Details

sample60.0ms

Algorithm

intervals

Results

24.0ms	306×	body	80	valid
8.0ms	28×	body	640	valid
8.0ms	20×	body	1280	valid
3.0ms	15×	body	320	valid
2.0ms	10×	body	160	valid

simplify38.0ms

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: 25.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.5b	(* (* x (pow sin 2.0)) x)
9.1b	(* x (pow sin 2.0))
16.5b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite38.0ms

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)))
9.0ms	(* (* 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))

series807.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
144.0ms	(* (* x (pow sin 2.0)) x)
130.0ms	(* x (pow sin 2.0))
249.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify57.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (11.0ms)

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

prune231.0ms

Filtered

127 candidates to 65 candidates (51.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	8	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	8	128

Merged error: 13.6b

Counts

128 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.5b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
16.5b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite48.0ms

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))
14.0ms	(/ (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)
12.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series736.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cos (* 2.0 x))
313.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
158.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
253.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify78.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (61.0ms)

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

prune207.0ms

Filtered

175 candidates to 56 candidates (32.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	174	9	183

Merged error: 2.1b

Counts

183 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
43×	`prod-exp`
19×	`add-cbrt-cube`
14×	`pow-to-exp` `associate-l` `pow-exp`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-unprod`
6×	`unpow-prod-down`
4×	`pow1` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-r` `*-commutative` `sqr-pow`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 88

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
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))))

series535.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cos (* 2.0 x))
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)))))))
214.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
206.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify168.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	301	1085
1	1016	903
2	4858	897
3	5002	897

prune293.0ms

Filtered

100 candidates to 60 candidates (60.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	91	9	100
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	93	16	109

Merged error: 0.0b

Counts

109 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.5b	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
3.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
3.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
42×	`prod-exp`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
14×	`pow-to-exp` `associate-l` `pow-exp`
9×	`times-frac`
6×	`unpow-prod-down` `cbrt-unprod`
4×	`pow1` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r` `*-commutative` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 94

Calls

4 calls:

2.0ms	(cos (* 2.0 x))
4.0ms	(/ (cos (* 2.0 x)) (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))))
7.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cos (* 2.0 x))
66.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
218.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
209.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	279	1031
1	975	918
2	5001	918

prune242.0ms

Filtered

106 candidates to 65 candidates (61.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	108	14	122

Merged error: 0.0b

Counts

122 → 14

regimes367.0ms

Accuracy

0% (2.7b remaining)

Error of 2.8b against oracle of 0.2b and baseline of 2.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	28
1	20	28

end0.0ms

sample1.9s

Algorithm

intervals

Results

734.0ms	9062×	body	80	valid
350.0ms	779×	body	1280	valid
304.0ms	947×	body	640	valid
164.0ms	643×	body	320	valid
49.0ms	300×	body	160	valid