Details

sample65.0ms

Algorithm

intervals

Results

26.0ms	306×	body	80	valid
9.0ms	28×	body	640	valid
9.0ms	20×	body	1280	valid
4.0ms	15×	body	320	valid
2.0ms	10×	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: 25.5b

Counts

2 → 1

localize14.0ms

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))

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` `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:

11.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
6.0ms	(* (* x (pow sin 2.0)) x)
9.0ms	(* x (pow sin 2.0))
9.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series840.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
148.0ms	(* (* x (pow sin 2.0)) x)
135.0ms	(* x (pow sin 2.0))
262.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify61.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (12.0ms)

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

prune281.0ms

Filtered

135 candidates to 73 candidates (54.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	127	8	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 13.6b

Counts

136 → 8

localize16.0ms

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))

rewrite53.0ms

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×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `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 → 171

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))

series796.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cos (* 2.0 x))
317.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
200.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
260.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify82.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	566	2020
1	2548	1394
2	5001	1382

prune235.0ms

Filtered

183 candidates to 64 candidates (35.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	178	5	183
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Merged error: 2.1b

Counts

191 → 9

localize19.0ms

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))))

rewrite25.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 96

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)))))))
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))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cos (* 2.0 x))
108.0ms	(/ (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)))))))
212.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
209.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify165.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (153.0ms)

Iter	Nodes	Cost
0	311	1157
1	1034	974
2	4912	965
3	5001	939

prune315.0ms

Filtered

108 candidates to 68 candidates (63.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	101	16	117

Merged error: 0.0b

Counts

117 → 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))))

rewrite24.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 102

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

series523.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cos (* 2.0 x))
83.0ms	(/ (cos (* 2.0 x)) (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))))
213.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify42.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	289	1087
1	993	973
2	5001	973

prune282.0ms

Filtered

114 candidates to 73 candidates (64.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	115	15	130

Merged error: 0.0b

Counts

130 → 15

regimes404.0ms

Accuracy

0% (2.6b 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	20
1	20	20

end0.0ms

sample2.0s

Algorithm

intervals

Results

776.0ms	9062×	body	80	valid
377.0ms	779×	body	1280	valid
339.0ms	947×	body	640	valid
167.0ms	643×	body	320	valid
51.0ms	300×	body	160	valid