Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	301×	body	80	valid
8.0ms	32×	body	640	valid
8.0ms	24×	body	1280	valid
4.0ms	21×	body	320	valid
0.0ms	2×	body	160	valid

simplify40.0ms

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: 24.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
2.8b	(* (* x (pow sin 2.0)) x)
6.8b	(* x (pow sin 2.0))
16.9b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite69.0ms

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:

25.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
9.0ms	(* (* x (pow sin 2.0)) x)
5.0ms	(* x (pow sin 2.0))
25.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series857.0ms

Counts

4 → 12

Calls

4 calls:

301.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
151.0ms	(* (* x (pow sin 2.0)) x)
141.0ms	(* x (pow sin 2.0))
263.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify57.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (10.0ms)

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

prune292.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
2.8b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.9b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite246.0ms

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:

12.0ms	(* (* 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)))
34.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
95.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.0s

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
306.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
305.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
277.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify91.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (72.0ms)

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

prune273.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (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))))))
4.7b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.7b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite33.0ms

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))))

series579.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (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))))))
223.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
219.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (33.0ms)

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

prune354.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
0.2b	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
4.7b	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
27×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
21×	`prod-exp`
18×	`pow-exp`
16×	`unpow-prod-down`
9×	`pow-to-exp`
8×	`associate-/r*`
7×	`add-cbrt-cube` `sqr-pow`
5×	`associate-l` `unpow2`
4×	`pow1`
3×	`pow-unpow` `div-exp` `associate-r` `associate-/l*` `add-log-exp`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-pow` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 98

Calls

3 calls:

5.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
1.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
7.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series457.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
29.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
327.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify43.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	329	1314
1	1143	1198
2	5002	1189

prune317.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes309.0ms

Accuracy

7.1% (2.4b remaining)

Error of 2.5b against oracle of 0.2b and baseline of 2.7b

bsearch175.0ms

Steps

Iters	Range		Point
6	2.1285005641463748e+145	1.7958241045161027e+146	7.576854927319505e+145
8	-6.75216425001212e-306	6.311120560139708e-307	4.1989922527869865e-308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	52
1	51	52

end0.0ms

sample1.5s

Algorithm

intervals

Results

549.0ms	8953×	body	80	valid
269.0ms	783×	body	1280	valid
250.0ms	970×	body	640	valid
107.0ms	574×	body	320	valid
38.0ms	310×	body	160	valid