Details

sample462.0ms

Algorithm

intervals

Results

136.0ms	32×	body	5120	valid
135.0ms	67×	body	2560	valid
93.0ms	114×	body	1280	valid
47.0ms	89×	body	640	valid
15.0ms	40×	body	320	valid
8.0ms	64×	body	80	valid
4.0ms	18×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	44	13
1	149	13
2	869	12
3	5001	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
19.2b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.8b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite87.0ms

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×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `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 → 187

Calls

4 calls:

3.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
46.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
21.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series910.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ k t) 2.0)
240.0ms	(* (pow t 3.0) (tan k))
361.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
244.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify39.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune493.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k)))
0.3b	(/ (sin k) (cos k))
6.7b	(* (pow k 2.0) (pow t 1.0))
19.2b	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k))) (sin k)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

511×	`add-exp-log`
330×	`prod-exp`
134×	`pow-exp`
127×	`div-exp`
67×	`add-cbrt-cube`
62×	`pow-to-exp`
44×	`add-sqr-sqrt`
30×	`cbrt-unprod`
24×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
20×	`associate-r`
17×	`cbrt-undiv`
13×	`unpow-prod-down` `unswap-sqr`
12×	`associate-l`
11×	`sqr-pow`
4×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`quot-tan` `associate-*l/` `associate-/r/`

Counts

4 → 238

Calls

4 calls:

12.0ms	(* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k)))
3.0ms	(/ (sin k) (cos k))
8.0ms	(* (pow k 2.0) (pow t 1.0))
24.0ms	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k))) (sin k)))

series940.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k)))
19.0ms	(/ (sin k) (cos k))
329.0ms	(* (pow k 2.0) (pow t 1.0))
345.0ms	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k 2.0) (pow t 1.0)) 1.0) (/ (sin k) (cos k))) (sin k)))

simplify51.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1144	2986
1	5002	2604

prune565.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k))
0.2b	(* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k)))
0.3b	(/ (sin k) (cos k))
19.2b	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

1794×	`add-exp-log`
1372×	`prod-exp`
590×	`pow-exp`
370×	`div-exp`
290×	`pow-to-exp`
74×	`add-cbrt-cube`
34×	`cbrt-unprod`
29×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`cbrt-undiv`
16×	`associate-r`
6×	`pow1` `associate-l`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`unpow-prod-down` `quot-tan` `pow-prod-down` `associate-/r/`

Counts

4 → 449

Calls

4 calls:

31.0ms	(* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k))
18.0ms	(* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k)))
3.0ms	(/ (sin k) (cos k))
38.0ms	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k))
251.0ms	(* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k)))
19.0ms	(/ (sin k) (cos k))
359.0ms	(/ (* 2.0 (* l l)) (* (* (pow (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (sin k) (cos k))) (sin k)))

simplify88.0ms

Algorithm

egg-herbie

Counts

461 → 461

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1285	7620
1	5001	5452

prune536.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.7b

localize21.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ l (pow (sin k) 2))
3.7b	(* (/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0)) (/ l (pow (sin k) 2)))
5.6b	(/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0))
6.7b	(* (pow k 2.0) (pow t 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

495×	`add-exp-log`
259×	`prod-exp`
198×	`div-exp`
192×	`pow-exp`
102×	`pow-to-exp`
68×	`add-sqr-sqrt`
62×	`times-frac`
44×	`add-cube-cbrt` `*-un-lft-identity`
37×	`unpow-prod-down`
35×	`associate-r`
34×	`add-cbrt-cube`
19×	`sqr-pow`
16×	`associate-l`
14×	`unswap-sqr`
13×	`associate-/r*`
10×	`cbrt-undiv` `cbrt-unprod`
8×	`unpow2`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/`

Counts

4 → 305

Calls

4 calls:

4.0ms	(/ l (pow (sin k) 2))
31.0ms	(* (/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0)) (/ l (pow (sin k) 2)))
5.0ms	(/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0))
8.0ms	(* (pow k 2.0) (pow t 1.0))

series935.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ l (pow (sin k) 2))
320.0ms	(* (/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0)) (/ l (pow (sin k) 2)))
202.0ms	(/ (* 2.0 l) (pow (* (pow k 2.0) (pow t 1.0)) 1.0))
340.0ms	(* (pow k 2.0) (pow t 1.0))

simplify129.0ms

Algorithm

egg-herbie

Counts

317 → 317

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	1105	3051
1	4795	2827
2	5001	2826

prune737.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.4b

regimes573.0ms

Accuracy

78.4% (1.3b remaining)

Error of 9.3b against oracle of 8.0b and baseline of 13.8b

bsearch227.0ms

Steps

Iters	Range		Point
3	1.8305461003977325e+147	2.3452398986773444e+147	2.0557246371450623e+147
9	-3.823050932074918e+153	-6.633132287973284e+146	-2.9620071106894416e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	29
1	43	29

end0.0ms

sample14.4s

Algorithm

intervals

Results

4.5s	2215×	body	2560	valid
3.8s	901×	body	5120	valid
3.6s	4170×	body	1280	valid
1.3s	2400×	body	640	valid
403.0ms	1019×	body	320	valid
260.0ms	2012×	body	80	valid
121.0ms	461×	body	160	valid