Details

sample57.0ms

Algorithm

intervals

Results

17.0ms	291×	body	80	valid
11.0ms	36×	body	640	valid
7.0ms	22×	body	1280	valid
3.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify42.0ms

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: 29.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.2b	(* (* x (pow sin 2.0)) x)
6.5b	(* x (pow sin 2.0))
22.2b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite154.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 123

Calls

4 calls:

58.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
21.0ms	(* (* x (pow sin 2.0)) x)
11.0ms	(* x (pow sin 2.0))
58.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series786.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
130.0ms	(* (* x (pow sin 2.0)) x)
125.0ms	(* x (pow sin 2.0))
240.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify58.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	448	971
1	2063	815
2	5002	815

prune291.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.8b

localize15.0ms

Local error

Found 4 expressions with local error:

4.2b	(* (* x (pow sin 2.0)) x)
6.2b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
6.5b	(* x (pow sin 2.0))
8.6b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-exp-log`
202×	`prod-exp`
50×	`pow-to-exp` `pow-exp`
34×	`add-cbrt-cube`
20×	`cbrt-unprod`
18×	`associate-l`
17×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down`
6×	`pow1`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 154

Calls

4 calls:

20.0ms	(* (* x (pow sin 2.0)) x)
154.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
11.0ms	(* x (pow sin 2.0))
57.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series762.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (* x (pow sin 2.0)) x)
249.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
125.0ms	(* x (pow sin 2.0))
242.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify64.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	450	1288
1	1879	989
2	5001	989

prune306.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
4.2b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
6.2b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
8.6b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1410×	`add-exp-log`
1300×	`prod-exp`
338×	`pow-to-exp` `pow-exp`
130×	`div-exp`
74×	`add-cbrt-cube`
46×	`cbrt-unprod`
15×	`associate-l`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-undiv` `unpow-prod-down`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 402

Calls

4 calls:

467.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
71.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
503.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
185.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series944.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))))
146.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
254.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
256.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify124.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	831	6060
1	3161	4041
2	5002	3451

prune301.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.5b

localize19.0ms

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))))))
7.7b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
7.7b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite78.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 114

Calls

4 calls:

15.0ms	(/ (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)))))))
6.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
27.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
26.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (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)))))))
38.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
200.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
205.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify48.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	325	1562
1	1244	1292
2	5001	1217

prune343.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes267.0ms

Accuracy

19.1% (2.2b remaining)

Error of 2.4b against oracle of 0.1b and baseline of 2.9b

bsearch201.0ms

Steps

Iters	Range		Point
8	1.5732228810007756e+219	8.884626979327498e+221	1.0782840583650844e+220
10	7.30404624184028e-264	2.2412670894539055e-251	6.232019318103981e-261

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

528.0ms	9048×	body	80	valid
272.0ms	820×	body	1280	valid
226.0ms	1001×	body	640	valid
102.0ms	564×	body	320	valid
38.0ms	333×	body	160	valid