Details

sample71.0ms

Algorithm

intervals

Results

28.0ms	306×	body	80	valid
11.0ms	19×	body	1280	valid
11.0ms	32×	body	640	valid
4.0ms	18×	body	320	valid
2.0ms	11×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	8
1	68	8
2	243	8
3	1266	8
4	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.7b	(* (* x (pow sin 2.0)) x)
6.9b	(* x (pow sin 2.0))
17.3b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
82×	`prod-exp`
34×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 115

Calls

4 calls:

27.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms	(* (* x (pow sin 2.0)) x)
6.0ms	(* x (pow sin 2.0))
25.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series815.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
143.0ms	(* (* x (pow sin 2.0)) x)
131.0ms	(* x (pow sin 2.0))
251.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify57.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	435	927
1	2042	771
2	5002	771

prune270.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.1b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
3.7b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.3b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 186

Calls

4 calls:

11.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
92.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
33.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
94.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series882.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
304.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
157.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
275.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify87.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	586	2140
1	2792	1433
2	5002	1421

prune283.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
0.2b	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
2.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
2.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
44×	`prod-exp`
21×	`add-cbrt-cube`
17×	`associate-l`
16×	`add-sqr-sqrt`
14×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
11×	`pow1`
8×	`cbrt-unprod`
6×	`unpow-prod-down`
5×	`associate-r`
4×	`add-log-exp`
3×	`times-frac` `swap-sqr` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

5.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
3.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series574.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))))
34.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
222.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
214.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	316	1464
1	1229	1194
2	5001	1122

prune373.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
1.1b	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
2.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
2.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
63×	`add-exp-log`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`prod-exp`
21×	`add-cbrt-cube`
16×	`associate-/l*`
14×	`pow-to-exp` `associate-l` `pow-exp`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative` `sqr-pow`
1×	`associate-/l/`

Counts

4 → 157

Calls

4 calls:

7.0ms	(/ (/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
66.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
219.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
214.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify72.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	510	3289
1	1830	2994
2	5001	2909

prune503.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

0% (2.6b remaining)

Error of 2.8b against oracle of 0.2b and baseline of 2.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms

sample2.1s

Algorithm

intervals

Results

908.0ms	9155×	body	80	valid
366.0ms	818×	body	1280	valid
314.0ms	949×	body	640	valid
143.0ms	558×	body	320	valid
55.0ms	306×	body	160	valid