Details

sample503.0ms

Algorithm

intervals

Results

171.0ms	40×	body	5120	valid
143.0ms	71×	body	2560	valid
91.0ms	115×	body	1280	valid
50.0ms	93×	body	640	valid
9.0ms	26×	body	320	valid
7.0ms	61×	body	80	valid
5.0ms	23×	body	160	valid

simplify27.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
22.5b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.5b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite166.0ms

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:

6.0ms	(pow (/ k t) 2.0)
15.0ms	(* (pow t 3.0) (tan k))
89.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
45.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series856.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow (/ k t) 2.0)
221.0ms	(* (pow t 3.0) (tan k))
349.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
231.0ms	(* (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

prune440.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
6.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.3b	(* (pow k 2.0) (pow t 1.0))
17.9b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 567

Calls

4 calls:

4.0ms	(pow (sin k) 2)
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0ms	(* (pow k 2.0) (pow t 1.0))
73.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (sin k) 2)
79.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
316.0ms	(* (pow k 2.0) (pow t 1.0))
611.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify135.0ms

Algorithm

egg-herbie

Counts

579 → 579

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1180	6917
1	3731	6762
2	5003	6761

prune549.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.3b	(pow (sin k) 2)
6.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.9b	(* (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)))

rewrite405.0ms

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:

46.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.0ms	(pow (sin k) 2)
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
134.0ms	(* (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)))

series1.0s

Counts

4 → 12

Calls

4 calls:

321.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms	(pow (sin k) 2)
82.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
612.0ms	(* (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)))

simplify288.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (86.0ms)

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

prune734.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
0.8b	(pow (cbrt (sin k)) 4)
2.0b	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
17.9b	(* (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)))

rewrite3.3s

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:

45.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
4.0ms	(pow (cbrt (sin k)) 4)
188.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.5s	(* (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)))

series980.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
116.0ms	(pow (cbrt (sin k)) 4)
82.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
609.0ms	(* (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)))

simplify2.7s

Algorithm

egg-herbie

Counts

9913 → 9913

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	10810	276353

prune1.2m

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 7.8b

regimes859.0ms

Accuracy

32.9% (3.8b remaining)

Error of 10.7b against oracle of 6.9b and baseline of 12.6b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	96
1	81	96

end0.0ms

sample14.4s

Algorithm

intervals

Results

4.2s	2225×	body	2560	valid
4.2s	991×	body	5120	valid
3.4s	4062×	body	1280	valid
1.4s	2524×	body	640	valid
356.0ms	965×	body	320	valid
240.0ms	2013×	body	80	valid
128.0ms	484×	body	160	valid