Details

sample58.0ms

Algorithm

intervals

Results

20.0ms	290×	body	80	valid
13.0ms	25×	body	1280	valid
8.0ms	29×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	6×	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

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: 24.2b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.1b	(* (* x (pow sin 2.0)) x)
5.8b	(* x (pow sin 2.0))
16.6b	(* (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` `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:

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

series810.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
138.0ms	(* (* x (pow sin 2.0)) x)
132.0ms	(* x (pow sin 2.0))
251.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify59.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (12.0ms)

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

prune291.0ms

Filtered

135 candidates to 73 candidates (54.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	10	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Merged error: 11.4b

Counts

136 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (* x (pow sin 2.0)) x)
4.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
5.8b	(* x (pow sin 2.0))
5.9b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite40.0ms

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:

6.0ms	(* (* x (pow sin 2.0)) x)
12.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
5.0ms	(* x (pow sin 2.0))
9.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

series810.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (* x (pow sin 2.0)) x)
258.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
140.0ms	(* x (pow sin 2.0))
262.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify65.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (11.0ms)

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

prune288.0ms

Filtered

166 candidates to 71 candidates (42.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	165	11	176

Merged error: 8.3b

Counts

176 → 11

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))))
3.1b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
4.9b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.9b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite106.0ms

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:

22.0ms	(/ (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))))
10.0ms	(* (* (* 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))

series991.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(/ (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)
269.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
271.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify137.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 2 (81.0ms)

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

prune290.0ms

Filtered

414 candidates to 71 candidates (17.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	409	5	414
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	414	11	425

Merged error: 1.4b

Counts

425 → 11

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))))))
0.5b	(/ (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)))))))
3.8b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.8b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite28.0ms

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))))))
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)))))))
8.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
8.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (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)))))))
211.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
214.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify54.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (35.0ms)

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

prune324.0ms

Filtered

126 candidates to 75 candidates (59.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	124	13	137

Merged error: 0.1b

Counts

137 → 13

regimes305.0ms

Accuracy

0% (2.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms

sample1.7s

Algorithm

intervals

Results

628.0ms	8984×	body	80	valid
325.0ms	829×	body	1280	valid
279.0ms	951×	body	640	valid
120.0ms	569×	body	320	valid
45.0ms	324×	body	160	valid