Details

sample59.0ms

Algorithm

intervals

Results

27.0ms	57×	body	1280	valid
11.0ms	36×	body	640	valid
8.0ms	137×	body	80	valid
3.0ms	13×	body	320	valid
2.0ms	13×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.1b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
5×	`associate-*l/`
4×	`pow-prod-down`
3×	`associate-/r*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 79

Calls

3 calls:

20.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
19.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series167.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
77.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	402	818
1	2097	614
2	5002	599

prune209.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-l`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/l*`
3×	`associate-r` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 110

Calls

3 calls:

4.0ms	(/ (sin x) (sin (* 0.5 x)))
11.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (sin x) (sin (* 0.5 x)))
78.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify65.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	540	1166
1	2701	980
2	5001	956

prune319.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
20×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-l`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
5×	`pow1`
4×	`associate-/r` `associate-/l`
3×	`associate-r` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative`

Counts

3 → 85

Calls

3 calls:

10.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
4.0ms	(/ (sin x) (sin (* 0.5 x)))
8.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

series177.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
38.0ms	(/ (sin x) (sin (* 0.5 x)))
77.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	423	884
1	2225	705
2	5001	686

prune238.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) 3.0)
0.2b	(/ 8.0 (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(* (/ 8.0 (/ (sin x) (sin (* 0.5 x)))) (/ (sin (* 0.5 x)) 3.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
125×	`add-sqr-sqrt`
104×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
34×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r`
12×	`div-inv`
9×	`associate-/l*`
6×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 211

Calls

4 calls:

3.0ms	(/ (sin (* 0.5 x)) 3.0)
6.0ms	(/ 8.0 (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
34.0ms	(* (/ 8.0 (/ (sin x) (sin (* 0.5 x)))) (/ (sin (* 0.5 x)) 3.0))

series218.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (sin (* 0.5 x)) 3.0)
54.0ms	(/ 8.0 (/ (sin x) (sin (* 0.5 x))))
45.0ms	(/ (sin x) (sin (* 0.5 x)))
78.0ms	(* (/ 8.0 (/ (sin x) (sin (* 0.5 x)))) (/ (sin (* 0.5 x)) 3.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	866	2321
1	4052	2128
2	5001	2104

prune567.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	17	9
2	17	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

749.0ms	1538×	body	1280	valid
386.0ms	1235×	body	640	valid
271.0ms	4303×	body	80	valid
133.0ms	614×	body	320	valid
46.0ms	310×	body	160	valid