Details

sample86.0ms

Algorithm

intervals

Results

39.0ms	294×	body	80	valid
15.0ms	25×	body	1280	valid
12.0ms	27×	body	640	valid
4.0ms	13×	body	320	valid
2.0ms	9×	body	160	valid

simplify43.0ms

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: 27.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.4b	(* (* x (pow sin 2.0)) x)
7.1b	(* x (pow sin 2.0))
19.6b	(* (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` `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:

25.0ms	(/ (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))

series855.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
150.0ms	(* (* x (pow sin 2.0)) x)
139.0ms	(* x (pow sin 2.0))
268.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify59.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (11.0ms)

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

prune290.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.5b

localize18.0ms

Local error

Found 4 expressions with local error:

4.4b	(* (* x (pow sin 2.0)) x)
4.8b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
6.9b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
7.1b	(* x (pow sin 2.0))

rewrite116.0ms

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:

9.0ms	(* (* x (pow sin 2.0)) x)
69.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
25.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
5.0ms	(* x (pow sin 2.0))

series809.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (* x (pow sin 2.0)) x)
258.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
261.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
139.0ms	(* x (pow sin 2.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	450	1288
1	1880	989
2	5002	989

prune327.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (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))))
4.4b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
4.8b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
6.9b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite660.0ms

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:

242.0ms	(/ (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))))
31.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
255.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
91.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series971.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(/ (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))))
151.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
262.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
261.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify132.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 2 (79.0ms)

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

prune313.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize16.0ms

Local error

Found 4 expressions with local error:

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))))))
0.5b	(/ (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)))))))
5.1b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.1b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite35.0ms

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:

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))))))
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)))))))
10.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
11.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

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))))))
102.0ms	(/ (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)))))))
209.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
208.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (35.0ms)

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

prune339.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

0% (2.6b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	18
1	18	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	9087×	body	80	valid
480.0ms	824×	body	1280	valid
417.0ms	970×	body	640	valid
196.0ms	574×	body	320	valid
73.0ms	324×	body	160	valid