Details

sample71.0ms

Algorithm

intervals

Results

26.0ms	287×	body	80	valid
14.0ms	34×	body	1280	valid
10.0ms	31×	body	640	valid
4.0ms	18×	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: 28.0b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.0b	(* (* x (pow sin 2.0)) x)
8.6b	(* x (pow sin 2.0))
18.5b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite35.0ms

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)
5.0ms	(* x (pow sin 2.0))
9.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series858.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
141.0ms	(* (* x (pow sin 2.0)) x)
135.0ms	(* x (pow sin 2.0))
280.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify60.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (12.0ms)

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

prune287.0ms

Filtered

135 candidates to 73 candidates (54.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	122	13	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	13	136

Merged error: 14.5b

Counts

136 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.0b	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.5b	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite49.0ms

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))
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))

series706.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cos (* 2.0 x))
289.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
147.0ms	(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
258.0ms	(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify85.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (62.0ms)

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

prune238.0ms

Filtered

183 candidates to 62 candidates (33.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	176	7	183
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	181	15	196

Merged error: 2.6b

Counts

196 → 15

localize19.0ms

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))))))
0.4b	(/ (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)))))))
4.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.6b	(* (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))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
104.0ms	(/ (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)))))))
206.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
206.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

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

prune355.0ms

Filtered

126 candidates to 75 candidates (59.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	115	11	126
Fresh	10	3	13
Picked	0	1	1
Done	1	0	1
Total	126	15	141

Merged error: 0.0b

Counts

141 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(cos (* 2.0 x))
0.8b	(/ (cos (* 2.0 x)) (fabs (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))))
4.6b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
4.6b	(* (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))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cos (* 2.0 x))
65.0ms	(/ (cos (* 2.0 x)) (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))))
206.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (8.0ms)

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

prune283.0ms

Filtered

114 candidates to 73 candidates (64.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	10	13
Picked	1	0	1
Done	1	0	1
Total	116	13	129

Merged error: 0.0b

Counts

129 → 13

regimes376.0ms

Accuracy

-16.5% (2.9b remaining)

Error of 3.1b against oracle of 0.1b and baseline of 2.7b

bsearch68.0ms

Steps

Iters	Range		Point
5	9.41379812154584e-180	2.0314395371387087e-179	1.5822600582258713e-179

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	30
1	35	30

end0.0ms

sample1.9s

Algorithm

intervals

Results

755.0ms	9066×	body	80	valid
371.0ms	843×	body	1280	valid
308.0ms	940×	body	640	valid
137.0ms	551×	body	320	valid
46.0ms	283×	body	160	valid