Details

sample60.0ms

Algorithm

intervals

Results

28.0ms	60×	body	1280	valid
10.0ms	33×	body	640	valid
9.0ms	136×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize11.0ms

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)))
12.0b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite55.0ms

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:

23.0ms	(* (* (/ 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))

series361.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
269.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify58.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (50.0ms)

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

prune222.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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:

11.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
3.0ms	(/ (sin x) (sin (* 0.5 x)))
12.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
43.0ms	(/ (sin x) (sin (* 0.5 x)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify67.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (56.0ms)

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

prune324.0ms

Filtered

119 candidates to 89 candidates (74.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

59×	`times-frac`
50×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
32×	`associate-l`
28×	`sqrt-prod`
16×	`associate-/r*`
11×	`pow1`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
9×	`sqrt-div`
7×	`associate-*l/`
6×	`div-inv`
4×	`associate-r` `pow-prod-down` `associate-/l*` `add-log-exp`
3×	`associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`associate-/r/`

Counts

4 → 148

Calls

4 calls:

13.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
26.0ms	(/ (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
3.0ms	(/ (sin x) (sin (* 0.5 x)))
31.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))
153.0ms	(/ (* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5)))) (/ (sin x) (sin (* 0.5 x))))
43.0ms	(/ (sin x) (sin (* 0.5 x)))
92.0ms	(* (sqrt (/ 8.0 3.0)) (* (sqrt (/ 8.0 3.0)) (sin (* x 0.5))))

simplify91.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	647	1701
1	3173	1408
2	5001	1369

prune491.0ms

Filtered

160 candidates to 121 candidates (75.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

3.0ms	(/ (sin (* x 0.5)) (sin x))
21.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (sin (* x 0.5)) (sin x))
70.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify65.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	453	978
1	2462	779
2	5002	764

prune237.0ms

Filtered

107 candidates to 78 candidates (72.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	19	13
2	19	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

728.0ms	1512×	body	1280	valid
387.0ms	1218×	body	640	valid
291.0ms	4302×	body	80	valid
134.0ms	629×	body	320	valid
55.0ms	339×	body	160	valid