Details

sample459.0ms

Algorithm

intervals

Results

150.0ms	34×	body	5120	valid
115.0ms	135×	body	1280	valid
97.0ms	54×	body	2560	valid
48.0ms	78×	body	640	valid
14.0ms	36×	body	320	valid
8.0ms	62×	body	80	valid
5.0ms	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	147	13
2	857	12
3	5002	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.3b	(* (pow t 3.0) (tan k))
20.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
25.8b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite55.0ms

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:

8.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
18.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series914.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ k t) 2.0)
242.0ms	(* (pow t 3.0) (tan k))
365.0ms	(/ (* 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)))

simplify138.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (21.0ms)

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

prune461.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.7b	(* (pow k 2.0) (pow t 1.0))
16.8b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite110.0ms

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	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
22.0ms	(* (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:

336.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
326.0ms	(* (pow k 2.0) (pow t 1.0))
655.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify154.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (84.0ms)

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

prune630.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.5b

localize25.0ms

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))))
3.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.8b	(* (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)))

rewrite299.0ms

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:

3.0ms	(pow (sin k) 2)
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
41.0ms	(* (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:

19.0ms	(pow (sin k) 2)
342.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
656.0ms	(* (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

prune756.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos k) (sin k))
0.8b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.8b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
16.8b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

3841×	`add-exp-log`
2622×	`prod-exp`
1370×	`div-exp`
1330×	`pow-exp`
679×	`pow-to-exp`
248×	`rec-exp` `1-exp`
99×	`times-frac`
80×	`add-sqr-sqrt`
65×	`add-cbrt-cube`
59×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
24×	`associate-l`
22×	`cbrt-undiv` `cbrt-unprod`
8×	`div-inv`
7×	`pow1` `unpow-prod-down`
6×	`associate-/l*` `unswap-sqr`
5×	`associate-*r/`
4×	`associate-/r*` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `inv-pow` `sqr-pow`

Counts

4 → 931

Calls

4 calls:

4.0ms	(/ (cos k) (sin k))
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
22.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
37.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (cos k) (sin k))
343.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
90.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
643.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify175.0ms

Algorithm

egg-herbie

Counts

943 → 943

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2147	15097
1	5002	12259

prune731.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.5b

regimes421.0ms

Accuracy

51% (3.4b remaining)

Error of 11.9b against oracle of 8.5b and baseline of 15.4b

bsearch1.1s

Steps

Iters	Range		Point
8	1.4340110496867217e+151	1.1272970871767278e+155	3.912578152959539e+153
7	8.316703124824052e-161	8.630576680100012e-159	3.062784656086729e-159
6	-1.4773917663625897e-168	-1.770571560429151e-169	-1.2495359247218516e-168
7	-4.0387374422910434e+145	-2.3578160794753884e+144	-4.3481340441220306e+144

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	84
1	71	84
2	74	84
3	74	84

end0.0ms

sample14.9s

Algorithm

intervals

Results

4.4s	2239×	body	2560	valid
4.3s	987×	body	5120	valid
3.6s	4056×	body	1280	valid
1.4s	2484×	body	640	valid
391.0ms	983×	body	320	valid
279.0ms	1990×	body	80	valid
118.0ms	447×	body	160	valid