Details

sample75.0ms

Algorithm

intervals

Results

26.0ms	285×	body	80	valid
15.0ms	29×	body	1280	valid
9.0ms	26×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	9×	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: 27.1b

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)))
4.1b	(* (* x (pow sin 2.0)) x)
7.9b	(* x (pow sin 2.0))
18.2b	(* (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)))
10.0ms	(* (* 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))

series930.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
153.0ms	(* (* x (pow sin 2.0)) x)
151.0ms	(* x (pow sin 2.0))
298.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify60.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (11.0ms)

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

prune274.0ms

Filtered

127 candidates to 65 candidates (51.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	118	9	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	9	128

Merged error: 13.6b

Counts

128 → 9

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)))
4.1b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.2b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite51.0ms

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))
17.0ms	(/ (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))

series781.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cos (* 2.0 x))
309.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* 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)
308.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify87.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (68.0ms)

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

prune255.0ms

Filtered

175 candidates to 55 candidates (31.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	168	7	175
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	174	10	184

Merged error: 2.4b

Counts

184 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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:

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)))))))
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))))))
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))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (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)))))))
39.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
216.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
222.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	316	1464
1	1229	1194
2	5001	1122

prune378.0ms

Filtered

118 candidates to 67 candidates (56.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	106	12	118
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	113	15	128

Merged error: 0.3b

Counts

128 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.3b	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
0.3b	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
3.3b	(* (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))
5.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
2.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
7.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

series486.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cos (* 2.0 x))
102.0ms	(/ (cos (* 2.0 x)) (pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2))
29.0ms	(pow (fabs (* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)) 2)
341.0ms	(* (pow (* (pow cos 1.0) (pow sin 1.0)) 1.0) x)

simplify49.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	346	1354
1	1223	1233
2	5001	1224

prune373.0ms

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	5	9	14
Picked	1	0	1
Done	0	0	0
Total	117	15	132

Merged error: 0.3b

Counts

132 → 15

regimes374.0ms

Accuracy

0% (2.8b remaining)

Error of 2.9b against oracle of 0.1b and baseline of 2.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

674.0ms	9010×	body	80	valid
328.0ms	809×	body	1280	valid
268.0ms	934×	body	640	valid
139.0ms	615×	body	320	valid
50.0ms	311×	body	160	valid