Details

sample54.0ms

Algorithm

intervals

Results

17.0ms	285×	body	80	valid
9.0ms	23×	body	1280	valid
8.0ms	32×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	16×	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: 29.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.2b	(* (* x (pow sin 2.0)) x)
7.3b	(* x (pow sin 2.0))
21.4b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite40.0ms

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:

11.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
6.0ms	(* (* x (pow sin 2.0)) x)
5.0ms	(* x (pow sin 2.0))
13.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series874.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
154.0ms	(* (* x (pow sin 2.0)) x)
139.0ms	(* x (pow sin 2.0))
271.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify61.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (11.0ms)

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

prune271.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.4b

localize15.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (* x (pow sin 2.0)) x)
7.0b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
7.2b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
7.3b	(* x (pow sin 2.0))

rewrite45.0ms

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×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 146

Calls

4 calls:

6.0ms	(* (* x (pow sin 2.0)) x)
17.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
10.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
5.0ms	(* x (pow sin 2.0))

series990.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (* x (pow sin 2.0)) x)
276.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
412.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))
145.0ms	(* x (pow sin 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	429	1240
1	1851	941
2	5002	941

prune293.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

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))))
3.2b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
7.0b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
7.2b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite114.0ms

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×	`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 → 394

Calls

4 calls:

24.0ms	(/ (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))))
13.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
13.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.0s

Counts

4 → 12

Calls

4 calls:

309.0ms	(/ (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))))
159.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
276.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
275.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify131.0ms

Algorithm

egg-herbie

Counts

406 → 406

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	797	5960
1	3112	3941
2	5001	3351

prune283.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

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)))))))
5.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite26.0ms

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:

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

series576.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
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)))))))
225.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
215.0ms	(* (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	5002	1122

prune311.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes172.0ms

Accuracy

2.7% (2.4b remaining)

Error of 2.5b against oracle of 0.2b and baseline of 2.6b

bsearch126.0ms

Steps

Iters	Range		Point
10	-1.2338451977441667e-217	-6.912057286316748e-234	-2.614521882835997e-226

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	28
1	32	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

573.0ms	9065×	body	80	valid
295.0ms	814×	body	1280	valid
232.0ms	933×	body	640	valid
103.0ms	577×	body	320	valid
38.0ms	313×	body	160	valid