Details

sample68.0ms

Algorithm

intervals

Results

28.0ms	286×	body	80	valid
12.0ms	26×	body	1280	valid
9.0ms	28×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	6×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.6b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.0b	(* (* x (pow sin 2.0)) x)
7.2b	(* x (pow sin 2.0))
20.4b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite35.0ms

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:

10.0ms	(/ (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))
9.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series834.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
151.0ms	(* (* x (pow sin 2.0)) x)
137.0ms	(* x (pow sin 2.0))
255.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify58.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (11.0ms)

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

prune248.0ms

Filtered

127 candidates to 65 candidates (51.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	10	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Merged error: 15.7b

Counts

128 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.6b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.0b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
20.4b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
322×	`prod-exp`
77×	`pow-to-exp` `pow-exp`
47×	`add-cbrt-cube`
43×	`div-exp`
26×	`cbrt-unprod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
6×	`pow1`
5×	`cbrt-undiv`
4×	`associate-r` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
18.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
9.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
13.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series707.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cos (* 2.0 x))
294.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
142.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
258.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify81.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	548	1952
1	2515	1327
2	5002	1315

prune226.0ms

Filtered

175 candidates to 55 candidates (31.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	175	10	185

Merged error: 3.2b

Counts

185 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
0.6b	(/ (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))))

rewrite30.0ms

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

series568.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
122.0ms	(/ (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)))))))
205.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
205.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	316	1464
1	1229	1194
2	5002	1122

prune381.0ms

Filtered

118 candidates to 67 candidates (56.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	108	10	118
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	115	13	128

Merged error: 0.1b

Counts

128 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.3b	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
0.6b	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
3.5b	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
2.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
5.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
6.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series444.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cos (* 2.0 x))
28.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
96.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
309.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify48.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	346	1354
1	1220	1233
2	5001	1224

prune302.0ms

Filtered

117 candidates to 73 candidates (62.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	111	6	117
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	115	15	130

Merged error: 0.0b

Counts

130 → 15

regimes439.0ms

Accuracy

17% (2.2b remaining)

Error of 2.3b against oracle of 0.1b and baseline of 2.8b

bsearch168.0ms

Steps

Iters	Range		Point
10	1.7432364665779678e+288	2.118156350876705e+306	2.0769575192177132e+306
9	-2.1488932916491584e-125	-1.7133659756817817e-130	-2.1299061337171467e-130

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	48
1	42	48

end0.0ms

sample1.9s

Algorithm

intervals

Results

773.0ms	9163×	body	80	valid
366.0ms	782×	body	1280	valid
312.0ms	906×	body	640	valid
148.0ms	609×	body	320	valid
52.0ms	312×	body	160	valid

Details

sample68.0ms

simplify42.0ms

prune3.0ms

localize13.0ms

rewrite35.0ms

series834.0ms

simplify58.0ms

prune248.0ms

localize29.0ms

rewrite54.0ms

series707.0ms

simplify81.0ms

prune226.0ms

localize16.0ms

rewrite30.0ms

series568.0ms

simplify47.0ms

prune381.0ms

localize17.0ms

rewrite19.0ms

series444.0ms

simplify48.0ms

prune302.0ms

regimes439.0ms

bsearch168.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling