Details

sample100.0ms

Algorithm

intervals

Results

35.0ms	286×	body	80	valid
19.0ms	28×	body	1280	valid
18.0ms	38×	body	640	valid
4.0ms	13×	body	320	valid
3.0ms	11×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	8
1	68	8
2	243	8
3	1266	8
4	5001	8

prune5.0ms

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: 29.8b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.5b	(* (* x (pow sin 2.0)) x)
7.7b	(* x (pow sin 2.0))
19.2b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite51.0ms

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)))
10.0ms	(* (* x (pow sin 2.0)) x)
9.0ms	(* x (pow sin 2.0))
16.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series802.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
141.0ms	(* (* x (pow sin 2.0)) x)
129.0ms	(* x (pow sin 2.0))
253.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify63.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (12.0ms)

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

prune277.0ms

Filtered

135 candidates to 73 candidates (54.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	9	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Merged error: 16.2b

Counts

136 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.5b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
19.2b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
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 → 194

Calls

4 calls:

8.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
15.0ms	(/ (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)
15.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series813.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
284.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
142.0ms	(* (* (* 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))

simplify89.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	603	2216
1	2821	1509
2	5002	1497

prune237.0ms

Filtered

206 candidates to 70 candidates (34.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	201	5	206
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	206	9	215

Merged error: 2.5b

Counts

215 → 9

localize15.0ms

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))))))
0.7b	(/ (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)))))))
5.1b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.1b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite27.0ms

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))))

series548.0ms

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))))))
100.0ms	(/ (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)))))))
218.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
197.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (35.0ms)

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

prune333.0ms

Filtered

126 candidates to 75 candidates (59.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	124	11	135

Merged error: 0.1b

Counts

135 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (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))))))
0.5b	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
5.1b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.1b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
63×	`add-exp-log`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`prod-exp`
21×	`add-cbrt-cube`
16×	`associate-/l*`
14×	`pow-to-exp` `associate-l` `pow-exp`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative` `sqr-pow`
1×	`associate-/l/`

Counts

4 → 165

Calls

4 calls:

6.0ms	(/ (/ (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))))))
4.0ms	(/ (cos (* 2.0 x)) (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))))
8.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

series607.0ms

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))))))
67.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
201.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
233.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify68.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	519	3377
1	1844	3082
2	5001	2997

prune424.0ms

Filtered

177 candidates to 116 candidates (65.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	176	12	188

Merged error: 0.0b

Counts

188 → 12

regimes290.0ms

Accuracy

0% (2.5b remaining)

Error of 2.7b against oracle of 0.2b and baseline of 2.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms

sample1.9s

Algorithm

intervals

Results

723.0ms	9022×	body	80	valid
334.0ms	1038×	body	640	valid
329.0ms	723×	body	1280	valid
139.0ms	584×	body	320	valid
53.0ms	336×	body	160	valid