Details

sample497.0ms

Algorithm

intervals

Results

159.0ms	78×	body	2560	valid
139.0ms	33×	body	5120	valid
109.0ms	131×	body	1280	valid
41.0ms	79×	body	640	valid
16.0ms	40×	body	320	valid
7.0ms	61×	body	80	valid
2.0ms	5×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
22.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.3b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite88.0ms

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:

4.0ms	(pow (/ k t) 2.0)
7.0ms	(* (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)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow (/ k t) 2.0)
233.0ms	(* (pow t 3.0) (tan k))
357.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
241.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify134.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	974	1954
1	4995	1620
2	5001	1620

prune448.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.3b	(* (pow k 2.0) (pow t 1.0))
8.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.2b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite116.0ms

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:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms	(* (pow k 2.0) (pow t 1.0))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
37.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

332.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
323.0ms	(* (pow k 2.0) (pow t 1.0))
86.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
640.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify152.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	1316	7194
1	4162	7025
2	5002	7018

prune608.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 19.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.8b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.2b	(* (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)))

rewrite291.0ms

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:

1.0ms	(pow (sin k) 2)
21.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
61.0ms	(* (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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin k) 2)
347.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
90.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
657.0ms	(* (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)))

simplify281.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1742	23543
1	4574	19111
2	5002	17858

prune758.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (cbrt (sin k)) 4)
1.0b	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
2.8b	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
17.2b	(* (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)))

rewrite3.1s

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:

2.0ms	(pow (cbrt (sin k)) 4)
29.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
165.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.4s	(* (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)))

series1.0s

Counts

4 → 12

Calls

4 calls:

128.0ms	(pow (cbrt (sin k)) 4)
179.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
85.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
631.0ms	(* (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)))

simplify2.6s

Algorithm

egg-herbie

Counts

9913 → 9913

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	10810	272393

prune58.4s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 7.9b

regimes602.0ms

Accuracy

17.6% (5.1b remaining)

Error of 12.0b against oracle of 6.9b and baseline of 13.1b

bsearch437.0ms

Steps

Iters	Range		Point
8	2.4105644391752822e+144	1.1894446744325996e+147	2.1181975674542142e+146
3	5.054959164398525e-170	6.652874592318804e-170	6.5396280149036325e-170

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	96
1	75	96

end0.0ms

sample14.4s

Algorithm

intervals

Results

4.4s	2286×	body	2560	valid
4.0s	950×	body	5120	valid
3.5s	4108×	body	1280	valid
1.4s	2436×	body	640	valid
367.0ms	978×	body	320	valid
269.0ms	2156×	body	80	valid
126.0ms	465×	body	160	valid