pow-exp`
3175×	`div-exp`
2004×	`pow-to-exp`
440×	`rec-exp` `1-exp`
167×	`times-frac`
129×	`unpow-prod-down`
124×	`add-sqr-sqrt`
96×	`associate-r`
93×	`add-cube-cbrt` `*-un-lft-identity`
47×	`sqr-pow`
41×	`unpow2`
32×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-l` `cbrt-unprod`
8×	`associate-/r` `associate-/l`
7×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow`
2×	`*-commutative`
1×	`frac-times` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num`

Counts

4 → 1740

Calls

4 calls:

4.0ms	(pow (sin k) 2)
85.0ms	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2)))
144.0ms	(* (* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2))) (/ (pow l 2) (pow k 2)))
17.0ms	(/ (pow l 2) (pow k 2))

series1.9s

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sin k) 2)
668.0ms	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2)))
1.2s	(* (* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2))) (/ (pow l 2) (pow k 2)))
42.0ms	(/ (pow l 2) (pow k 2))

simplify2.4s

Counts

1752 → 1752

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	790	52736
done	5000	46282

prune2.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (pow (sin k) 2))
0.4b	(pow (sin k) 2)
1.9b	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2)))
4.7b	(* (* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2))) (* (/ (pow l 1) (fabs k)) (/ (pow l 1) (fabs k))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

13780×	`add-exp-log`
8709×	`prod-exp`
6417×	`div-exp`
5188×	`pow-exp`
3028×	`pow-to-exp`
720×	`rec-exp` `1-exp`
80×	`add-cbrt-cube`
72×	`add-sqr-sqrt`
63×	`times-frac`
41×	`add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down` `cbrt-unprod`
29×	`associate-r`
19×	`cbrt-undiv`
17×	`sqr-pow`
15×	`unswap-sqr`
12×	`associate-l`
11×	`unpow2`
10×	`pow1` `associate-*r/`
8×	`associate-/r*`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `associate-l/` `div-inv` `associate-/l`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `clear-num`

Counts

4 → 2567

Calls

4 calls:

28.0ms	(/ (cos k) (pow (sin k) 2))
8.0ms	(pow (sin k) 2)
127.0ms	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2)))
241.0ms	(* (* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2))) (* (/ (pow l 1) (fabs k)) (/ (pow l 1) (fabs k))))

series1.9s

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (cos k) (pow (sin k) 2))
24.0ms	(pow (sin k) 2)
680.0ms	(* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2)))
1.2s	(* (* (pow (/ 1 (* (pow -1 2.0) (pow t 1.0))) 1.0) (/ (cos k) (pow (sin k) 2))) (* (/ (pow l 1) (fabs k)) (/ (pow l 1) (fabs k))))

simplify8.9s

Counts

2579 → 2579

Iterations

Useful iterations: done (8.7s)

Iter	Nodes	Cost
0	917	98338
done	5000	69607

prune1.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.5b

regimes877.0ms

Accuracy

64.5% (1.0b remaining)

Error of 2.7b against oracle of 1.7b and baseline of 4.6b

bsearch3.5s

Steps

Iters	Range		Point
11	4.4294153258537444e-154	1.0693360123295226e-130	2.033695468655644e-153
10	-8.135457287454602e-121	-1.1738702098008812e-130	-4.9218725271157975e-130

simplify14.0ms

Iterations

Useful iterations: done (13.0ms)

Iter	Nodes	Cost
0	39	114
1	52	74
done	52	72

end0.0ms

sample31.2s

Algorithm

intervals

Results

9.0s	2247×	body	2560	valid
7.8s	3994×	body	1280	valid
7.6s	961×	body	5120	valid
3.9s	2502×	body	640	valid
1.3s	1008×	body	320	valid
556.0ms	2040×	body	80	valid
200.0ms	441×	body	160	valid