Details

sample58.0ms

Algorithm

intervals

Results

22.0ms	291×	body	80	valid
9.0ms	23×	body	1280	valid
8.0ms	30×	body	640	valid
3.0ms	12×	body	320	valid
2.0ms	13×	body	160	valid

simplify39.0ms

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: 26.9b

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)))
3.6b	(* (* x (pow sin 2.0)) x)
6.9b	(* x (pow sin 2.0))
18.2b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite33.0ms

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)))
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))

series914.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
149.0ms	(* (* x (pow sin 2.0)) x)
204.0ms	(* x (pow sin 2.0))
265.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify55.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (10.0ms)

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

prune260.0ms

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: 13.9b

Counts

128 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (* x (pow sin 2.0)) x)
4.7b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
6.9b	(* x (pow sin 2.0))
7.5b	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

rewrite38.0ms

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×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 146

Calls

4 calls:

5.0ms	(* (* 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))

series818.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (* x (pow sin 2.0)) x)
269.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x)))
139.0ms	(* x (pow sin 2.0))
260.0ms	(* (pow cos (/ 2.0 2)) (* (* x (pow sin 2.0)) x))

simplify65.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	429	1240
1	1850	941
2	5001	941

prune288.0ms

Filtered

158 candidates to 63 candidates (39.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	152	6	158
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	156	11	167

Merged error: 9.9b

Counts

167 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (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))))
3.6b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
4.7b	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
7.5b	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite104.0ms

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×	`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 → 394

Calls

4 calls:

23.0ms	(/ (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))))
9.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
17.0ms	(* (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))

series1.0s

Counts

4 → 12

Calls

4 calls:

312.0ms	(/ (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))))
160.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
279.0ms	(* (pow cos (/ 2.0 2)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
282.0ms	(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify132.0ms

Algorithm

egg-herbie

Counts

406 → 406

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	797	5960
1	3112	3941
2	5001	3351

prune306.0ms

Filtered

406 candidates to 63 candidates (15.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	399	7	406
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	406	11	417

Merged error: 2.4b

Counts

417 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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	(/ (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)))))))
5.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.5b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite26.0ms

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

series593.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
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)))))))
226.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
224.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (36.0ms)

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

prune316.0ms

Filtered

118 candidates to 67 candidates (56.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	115	14	129

Merged error: 0.0b

Counts

129 → 14

regimes376.0ms

Accuracy

-2% (2.4b remaining)

Error of 2.6b against oracle of 0.1b and baseline of 2.5b

bsearch115.0ms

Steps

Iters	Range		Point
11	3.043339352598528e-296	3.962509604168077e-273	7.288490228303255e-274

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	28
1	32	28

end0.0ms

sample1.8s

Algorithm

intervals

Results

643.0ms	9166×	body	80	valid
364.0ms	865×	body	1280	valid
272.0ms	982×	body	640	valid
136.0ms	590×	body	320	valid
44.0ms	308×	body	160	valid